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School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Clear@y, x, starterx, starteryD; starterx = 1.71; startery = 18.06; sol = DSolve@8y '@xD = 3 y@xD, y@starterxD = startery<, y@xD, xD; y@xD . sol@1DD Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 09/26/2011 Fall 2011 Normal (Gaussian) Distribution. mean standard deviation N ,2 f (x ) = 1 2 e -( x - ) 2 2 2 , - < x < . Standard Normal Distribution N ( 0 , 1 ): Z ~ N( 0, 1 ) X ~ N ( , 2 ) Z = X - = 0, 2 = 1. X = +Z _ EXCEL
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Ruled surfaces A surface is called ruled if it is swept out by moving a line in space. That is, there exiss a family of lines so that each point of the surface lies on exactly one line from this family (so, the lines are either parallel, or skew). The lin
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
THE TNB FRAME, THE CURVATURE, ETC. Throughout, we consider a spacecurve r = r(t). t |r (u)| du (length of the arc of the curve Let s be the arclength parameter: s = a ds with a u t). Then = |r (t)|. dt dr r The unit tangent vector: T = = . ds |r | The
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Integrals as General & Particular Solutions dy = f (x) dx General Solution: y(x) = f (x) dx + C Particular Solution: dy = f (x), dx y(x0 ) = y0 dy Examples: 1) dx = (x 2)2 ; y(2) = 1; 2) dy dy 10 = x2 +1 ; y(0) = 0; 3) dx = xex ; y(0) = 1; dx p. 2/3 Inte
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Review of MATH 385, Section D2 The nal will cover: (*=the content you should know to understand other subject, but no problem is directly for this subject) Chapter 1 (30pts) (except Exact equations) : The order of dierential equations, particular solution
School: University Of Illinois, Urbana Champaign
Course: MATH
SURVEYUNTUKPENGEMBANGANUIBSECARABERKELANJUTAN KEPADAMAHASISWABARUANGKATAN2014/2015 PETUNJUKPENGISIANANGKET: Pengisiangket dirahasiakan identitasnya.JikakelakidentitasAndaakandigunakan,makakamiakanmintapersetujuanAndaterlebih dahulu. KEBEBASAN dan KEJUJURA
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
EXAM 1 REVIEW MATH 124 (1) All of the students in a class of 30 are majoring in either engineering, math, or both. If 22 are majoring in engineering and 16 are majoring in math, how many students are majoring in engineering but not in math? [Hint: Use a V
School: University Of Illinois, Urbana Champaign
| r srv s g kv 8 s r jeyvw4faaefCGyeaiuiIs wx!x o arvvs9!uEseA4yavuyyfyrGx Qynavu~vvsehaiv ywEsfCeavuinaCF wr x P s w x w | S r 8 s g x x sv u |yxay~eyvwaaG!daIiiG!veavuisA!x vw4!a!veavuisA!eleiu WEX2(811y)Ehv w r sd v sr x oud
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
The n-dimensional space Rn Basic facts: the n-dimensional space Rn is a generalization of R2 (the plane) or R3 (the 3-dimensional space) to the n-variable case. Formally Rn is the set of ordered n-tuples of real numbers: (x1 , . . . , xn ). We can identif
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Determinants, cross products, and triple products 1. Determinants. a1 a2 = a1 b2 a2 b1 . Geometrically, this determinant represents the signed b1 b2 area of the parallelogram formed by the vectors a1 , a2 and b1 , b2 . The sign is positive if we need to r
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
FORMULA SHEET FOR MIDTERM 1 Trigonometric identities: sin2 x+cos2 x = 1, tan2 x+1 = sec2 x, sin 2x = 2 sin x cos x, 1 1 cos2 x = (1 + cos 2x), sin2 x = (1 cos 2x), sec d = ln | sec + tan | + C. 2 2 Exponential and logarithmic functions: ln(ab) = ln a + ln
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 1 September 3, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. Pa
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 Fall 2013 Exam 1 September 26, 2013 Solutions 1. (6 points) Let U = cfw_1, 2, 3, 4, 5, 6, 7, 8, A = cfw_1, 2, 3, 5, and B = cfw_2, 4, 5, 6. Compute the following sets. (a) Ac Solution: Ac = cfw_4, 6, 7, 8 (b) A [ B Solution: A [ B = cfw_1, 2, 3,
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
MATH/STAT 409 Homework # 3 due 09/20/2013 1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution with pdf f (x; ) = 43 x , 0 < x < . 4 (a) Find the MLE . (b) Is a consistent estimator? Justify your answer. (c) Is an unbia
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #2 ( due Friday, September 14, by 4:00 p.m. ) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function ( ) f X ( x ) = f X ( x ; ) = 2 + x 1 (1 x ) , a) 0 < x < 1, > 0. ~ Obtain the m
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
MATH125 Final Exam Sections: 1.3-2.7, 3.1-3.4, 3.6, 4.1-4.5, 5.1-5.3 Definition Linear- all variables have at most degree 1 System of linear inequalities- a collection of more than 1 Feasibility region- the region determined by simultaneously solving the
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Section VC.01 Here are the concepts you should know. You should be able to do problems but also be able to answer true/false or short answer questions about these concepts (think something like L13 or L16 in VC.01). Vector basics: adding, subtracting, mu
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
VC.10 Problem 1 F = ex x sin y + 2y 2 z. We evaluate this at (0, 1, 5) to obtain e0 0 sin(1) + 2 5 = 1 + 10 = 11 > 0 so the point (0, 1, 5) is a source. VC.10 Problem 2 We want to calculate R F dA. First calculate the divergence F = 3x2 + 3y 2 + 3z 2 S
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
VC.05 Problem 1 Here we just compute F (x (t), y (t) and F (y (t), x (t) and check what matches. The answers are along, across, across, along. VC.05 Problem 2 The ow along the curve is 2 2 F (x (t), y (t) dt = 0 (3x(t)y(t), 2x(t) (2t 1, 5t) dt 0 2 3(t2 t)
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Math 241 C8 Quiz 9 12 April 2011 Name: Problem 1: Let C be the cone with vertex at (0, 0, 0), aperture of radians, axis aligned 2 with the z-axis, and 22 z 2 (see the picture below). The aperture of a cone is the angle between the two sides, therefore the
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Section VC.05 Here are the concepts you should know. You should be able to do problems but also be able to answer true/false or short answer questions about these concepts. Flow across a curve: Flow along a curve: thigh tlow thigh tlow F normaldt, where
School: University Of Illinois, Urbana Champaign
Course: College Algebra
MATH 115 PREPARATION FOR CALCULUS FALL 2013 Instructor Office E-mail Lecture A1 8am 100 Gregory Hall Lecture D1 11am 114 DKH Jennifer McNeilly 121 Altgeld Hall jrmcneil@illinois.edu Lecture X1 Noon 217 Noyes Lab Theodore Molla 226 Illini Hall molla@illino
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Syllabus for the Midterm Exam on February 23 * Systems of linear equations and their applications (Sections 1.1, 1.2) * Gaussian elimination, row-echelon form (Section 1.2) * Matrix operations (Sections 1.3, 1.4, 1.5) * Nonsingular matrices, computing
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH416AbstractLinearAlgebra I. GeneralInformation Instructor:BenjaminWyser ContactInfo: TimeandPlace:MWF9:00am 9:50am,141AltgeldHall Email:bwyser@illinois.edu OfficePhone:(217)3000363 OfficeLocation:222AIlliniHall OfficeHours:MWF1:002:00,orby appointment
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: ACTUARIAL THEORY II/ TOPICS IN ACTUARIAL THEORY I SPRING 2012 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohns
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 Sections D1 & X1 Introduction to Differential Equations Plus Spring 2014 Course Information Sheet INSTRUCTOR: Michael Brannan CONTACT INFORMATION: Ofce: 376 Altgeld Hall. Email: mbrannan@illinois.edu COURSE WEB PAGE: http:/www.math.uiuc.edu/~mbra
School: University Of Illinois, Urbana Champaign
Course: Actuarial Problem Solving
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 370 (Section Z) Actuarial Problem Solving Spring 2014 245 Altgeld Hall 7:00-8:50 pm Tuesday Starting February 4, 2014 12 Lectures Sarah Manuel Office Hours
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Clear@y, x, starterx, starteryD; starterx = 1.71; startery = 18.06; sol = DSolve@8y '@xD = 3 y@xD, y@starterxD = startery<, y@xD, xD; y@xD . sol@1DD Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 09/26/2011 Fall 2011 Normal (Gaussian) Distribution. mean standard deviation N ,2 f (x ) = 1 2 e -( x - ) 2 2 2 , - < x < . Standard Normal Distribution N ( 0 , 1 ): Z ~ N( 0, 1 ) X ~ N ( , 2 ) Z = X - = 0, 2 = 1. X = +Z _ EXCEL
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
f@xD = a x + b, The calculation reveals that when you take a line function f@x + hD - f@xD = a h. then you find that This tells you that when x advances by h units, then f@xD grows by Consequently a line function f@xD = a x + b has constant growth rate of
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Part II Discrete-time Markov chains 61 Chapter 6 Introduction to Stochastic Processes This chapter of the book is modeled on Chapter 1 of [Nor07], but with some additional material and a dierent structure. Denition 6.0.6. Let (, B ) be a probability space
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
y y = f@xD Accumulation Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 a 2.01 Integrals for Measuring Area BASICS B.1) a f @xD x measures the signed area between x b the plot of f @xD and the x-axis
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
MATH/STAT 409 Homework # 3 due 09/20/2013 1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution with pdf f (x; ) = 43 x , 0 < x < . 4 (a) Find the MLE . (b) Is a consistent estimator? Justify your answer. (c) Is an unbia
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #2 ( due Friday, September 14, by 4:00 p.m. ) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function ( ) f X ( x ) = f X ( x ; ) = 2 + x 1 (1 x ) , a) 0 < x < 1, > 0. ~ Obtain the m
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #10 (due Friday, April 6, by 3:00 p.m.) 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x, zero elsewhere. a) Find f X | Y ( x | y ). b) Find E ( X | Y = y ). c) Find f Y | X ( y | x ).
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 3 Solutions. Problem 1. Compute the following limits. Justify your answer. a. lim x2 6x + 4 x2 2x + 1 c. lim x1 (x 2)2 x2 6x + 4 b. lim x1 x2 d. lim x1 sin(x6 ) x e. lim x0 ex 1 x2 2x + 1 x1 (x 1)2 f. lim x0 sin(x) x ex 1 Solution
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
HW 71 1. Sec. 3.6: 3. We have x00 + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375; x0 (0) = 0: The characteristic equation is r2 + 100 = 0 =) r = mentary solution is 10i: The compli- xc (t) = c1 cos 10t + c2 sin 10t: r = 5i is not a root of the characteristi
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 2. Solutions. Problem 1. Let X, Y, Z, W be independent U (0, 1) random variables. Use a Monte Carlo method to compute E[XY 2 + eZ cos(W )]. How much computation should you do to be condent in your answer to three decimal places? (Turn in
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #6 1. 3.3-2 (a), 3.3-4 (a) ( , ) 2. 3.3-2 (b), 3.3-4 (b) ( , ) 3. 3.3-2 (c), 3.3-4 (c) ( , ) ( 4. 3.3-8 5. 3.3-24 (a),(b) ) ( ) 6. 3.4-4 ( ) 7. 3.4-8 ( ) 8. Suppose a random variable X has the following probability density fu
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2011 Homework Assignment # 8 (max. points = 10) Due at the beginning of class on Thursday, November 17, 201
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Approximation Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 3.01 Splines BASICS f@x_D = 1 + Sin@xD; g@x_D = 60 + 60 x + 3 x2 - 7 x3 60 + 3 x2 ; Plot@8f@xD, g@xD<, 8x, - 3, 3<, AxesLabel 8"x", "<, P
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
Practice Problems 3 1. During a radio trivia contest, the radio station receives phone calls according to Poisson process with the average rate of five calls per minute. Find the probability that the ninth phone call would arrive during the third minute.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #11 (due Thursday, April 12, by 4:30 p.m.) 1. 5.1-5 ( ) The p.d.f. of X is f X ( x ) = x 1 , 0 < x < 1, 0 < < . Let Y = 2 ln X. How is Y distributed? a) Determine the probability distribution of Y by finding the c.d.f. of Y F
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Growth f@xD 0.34 Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 0.32 Publisher: Math Everywhere, Inc. Version 6.0 1.05 Using the Tools BASICS 0.30 0.28 B.1) Using the derivative for finding maximum values and minimum values You can tell what h
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 (10 points) (due Friday, November 7, by 3:00 p.m.) Homework #10 Fall 2008 1. Can a corporation's annual profit be predicted from information about the company's chief executive officer (CEO)? Forbes (May, 1999) presented data on company profit (
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
Practice Problems 8 1. Suppose that the actual weight of "10-pound" sacks of potatoes varies from sack to sack and that the actual weight may be considered a random variable having a normal distribution with the mean of 10.2 pounds and the standard deviat
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
Approximation 5 Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 4 Publisher: Math Everywhere, Inc. Version 6.0 3 3.06 Power Series BASICS 2 1 B.1) Functions defined by power series - 1.5 B.1.a) What is a power series? Why are power series big
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 1 Due Tuesday September 10, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon1s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c raw
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #5 (due Friday, February 24, by 3:00 p.m.) 1. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ln 2 ) k k! , k = 1, 2, 3, . Recall ( Homework #1 Problem 9 ): This is a valid prob
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 2 Solutions. Problem 1. Recall the Taylor series for ex at a = 0. a. Find the Taylor polynomial of degree 4 for f (x) = ex about the point a = 0. Solution: T4 (x) = 1 + x + x2 x3 x4 + +. 2 6 24 b. Use your answer to part (a) to es
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #12 (due Friday, April 20, by 3:00 p.m.) 1 5. Let the joint probability density function for ( X , Y ) be f ( x, y ) = 1. x+ y 3 0 < x < 2, 0 < y < 1, , zero otherwise. a) Find the probability P ( X > Y ). b) Find the margina
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
measures out to f @xD * jump. So the accumulated area of all the boxes measures out to Sum@f @xD jump, 8x, a, b - jump, jump<D As n , jump 0, these sums close in on Integrate@f @xD, 8x, a, b<D = a f @xD x. See what happens as n gets large and the jump get
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
L.6) Here are two points 81, 2< and 85, 4< conveniently plotted on the axes below: y 5 Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 Publisher: Math Everywhere, Inc. Version 6.0 85,4< 4 1.01 Growth LITERACY L.1) A function f@xD starts
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #2 (10 points) (due Friday, February 3, by 3:00 p.m.) 1. A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are made to those in the "high risk" category. Of all the bank's loans, 5% are in default
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 Homework #4 (10 points) (due Friday, September 26, by 3:00 p.m.) Fall 2008 1. Hogg and Ledolter report on an engineer in a textile mill who studies the effects of temperature and time in a process involving dye on the brightness of a synthetic fa
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 476 / 567 Actuarial Risk Theory Prof. Rick Gorvett Fall, 2010 Homework Assignment # 4 (max. points = 8) Due at the beginning of class on Thursday, October
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
(* Content-type: application/mathematica *) (* Wolfram Notebook File *) (* http:/www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPositi
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #3 ( due Friday, September 21, by 4:00 p.m. ) 1. Let > 0 and let X 1 , X 2 , , X n be a random sample from the distribution with the probability density function f X (x) = f X ( x ; ) = a) x 2 e x , x > 0. Find the sufficient s
School: University Of Illinois, Urbana Champaign
Course: Hw01&ans
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2011 Homework Assignment # 1 (max. points = 10) Due at the beginning of class on Thursday, January 2
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
This output reflects the fact that NDSolve first produces a bunch of points and then strings them together with an interpolating function - just as Euler's method does. The formula for this interpolating function is not available, but you can plot it: Gro
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
4 Growth Authors: Bill Davis, Horacio Porta and Jerry Uhl 1996-2007 2 Publisher: Math Everywhere, Inc. Version 6.0 1.09 Parametric Plotting BASICS -4 B.1) Parametric plots in two dimensions: Circular parameters A handy way to plot the circle x2 + y 2 = 9
School: University Of Illinois, Urbana Champaign
Course: C&M Calc 2
You can plot a surface z = f @x, yD like this: In[1]:= Accumulation Clear@f, x, yD; f@x_, y_D = 3.1 x2 + 2.3 y2 ; 88a, b<, 8c, d< = 88- 2, 3<, 8- 1, 4<; surfaceplot = Plot3D@f@x, yD, 8x, a, b<, 8y, c, d<D; Authors: Bill Davis, Horacio Porta and Jerry Uhl
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Examples for 08/22/2011 random variables Fall 2011 discrete probability mass function p.m.f. continuous probability density function p.d.f. p( x ) = P ( X = x ) x 0 p( x ) 1 f( x ) x f( x ) 0 =1 p(x ) = 1 all x f (x) d x - cumulative distributi
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Strang-5060 book May 5, 2005 13:52 69 Chapter 2 Vector Spaces 2.1 VECTOR SPACES AND SUBSPACES Elimination can simplify, one entry at a time, the linear system Ax = b. Fortunately it also simplies the theory. The basic questions of existence and uniqueness
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Strang-5060 book May 5, 2005 13:52 69 Chapter 2 Vector Spaces 2.1 VECTOR SPACES AND SUBSPACES Elimination can simplify, one entry at a time, the linear system Ax = b. Fortunately it also simplies the theory. The basic questions of existence and uniqueness
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
Notes on Diffy Qs Differential Equations for Engineers by Ji Lebl r July 16, 2010 2 A Typeset in LTEX. Copyright c 20082010 Ji Lebl r This work is licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License. To view
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Class notes, MATH 564 Lee DeVille November 18, 2013 2 Contents I Background 7 1 Introduction 9 2 Set and Measure Theory 2.1 Notation about limits and sets . . . . . . . . . . 2.1.1 Sequences and Limits . . . . . . . . . . . 2.1.2 Sets and Limits . . . . .
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Ruled surfaces A surface is called ruled if it is swept out by moving a line in space. That is, there exiss a family of lines so that each point of the surface lies on exactly one line from this family (so, the lines are either parallel, or skew). The lin
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
THE TNB FRAME, THE CURVATURE, ETC. Throughout, we consider a spacecurve r = r(t). t |r (u)| du (length of the arc of the curve Let s be the arclength parameter: s = a ds with a u t). Then = |r (t)|. dt dr r The unit tangent vector: T = = . ds |r | The
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Integrals as General & Particular Solutions dy = f (x) dx General Solution: y(x) = f (x) dx + C Particular Solution: dy = f (x), dx y(x0 ) = y0 dy Examples: 1) dx = (x 2)2 ; y(2) = 1; 2) dy dy 10 = x2 +1 ; y(0) = 0; 3) dx = xex ; y(0) = 1; dx p. 2/3 Inte
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Review of MATH 385, Section D2 The nal will cover: (*=the content you should know to understand other subject, but no problem is directly for this subject) Chapter 1 (30pts) (except Exact equations) : The order of dierential equations, particular solution
School: University Of Illinois, Urbana Champaign
Solutions to Midterm 2 Review Problems for Math 231 Page 1 Solutions to Midterm 2 Review Problems for Math 231 Page 2 Solutions to Midterm 2 Review Problems for Math 231 Page 3 Solutions to Midterm 2 Review Problems for Math 231 Page 4 Solutions to Midter
School: University Of Illinois, Urbana Champaign
Math 231 Fall 2014. Worksheet 12. 10/23/14
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Math 231. Fall 2014. More review problems for Midterm 2. Some of these are old exam problems. This is neither a comprehensive list of review problems nor a complete study guide. Solutions will be posted. The problems will not be collected. 2 1. Consider t
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Group: Name: Math 231 A. Fall, 2013. Worksheet 15. 11/12/13 You will need Taylors Theorem, which says that f (x) = TN (x) + RN (x), where TN (x) is the degree N Taylor polynomial for f at a, and the remainder RN (x) equals RN (x) = f (N +1) (z) (x (N + 1)
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Group: Name: Math 231 A. Fall, 2013. Worksheet 13. 11/5/13 1. Augustin-Jean Fresnel (1788-1827) was an engineer, mathematician and the French commissioner of lighthouses. He is famous for his work in optics and for developing the Fresnel lens. Originally
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. Solutions to limit review problems. For each of the following, set up and solve an inequality which veries the asserted limit. 1. lim 4x 3 = 5 x2 Start with |4x 3 5| < and simplify to |4x 8| < 4|x 2| < |x 2| < /4. So = /4 works. Form
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. A few review problems. 1. Calculate the limit, or show that it does not exist. ex1 sin(x 1) cos(x 1) x1 (ln(x)2 lim 2. Find the Taylor series for f (x) = ln(cos(x2 ) about 0, to fourth degree. Then dierentiate the series to evaluate
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Fall 2012. limit review problems. Not to turn in. For each of the following, set up and solve an inequality which veries the asserted limit. 1. lim 4x 3 = 5 x2 2. lim x2 = 0 x0 3. lim x2 = 16 x4 4. (1 + h)2 1 lim =2 h0 h
School: University Of Illinois, Urbana Champaign
Course: Solution
4. Find the volume of the solid obtained by rotating the region bounded by the curves x=1 about the y-axis. 10. Find the volume of the solid obtained by rotating the region bounded by the curves and y=1 about the x-axis. y=x 2 , x= y , y=0, and x=0, 15. F
School: University Of Illinois, Urbana Champaign
Course: Solution
MATH 231E. Practice Final Exam Solutions. There are 5 problems all worth equal points. You must not communicate with other students during this test. No books, notes, calculators, or electronic devices allowed. This is a 20 minute exam. Do not turn t
School: University Of Illinois, Urbana Champaign
Course: Calculus I
The Fundamental Theorem of Calculus 1 The Fundamental Theorem of Calculus 1.1 Part I 1.2 Part II 2 Proofs 2.1 Proof of Part II of FTC Complete the steps below to prove the second part of the Fundamental Theorem of Calculus. (Note, this only holds for a <
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Properties of Summation Notation and the Definite Integral 1 1.1 Summation Properties Examples of summation notation n i f (i) = f (1) + 2f (2) + 3f (x) + + (n 1)f (n 1) + nf (n). (1) i=1 5 i2 = 1 + 4 + 9 + 16 + 25. (2) i=1 5 i=0 1.2 1 2 i =1+ 1 1 1 1 1 +
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Schedule for Math 221.AL1 Fall 2014 (This schedule is subject to change.) All section numbers correspond to Stewarts Calculus: Early Transcendentals (7e). W = Group Worksheet. Q = Quiz. Week Date Topics 1 Monday, August 25 2.1 Tuesday, August 26 W1 Wednes
School: University Of Illinois, Urbana Champaign
Course: Calculus I
How to do your best in Calculus To do well in a course, you must develop eective learning habits. This list is just a few. Make sure you have mastered the pre-requisites. You wont do well in Calculus I without being good in Algebra and Trigonometry. Like
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Sections covered from Stewarts Calculus: Early Transcendentals (7e) in Math 221 - Fall 2014 Chapter 2: Limits and Derivatives 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.5 Continuity 2.6
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Additional Exercises for Math 221 All section numbers correspond to Stewarts Calculus: Early Transcendentals (7e). Chapter 1 1.1: 1-2, 3, 7-10, 14, 21, 25, 27-30, 31-37, 38, 39-50, 58, 69-70, 71, 73-78, 79-80. 1.2: 1-2, 6, 16, 19-20. 1.3: 3, 6-7, 9-24, 2
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Midterm 2: Time: 9:00-9:50 AM on October 27th, 2014 Place: 066 Library (the standard classroom) Sections: 3.5 - 3.11, 4.1 - 4.5 and 4.7 - 4.9 Topics: 1. (5 points) From Exam I 2. (13 points) Curve Sketching 3. (14 points) 3.5 - 3.11 material (but not rela
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Lesson 8b: Optimization 1 The idea behind optimization We recently saw how we could use knowledge about functions to determine precisely when a function has a maximum or a minimum. In this section, we will see applications of using these skills. For examp
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Taalman-62052 book 400 December 31, 2003 10:56 CHAPTER 5 Polynomial Functions much as possible. Check your answers by multiplying out your factorization. 79. f (x) = x 3 2x 2 5x + 6 80. f (x) = 3x 3 8x 2 + 5x 2 81. f (x) = x 3 + 4x 2 11x + 6 82. f (x) = x
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Inverse Functions What you may remember from high school. Example 1: Find the inverse function of f (x) := and f 1 . 1 . Determine the domain and range of f x2 This technique will help us determine the inverse function, but what exactly is an inverse func
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Logarithmic Functions Consider any basic exponential function: To nd an inverse function algebraically, we switch the role of x and y and solve for y. Denition: For b > 0 and b = 1, the base b logarithmic function is dened by Remarks: We will begin with s
School: University Of Illinois, Urbana Champaign
Course: College Algebra
1 1.1 Function Review Function Review Discussion Question: What do you remember about functions? Denition: A function, f dened on a subset of real numbers, D is a rule that assigns to each value, , in D exactly one value, denoted f (). The set D is calle
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Sequences and Limits Motivational Example: Repeated Drug Doses Suppose a doctor orders you to take 16mg of a drug every 12 hours for 10 days. Assume your liver and kidneys remove 25% of the drug from your bloodstream every 12 hours. What happens to the dr
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Prep for Exam 2 Topics: Arithmetic and Geometric Sequences - denitions, generating functions/formulas, limits Series - denition, nite arithmetic and geometric series formulas, summation notation, innite series denition, theorems related to innite series
School: University Of Illinois, Urbana Champaign
Course: College Algebra
Finding Zeros of Polynomial Functions Some reminders. Theorem: The Rational Root Theorem p Let be a rational number written in fully reduced form. Consider the polynomial equation q cn xn + cn1 xn1 + . . . + c1 x + c0 = 0 p is a zero (or q a solution) of
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 8: Ratemaking II September 18, 2014 1 Last Time Ratemaking I Overall concept Two foundational techniques Pure premium method L
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 9: Risk Classification September 30, 2014 1 Agenda Ratemaking relativities Risk classification 2 Ratemaking Relativities T
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 11: Individual Risk Rating October 2, 2014 1 Agenda Individual Risk Rating Types of plans Prospective rating Retrospectiv
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 5: Loss Reserving II September 9, 2014 1 Agenda Review of basic loss development technique and essential metrics / quantities Oth
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 4: Loss Reserving I September 4, 2014 1 Agenda Purpose of Loss Reserving Loss data Types of reserves Key dates Types of
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 7: Ratemaking I September 16, 2014 1 Agenda Ratemaking I Overall concept Two basic techniques Pure premium method Loss ratio m
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 6: Loss Reserving III September 11, 2014 1 Agenda Accounting issues Statement of Loss Reserving Principles 2 Accounting Issues Ra
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479/568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 3: Economics and Insurance Markets September 2, 2014 1 Last Time Insurance contracts Lines of business Insurability Etc 2 C
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 1: Introduction and Overview August 26, 2014 Agenda Syllabus Moi The actuarial profession The casualty actuarial professi
School: University Of Illinois, Urbana Champaign
Course: Casualty Mathematics
Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 2: Risks and Risk Theory August 28, 2014 What Did We Discuss Last Time? What an actuary is, in words and numbers What actua
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Section 5.3 continued Integration Rules for Denite Integrals Let f and g be any functions continuous on a x b. Then b b kf (x)dx = k (1) Constant multiple rule: a b (2) Sum rule: g (x)dx a b b f (x)dx [f (x) f (x)]dx = g (x)dx a a a a b f (x)dx + a b (3)
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Section 5.1 Antidierentiation: The Indenite Integral Denition Antidierentiation A function F (x) is said to be an antiderivative of f (x) if F (x) = f (x) for every x in the domain of f (x). The process of nding antiderivatives is called antidierentiation
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Section 5.2 Integration by Substitution Example Compute (5x + 7)9 dx How can we go about evaluating this integral? One option would be to multiply it out, and integrate the resulting polynomial, but this seems like it would be a rather daunting choice. Wh
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Re be ka h Ar an a Section 7.3 Optimizing functions of partial derivatives 3 Denition Relative Extremum Co py rig ht 2 01 The function f (x, y ) is said to have a relative maximum at the point P (a, b) in the domain of f if f (a, b) f (x, y ) for all poin
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
The Natural Logarithm an a Recall from Wednesdays lecture that we said that we had a natural exponential base, e. The natural logarithm, denoted by ln x, is simply the function that undoes the base e exponential function. eln x = x for x > 0 and Example 8
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
Section 7.1 Functions of Several Variables Denition Functions of two variables A function f of the two independent variables x and y is a rule that assigns to each ordered pair (x, y ) in a given set D (the domain of f ) exactly one real number, denoted b
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
an a Section 4.3 Dierentiation of Exponential and Logarithmic Functions The derivative of ex For every real number x, (a) f (x) = x3 ex Re be We use the product rule to obtain: ka h Example 1 Dierentiate the following: Ar dx (e ) = ex dx f (x) = 3x2 ex +
School: University Of Illinois, Urbana Champaign
Course: Calculus For Business I
an a Section 3.2 Concavity and Points of Inection Re be ka h Ar The Point of Diminishing Returns ConcavityVerbally 3 If the function f (x) is dierentiable on the interval a < x < b then the graph of f (x) is Co py rig ht 2 01 concave upward on a < x < b
School: University Of Illinois, Urbana Champaign
Course: MATH
SURVEYUNTUKPENGEMBANGANUIBSECARABERKELANJUTAN KEPADAMAHASISWABARUANGKATAN2014/2015 PETUNJUKPENGISIANANGKET: Pengisiangket dirahasiakan identitasnya.JikakelakidentitasAndaakandigunakan,makakamiakanmintapersetujuanAndaterlebih dahulu. KEBEBASAN dan KEJUJURA
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
EXAM 1 REVIEW MATH 124 (1) All of the students in a class of 30 are majoring in either engineering, math, or both. If 22 are majoring in engineering and 16 are majoring in math, how many students are majoring in engineering but not in math? [Hint: Use a V
School: University Of Illinois, Urbana Champaign
| r srv s g kv 8 s r jeyvw4faaefCGyeaiuiIs wx!x o arvvs9!uEseA4yavuyyfyrGx Qynavu~vvsehaiv ywEsfCeavuinaCF wr x P s w x w | S r 8 s g x x sv u |yxay~eyvwaaG!daIiiG!veavuisA!x vw4!a!veavuisA!eleiu WEX2(811y)Ehv w r sd v sr x oud
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
The n-dimensional space Rn Basic facts: the n-dimensional space Rn is a generalization of R2 (the plane) or R3 (the 3-dimensional space) to the n-variable case. Formally Rn is the set of ordered n-tuples of real numbers: (x1 , . . . , xn ). We can identif
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
Determinants, cross products, and triple products 1. Determinants. a1 a2 = a1 b2 a2 b1 . Geometrically, this determinant represents the signed b1 b2 area of the parallelogram formed by the vectors a1 , a2 and b1 , b2 . The sign is positive if we need to r
School: University Of Illinois, Urbana Champaign
Course: Honors Calculus III
FORMULA SHEET FOR MIDTERM 1 Trigonometric identities: sin2 x+cos2 x = 1, tan2 x+1 = sec2 x, sin 2x = 2 sin x cos x, 1 1 cos2 x = (1 + cos 2x), sin2 x = (1 cos 2x), sec d = ln | sec + tan | + C. 2 2 Exponential and logarithmic functions: ln(ab) = ln a + ln
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 35 Tue, 04/01/2014 Remark 132. (April Fools Day!) 1 = 1= (1)(1) = 1 1 = ii = 1. When using the principal square-root (which basically takes the positive root, that is, the one with positive real part), the rule ab = a b does not hold u
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 34 Mon, 03/31/2014 Review. If x = Ax, with A an n n matrix (with constant entries), then n independent xn). solutions x1, , xn can be combined into a fundamental matrix = (x1 The Wronskian is W (t) = det. (t) satises the matrix equation
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 32 Wed, 03/19/2014 Review. generalized eigenvectors and corresponding solutions to x = Ax Recipe for solving x = Ax: nd eigenvalues for each , nd eigenvectors if is defective, nd enough chains 2 1 if = a bi is complex, take real and
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 33 Thu, 03/20/2014 Review. We now have a recipe to solve x = Ax. If A is n n (with constant entries), then we can nd n independent solutions x1, , xn. In particular, the general solution is c1x1(t) + mental matrix = (x1 xn). + cnxn(t) =
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 31 Example 125. Consider x = 1 3 3 7 Tue, 03/18/2014 x. The characteristic polynomial (1 )(7 ) + 9 = 2 8 + 16 = ( 4)2 has the double root = 4. However, 3 3 3 3 v = 0 has solution only v = c 1 1 . We say that the eigenvalue 4 is defective
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 28 Example 119. Solve x = Solution. 4 3 3 4 Tue, 03/11/2014 x. The characteristic polynomial (4 )2 + 9 has roots 4 3i. 3i 3 3 3i To nd the eigenvector for = 4 + 3i, we solve The complex solution x = e4t s in (3t) c o s (3t) 1 i v = 0. We
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 29 Wed, 03/12/2014 Review currently, all DEs considered are linear Homogeneous linear DEs of order n: Ly = 0 constant coecients non-constant coecients using the roots of the characteristic polynomial of L, we have a complete recipe for n
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 27 Mon, 03/10/2014 Review. complex numbers z = x + iy = rei, conjugate z = x iy = rei Note that z z = (x + iy)(x iy) = x2 + y 2 = |z |2. In particular, z z is always real. Example 114. 1 3 4i 3 + 4i 3 + 4i 3 4 = (3 4i)(3 + 4i) = 32 + 42
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 25 Wed, 03/05/2014 Review. solutions to the sytem discussed last time In order to solve x = Ax, we look for solutions x(t) = vet. Plugging into the DE, we get x = vet if and only if Av = v. ! Aetv. Cancelling the exponentials, we see tha
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 26 Thu, 03/06/2014 Review. eigenvectors, eigenvalues and corresponding solutions to systems Example 113. Find the general solution of x Solution. 5 3 3 0 1 2 x. = 6 5 2 The characteristic polynomial is 5 3 3 det 0 1 2 = (1 )det 6 5 2
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 40 Wed, 04/09/2014 There was nothing special about 2-periodic functions considered last time (except that cos (t) and sin (t) have period 2). Note that cos (t/L) has period 2L. Theorem 151. Every 2L-periodic function f can be written as
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 37 Thu, 04/03/2014 Review. undetermined coecients Example 140. Consider x = Ax + f (t), where A is a 7 7 matrix with eigenvalues 1 2i, 1 2i, 0, 3, 3. For dierent choices of f (t), we set up x p with undetermined coecients. f (t) get g g
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 39 Tue, 04/08/2014 Fourier series Denition 145. Let L > 0. f (t) is L-periodic if f (t + L) = f (t) for all t. The smallest such L is called the period of f . Example 146. The period of cos (nt) is 2/n. Example 147. The trigonometric fun
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 38 Mon, 04/07/2014 (t)1 f (t)dt solves x = Ax + f (t) Review. Variation of constants: x p(t) = (t) Here, (t) is any fundamental matrix of x = Ax. At In the special case that (t) = e , some things become easier. For instance, (t) Also, we
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 36 Wed, 04/02/2014 Inhomogeneous linear systems x = Ax + f (t) is the general form of a (rst-order25 ) inhomogeneous system of linear DEs. To solve it, we nd a particular solution x p(t). Then, the general solution is x(t) = x p(t) + xc(
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 23 Mon, 03/03/2014 Review. properties of determinants The determinant of any matrix can be computed by picking a row i and calculating det (A) = n (1)i+ jaij det(A[i,j]), where A[i, j] is obtained from A by deleting the ith row and jth c
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 24 Theorem 106. Let x1, x2, Tue, 03/04/2014 , xn be solutions of x = A(t) x. A(t) is n n, e ntrie s c o ntinu o u s o n I. c1x1 + c2x2 + + cnxn is the general solution x1, x2, , xn are independent the Wronskian W (t) = det ( x1 x2 xn ) 0
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 21 Wed, 02/26/2014 Review. systems of dierential equations; express DEs as rst-order systems Example 89. Express the non-linear DE x = x3 + (x )3 as a rst-order system14 . Solution. Introduce x1 = x, x2 = x to obtain the system x1 = x2,
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 20 Tue, 02/25/2014 External forces plus damping Example 85. Find the general solution of 2x + 2x + x = 10 sin (t). Solution. Old roots 2 48 1 1 = 2 2 i. So the system without external force is underdamped. [Why?!] After a routine calcul
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 18 Thu, 02/20/2014 Review. Let be angular displacement of a pendulum on a string of length L. Then its motion d2 g g is described by dt2 + L sin = 0. sin for small so, approximately13 , we get + L = 0. (This time, we used Newtons second
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 16 Tue, 02/18/2014 Review. solving nonhomogeneous linear DEs with constant coecients Example 70. Find a particular solution of y + 4y + 4y = 7e2x. Solution. Again, L = D 2 + 4D + 4 = (D + 2)2. Old roots 2, 2. New roots 2. Hence, there ha
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 22 Thu, 02/27/2014 A crash course in linear algebra Example 93. A typical 2 3 matrix is 1 2 3 . It is composed of column vectors like 1 4 5 6 4 and row vectors like ( 1 2 3 ). Matrices (and vectors) of the same dimensions can be added an
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 17 Wed, 02/19/2014 Theorem 74. The linear DE Ly = y + P (x)y + Q(x)y = f (x) has particular solution y p = y1(x) y2(x)f (x) dx + y2(x) W (x) y1(x)f (x) dx, W (x) where y1, y2 are independent solutions of Ly = 0 and W = y1 y2 y1 y2 is the
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 19 Mon, 02/24/2014 The qualitative eects of damping Let us consider x + d x + cx = 0 with c > 0 and d 0. The term d x models damping (e.g. friction, air resistance) proportional to the velocity x . d d2 4c The characteristic equation r
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 14 Wed, 02/12/2014 Review Basic understanding DEs and IVPs visualization of rst-order DEs via slope elds existence and uniqueness Basic modeling population models mixing problems modeling simple motions Solving techniques linear DEs with
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 13 Tue, 02/11/2014 Review. linear independence Fix some a I. Note that y(x) = C1 y1(x) + + Cnyn(x) is the general solution of a HLDE8 of order n if and only if we can solve for all initial values y(a) = b0, y (a) = b1, , y (n1)(a) = bn1.
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 15 Mon, 02/17/2014 Inhomogeneous linear DEs Recall that a linear DE is one of the form y (n) + pn1(x) y (n1) + + p1(x)y + p0(x)y = f (x). d Writing12 D = dx and setting L 6 D n + pn1(x) Dn1 + + p1(x)D + p0(x), this DE takes the concise f
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 12 Mon, 02/10/2014 Review. complex numbers Example 51. Here is another way, to look at Eulers identity eix = cos (x) + i sin (x). For this identity to make sense, one needs to somehow characterize the exponential function on the left-han
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 10 Wed, 02/05/2014 Example 38. Solve the IVP y + 7y + 14y + 8y = 0 with y(0) = 1, y (0) = 0, y (0) = 1. Solution. Last time, we found that the DE has the general solution y(x) = Aex + Be 2x + Ce 4x. y(x) = Aex + B e2x + Ce4x, y(0) = A +
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 11 Thu, 02/06/2014 Review. homogeneous linear DEs with constant coecients Example 43. Find the general solution of y y 5y 3y = 0. Solution. The characteristic equation is r 3 r 2 5r 3 = (r 3)(r + 1)2. This corresponds to the solutions y1
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 7 Thu, 01/30/2014 Review. Useful substitutions Example 27. Solve (x y)y = x + y. Solution. y y Divide the DE by x to get 1 x y = 1 + x . This is a homogeneous equation! 1+u 1 + u2 We therefore substitute u = to nd the new DE xu + u = 1 u
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 9 Tue, 02/04/2014 Review. population models Example 35. Short outbreaks of diseases among a population of constant size N . Model the population as consisting of S(t) susceptible, I(t) infected and R(t) recovered individuals (N = S(t) +
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 2 Wed, 01/22/2014 1 Review. Verify that x(t) = c kt is a one-parameter family of solutions to Solution. = kx2. k x (t) = (c k t)2 = kx(t)2 Solve the IVP: Solution. dx dt dx dt = kx2, x(0) = 2. [What about x(0) = 0, instead?] 7 1 1 ! =c c
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 8 Mon, 02/03/2014 Population models To model a population, let P (t) be its size at time t. (t), (t): birth and death rate [# of births/deaths (per unit of population per unit of time) at time t] P = (t)P (t)t (t)P (t)t dP = (t) (t)P dt
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 3 Thu, 01/23/2014 Understanding DEs without solving them Slope elds, or sketching solutions Example 9. Consider the DE y = x/y. Lets pick a point, say, (1, 2). If a solution y(x) is passing through that point, then its slope has to be y
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 5 Tue, 01/28/2014 Example 20. Solve y = ky. Solution. Write as dy dx 1 dy = k dx (note that y hence |y | = ek x+C . Since = ky, then we just lost the solution y = 0). Integrating gives ln |y| = kx + C, the RHS is never zero, y = ek x+C =
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Sketch of Lecture 4 Mon, 01/27/2014 Review. Existence and uniqueness of solutions Example 15. Discuss the IVP xy = 2y, y(a) = b. 3 Solution. f (x, y First, write as y = f (x, y) with f (x, y) = 2y/x. We compute y) = 2/x. Therefore, both f (x, y) and x 0.
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Name _ Version A Exam 2 Page Be sure to show all your work; your partial credit might depend on it. Earned 1 Put your final answers at the end of your work, and mark them clearly. 2 If the answer is a function, its support must be inc
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
Math 416 - Abstract Linear Algebra Fall 2011, section E1 Practice midterm 2 Name: This is a (long) practice exam. The real exam will consist of 4 problems. In the real exam, no calculators, electronic devices, books, or notes may be used. Show your wor
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Study Aid for Exam # 1, Math 210, Fall 2013 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2008 Exam # 1 (17 Problems Max possible points = 40) Thursday,
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: Actuarial Theory I Midterm #1 October 6, 2010 General Information: 1) There are 9 problems for a total of 50 points. 2) You have between 7:00-8:50pm to write the midterm. 3) You may refer to both sides of one 3in X 5in notecard. 4) You may use a
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 1 September 3, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. Pa
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 Fall 2013 Exam 1 September 26, 2013 Solutions 1. (6 points) Let U = cfw_1, 2, 3, 4, 5, 6, 7, 8, A = cfw_1, 2, 3, 5, and B = cfw_2, 4, 5, 6. Compute the following sets. (a) Ac Solution: Ac = cfw_4, 6, 7, 8 (b) A [ B Solution: A [ B = cfw_1, 2, 3,
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 3 September 17, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. P
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 4 September 24, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. P
School: University Of Illinois, Urbana Champaign
Course: Finite Mathematics
Math 124 M1 and Q1 Quiz 2 September 10, 2013 Name: You have fteen minutes to complete this quiz. No electronic devices are permitted during the quiz. Cheating will be punished with at least a zero on this quiz; there may be more severe consequences. P
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 Midterm 1 Practice Solution 1. (a) order 1, nonlinear, NA (b) order 2, nonlinear, non-homogeneous (c) order 1, linear, homogeneous (d) order 4, linear, homogeneous (e) order 2, nonlinear, NA 2. Refer the the book. 3. (a) H = e P (x)dx (b) H =
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Math 286 G1 Midterm 1 This is a mock-up exam for the real one. The actual exam will provide enough space for your writing. Here, we are saving trees in Brazil. 1. [?pt] Determine the orders of the following dierential equations. Also nd if they are linear
School: University Of Illinois, Urbana Champaign
Old exam questions from Math 231 Math 231 AL1. Exam 3. April 21, 2011 -Name: There are eight multiple choice problems series six 4. a) Use the binomial theorem to nd the MacLaurin worth for points each. Mark answers on Scantron forms in pencil. No partia
School: University Of Illinois, Urbana Champaign
Course: MATH
PENGUMUMAN BAGI MAHASISWA BARU UNIVERSITAS INTERNASIONAL BATAM ANGKATAN 2014/2015 1. Kegiatan Program Pengenalan Mahasiswa Baru Tahun 2014 bertema Reach to the Top Jadwal kegiatan mahasiswa baru UIB angkatan 2014/2015 sebagai berikut : AGUSTUS SEPTEMBER M
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
NAME 3. (20 points) Find the distance of the vector z to the Spancfw_v1 , v2 . 1 1 1 1 0 1 v1 = v2 = z= 0 0 1 1 1 2 NAME 6. (20 points) Solve the following linear system. If an exact solution does not exist, nd a least squares solution. x1 + x2 x
School: University Of Illinois, Urbana Champaign
School: University Of Illinois, Urbana Champaign
NAME MATH 410 - E13, Test 1, Fall 2014 September 24, 2014 Calculators, books, notes and extra papers are not allowed on this test Please show all your work and explain all answers to qualify for full credit 1. (20 points) Solve the following linear system
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Name: _ UIN: _ Version B UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Instructor: Jianan Xu Spring, 2011 Exam # 2 (6 Questions + 1 Bonus Question; Max possible points = 100+15) Wednesday, April 6, 2011 Y
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
Name: _ UIN: _ Version A UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Instructor: Jianan Xu Spring, 2011 Exam # 2 (6 Questions + 1 Bonus Question; Max possible points = 100+15) Wednesday, April 6, 2011 Y
School: University Of Illinois, Urbana Champaign
Course: Calculus
Math 220 (section AD?) Quiz 10 Fall 2012 Name You have 15 minutes No calculators x2 1. (3 points) Suppose w(x) = Show sucient work (t 4)(t + 1)6 dt. Determine all intervals upon which the 10 function w(x) is increasing. 2. (2 points) Precisely state Th
School: University Of Illinois, Urbana Champaign
Course: Calculus
AL1 (MWF 8:00-8:50) AL2 (MWF 9:00-9:50) MATH 220 AL3 (MWF 1:00-1:50) Test 2 Fall 2014 Name NetID Sit in your assigned seat (circled below). Circle your TA discussion section. Do not open this test booklet until I say START. Turn o all electronic devices a
School: University Of Illinois, Urbana Champaign
Course: Calculus
AL1 (MWF 8:00-8:50) AL2 (MWF 9:00-9:50) MATH 220 AL3 (MWF 1:00-1:50) Test 1 Fall 2014 Name NetID Sit in your assigned seat (circled below). Circle your TA discussion section. Do not open this test booklet until I say START. Turn o all electronic devices a
School: University Of Illinois, Urbana Champaign
Course: Calculus
Electric charge Glass rods, plastic tubes, silk, and fur can be used to demonstrate the movement of electrons and how their presence or absence make for powerful forces of attraction and repulsion. Q21.1 When you rub a plastic rod with fur, the plastic r
School: University Of Illinois, Urbana Champaign
Course: Calculus
Popular Chinese Religions Prof.JessicaVantineBirkenholtz RLST/ASST104 13November2014 Reminders Paper2dueonTuesday,Nov18thINCLASS Uploadelectronicversionpriortoclass Turninhardcopy Sourcesonlythosereadforclass DeptofReligionpizzaparty/infosession& RSSAm
School: University Of Illinois, Urbana Champaign
Course: Calculus
Confucianism Prof. Jessica Vantine Birkenholtz Exams returned next week Paper 2 due November 18th IN CLASS Announcements 2 Pre-dynastic period (legendary; Yao and Shun) Hsia Dynasty (22nd 18th c BCE; legendary; Yu) Shang Dynasty (14th 11th c BCE) Chou/Zho
School: University Of Illinois, Urbana Champaign
Course: Calculus
Ancient Chinese Myths Prof. Jessica Vantine Birkenholtz Spring Religion Courses Dept of Religion Pizza Party/Info session Nov 13th, 5:30-6:30pm, FLB 1038 RSSA movie night, 6:30pm, FLB G38 Announcements Final exam not cumulative, i.e., Chinese and Japanese
School: University Of Illinois, Urbana Champaign
Course: Solution
MATH 231E. Exam 3. Nov 8, 2012. Name: There are 6 problems worth a total of 100 points. Show your work. Circle your answers. You must not communicate with other students during this test. No books, notes, calculators, or electronic devices allowed. T
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E. Exam 1. Sept 19, 2012. Name: There are ve problems worth a total of 100 points. Show your work. Circle your answers. You must not communicate with other students during this test. No books, notes, calculators, or electronic devices allowed.
School: University Of Illinois, Urbana Champaign
Course: Solution
Math 231E, Exam 2. Oct 11, 2012. Name: There are 6 problems worth a total of 100 points. Show your work. Circle your answers. You must not communicate with other students during this test. No books, notes, calculators, or electronic devices allowed.
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Thanksgiving Break Practice Problems Math 221.AL1 1. Let f (x) be an even function that is integrable. If 3 3 f (x) dx = 4, f (x) dx = 6 and 1 1 1 f (x) dx? what is 0 2. In this question, we will use three dierent methods to compute the value of the denit
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Thanksgiving Break Practice Problems Math 221.AL1 1. Evaluate the following integrals. (a) x7 x4 + 7 dx (b) (c) (d) sin3 () d = 1 dy 3y + 8 t dt (1 + t)2 sin2 () sin() d
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Thanksgiving Break Practice Problems Math 221.AL1 1. Determine 1 1 1 + + + n 2n2 + n 2n2 + 2n 2n2 + n2 1 1 1 . = lim + + + n 1 2 n 2+ n n n 2+ n n 2+ n lim 2. Let R be the region bounded by the curves 2x2 + x and x3 + x2 + x. (a) At what points do these
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Thanksgiving Break Practice Problems Math 221.AL1 1. Evaluate the following integrals. x (a) dx. 1 + x4 w2 + 4 dw. (b) w2 (c) (d) 5 3 tan2 () d. 6 5q dq. 4 + q2 2. Use integration to show that the volume of a right circular cone with height h and radius (
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Thanksgiving Break Practice Problems Math 221.AL1 d 1. (a) Determine dx d (b) Determine dx x (t3 t2 + 5) dt. 5 cos(x) 1 + sin(t2 ) dt. x3 2. Let R be the region bounded by the curves x = sin(y) and x = y y 2 . (a) Sketch the region R. Label all relevant p
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Name: Form: A Math 220 Calculus Exam II Thursday, March 6, 2014 Scoring Information: This exam has 9 questions for a total of 100 points. The point values are listed in parenthesis at the beginning of the problem. You must show all work in order to rece
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Name: Form: A Math 221 Calculus I Exam II Wednesday, October 23, 2013 Scoring Information: This exam has 8 questions for a total of 100 points. The point values are listed in parenthesis at the beginning of the problem. You must show all work in order
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Name: Form: A Math 220 Calculus Exam III Thursday, April 3, 2014 Scoring Information: This exam has 8 questions for a total of 100 points. The point values are listed in parenthesis at the beginning of the problem. You must show all work and use proper
School: University Of Illinois, Urbana Champaign
Course: Calculus I
Name: Form: A Math 221 Calculus I Exam III Wednesday, November 20, 2013 Scoring Information: This exam has 9 questions for a total of 100 points. The point values are listed in parenthesis at the beginning of the problem. You must show all work in orde
School: University Of Illinois, Urbana Champaign
Math 231 ADF. Exam 1. September 14, 2011 Name: There are six multiple choice problems worth ve points each. Mark answers on Scantron forms in pencil. No partial credit for multiple choice questions. There are 5 free response questions worth 14 points ea
School: University Of Illinois, Urbana Champaign
Old exam questions from Math 231 4. a) Use the binomial theorem to nd the MacLaurin series for f (x) = x(1 + x2 )1/3 . Express your answer using summation notation, but DO NOT expand the binomial coecients which arise. 4. a) Use the binomial theorem to nd
School: University Of Illinois, Urbana Champaign
Math 231, ADF. Sample integrals from old Calc II exams. (1) These are sample integration problems from the rst midterms from previous versions of this course. (2) This is not a comprehensive list of problems. This is not a sample exam. (3) This is not a c
School: University Of Illinois, Urbana Champaign
Math 231 ADF. Fall 2011. More review problems for Midterm 2. Some of these are old exam problems. This is neither a comprehensive list of review problems nor a complete study guide. Solutions will be posted. The problems will not be collected. 2 1. Consid
School: University Of Illinois, Urbana Champaign
Sample nal questions These are sample questions taken from old nal exams. This will give some indication of your preparation for the basic course material. This is not a comprehensive list of problems. This is not a study guide. (1) Evaluate the integral:
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 3. Solutions. Problem 1. Here we systematically develop the solution of the system (11.2.4), which is the formula for hi , that satises the recursion hi = phi+1 + qhi1 , h0 = 1. (1) a. Show that any constant solution hi = A satises (1).
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 Fall 2011 Homework #5 (due Friday, October 7, by 3:00 p.m.) 1. Every month, the government of Neverland spends X million dollars purchasing guns and Y million dollars purchasing butter. Assume X and Y jointly follow a Bivariate Normal distributio
School: University Of Illinois, Urbana Champaign
Course: Statistics And Probability II
STAT 410 U3, G4 Fall 2011 Homework #1 (due Friday, September2, by 3:00 p.m.) 1. Below is a list of moment-generating functions. Provide (i) the values for mean and variance 2 , and (ii) P ( 1 X 2 ) for the random variable associated with each moment-gener
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics II
MATH/STAT 409 Homework # 3 due 09/20/2013 1. Let > 0 and let X1 , X2 , . . . , Xn be a random sample of size n from a distribution with pdf f (x; ) = 43 x , 0 < x < . 4 (a) Find the MLE . (b) Is a consistent estimator? Justify your answer. (c) Is an unbia
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 1. Solutions. Problem 1. Prove Proposition 0.2.2. A guide to this problem: start with the open set S = (a, b), for example. First assume that a > , and show that the number a has the properties that it is a lower bound for S , and, for a
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #2 ( due Friday, September 14, by 4:00 p.m. ) 1. Let X 1 , X 2 , , X n be a random sample from the distribution with probability density function ( ) f X ( x ) = f X ( x ; ) = 2 + x 1 (1 x ) , a) 0 < x < 1, > 0. ~ Obtain the m
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #10 (due Friday, April 6, by 3:00 p.m.) 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x, zero elsewhere. a) Find f X | Y ( x | y ). b) Find E ( X | Y = y ). c) Find f Y | X ( y | x ).
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 3 Solutions. Problem 1. Compute the following limits. Justify your answer. a. lim x2 6x + 4 x2 2x + 1 c. lim x1 (x 2)2 x2 6x + 4 b. lim x1 x2 d. lim x1 sin(x6 ) x e. lim x0 ex 1 x2 2x + 1 x1 (x 1)2 f. lim x0 sin(x) x ex 1 Solution
School: University Of Illinois, Urbana Champaign
Course: Intro Differential Equations
HW 71 1. Sec. 3.6: 3. We have x00 + 100x = 225 cos 5t + 300 sin 5t; x(0) = 375; x0 (0) = 0: The characteristic equation is r2 + 100 = 0 =) r = mentary solution is 10i: The compli- xc (t) = c1 cos 10t + c2 sin 10t: r = 5i is not a root of the characteristi
School: University Of Illinois, Urbana Champaign
Course: Applied Stochastic Processes
Math 564 Homework 2. Solutions. Problem 1. Let X, Y, Z, W be independent U (0, 1) random variables. Use a Monte Carlo method to compute E[XY 2 + eZ cos(W )]. How much computation should you do to be condent in your answer to three decimal places? (Turn in
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #6 1. 3.3-2 (a), 3.3-4 (a) ( , ) 2. 3.3-2 (b), 3.3-4 (b) ( , ) 3. 3.3-2 (c), 3.3-4 (c) ( , ) ( 4. 3.3-8 5. 3.3-24 (a),(b) ) ( ) 6. 3.4-4 ( ) 7. 3.4-8 ( ) 8. Suppose a random variable X has the following probability density fu
School: University Of Illinois, Urbana Champaign
Course: Theory Of Interest
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 210 Theory of Interest Prof. Rick Gorvett Fall, 2011 Homework Assignment # 8 (max. points = 10) Due at the beginning of class on Thursday, November 17, 201
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #4 (due Friday, February 17, by 3:00 p.m.) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Sally sells seashells by the seashore. The daily sales X of
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #11 (due Thursday, April 12, by 4:30 p.m.) 1. 5.1-5 ( ) The p.d.f. of X is f X ( x ) = x 1 , 0 < x < 1, 0 < < . Let Y = 2 ln X. How is Y distributed? a) Determine the probability distribution of Y by finding the c.d.f. of Y F
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 5 Due Tuesday November 19, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon5s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c rawl
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 (10 points) (due Friday, November 7, by 3:00 p.m.) Homework #10 Fall 2008 1. Can a corporation's annual profit be predicted from information about the company's chief executive officer (CEO)? Forbes (May, 1999) presented data on company profit (
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Calculus III
12/18/13 M ath 241 Honor s Homewor k 1 Due Tuesday September 10, in class This is the html vers ion of the file http:/www.math.uiuc .edu/~ oik hberg/F13/241/HMW /HONORS/hon1s ol.pdf. Google automatic ally generates html vers ions of doc uments as we c raw
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2014 Homework #4 (due Friday, February 21, by 3:00 p.m.) No credit will be given without supporting work. 1 3. Alex sells Exciting World of Statistics videos over the phone to earn some extra cash during the economic crisis. Only 10% of al
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #5 (due Friday, February 24, by 3:00 p.m.) 1. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ln 2 ) k k! , k = 1, 2, 3, . Recall ( Homework #1 Problem 9 ): This is a valid prob
School: University Of Illinois, Urbana Champaign
Course: Engineering Applications Of Calculus
Math 231E. Fall 2013. HW 2 Solutions. Problem 1. Recall the Taylor series for ex at a = 0. a. Find the Taylor polynomial of degree 4 for f (x) = ex about the point a = 0. Solution: T4 (x) = 1 + x + x2 x3 x4 + +. 2 6 24 b. Use your answer to part (a) to es
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 409 Spring 2012 Homework #12 (due Friday, April 20, by 3:00 p.m.) 1 5. Let the joint probability density function for ( X , Y ) be f ( x, y ) = 1. x+ y 3 0 < x < 2, 0 < y < 1, , zero otherwise. a) Find the probability P ( X > Y ). b) Find the margina
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2012 Homework #2 (10 points) (due Friday, February 3, by 3:00 p.m.) 1. A bank classifies borrowers as "high risk" or "low risk," and 16% of its loans are made to those in the "high risk" category. Of all the bank's loans, 5% are in default
School: University Of Illinois, Urbana Champaign
Course: Alex
STAT 420 Homework #4 (10 points) (due Friday, September 26, by 3:00 p.m.) Fall 2008 1. Hogg and Ledolter report on an engineer in a textile mill who studies the effects of temperature and time in a process involving dye on the brightness of a synthetic fa
School: University Of Illinois, Urbana Champaign
Course: Actuarial Risk Theory
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 476 / 567 Actuarial Risk Theory Prof. Rick Gorvett Fall, 2010 Homework Assignment # 4 (max. points = 8) Due at the beginning of class on Thursday, October
School: University Of Illinois, Urbana Champaign
STAT 409 Fall 2012 Homework #3 ( due Friday, September 21, by 4:00 p.m. ) 1. Let > 0 and let X 1 , X 2 , , X n be a random sample from the distribution with the probability density function f X (x) = f X ( x ; ) = a) x 2 e x , x > 0. Find the sufficient s
School: University Of Illinois, Urbana Champaign
Course: Hw01&ans
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2011 Homework Assignment # 1 (max. points = 10) Due at the beginning of class on Thursday, January 2
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Homework #5 Spring 2015 A. Stepanov (due Friday, February 27, by 3:00 p.m.) your name ( with your last name underlined ), Please include your NetID, and your discussion section number at the top of the first page. No credit will be given without
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2015 A. Stepanov Homework #4 (due Friday, February 20, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Homework #4 Spring 2015 A. Stepanov (due Friday, February 20, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2015 A. Stepanov Homework #2 (due Friday, February 6, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without s
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2015 A. Stepanov Homework #3 (due Friday, February 13, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. No credit will be given without
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 Spring 2015 A. Stepanov Homework #1 (due Friday, January 30, by 3:00 p.m.) Please include your name ( with your last name underlined ), your NetID, and your discussion section number at the top of the first page. 1 4. Do NOT use a computer. You m
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
7' I I I I I I I I L-: i /u\ t\J L 7x+7XL1 x- 32 -3 tF Ylo ?to t- I -t F I a I t- ( a\ /: t) \ ta('.) J (a I q t) . -t_/ r- l- tl* ( cfw_c hill,'n (s) flo.,* B-rt.* (orntn6.rU* I *or,b,!,? /O q* r^ Bru*^,.^ cfw_S yrrcn 2o Erown lo Cr T"+",1 frcfw_ Jrt<La
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
Math 125 Fall 2014 Homework 0 Due Friday, August 29 - Print this page and ll in the blanks Answers are based upon the course syllabus and the Student Code Course Syllabus www:math:illinois:edu=math125=F A14= Do Hyung Kim Name: Section: (circle one) X1 F1
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
1 1/1point Becauseofscarcity,everyeconomicdecisioninvolves Questionoptions: atradeoff. afreegood. atradein. anincreasingcost. Question 2 1/1point YourfriendwonderswhytrafficduringhereveningcommuteisalwaysworseonFridays.Sheisnotconsidering: Questionoptions
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
MATH125 Final Exam Sections: 1.3-2.7, 3.1-3.4, 3.6, 4.1-4.5, 5.1-5.3 Definition Linear- all variables have at most degree 1 System of linear inequalities- a collection of more than 1 Feasibility region- the region determined by simultaneously solving the
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Section VC.01 Here are the concepts you should know. You should be able to do problems but also be able to answer true/false or short answer questions about these concepts (think something like L13 or L16 in VC.01). Vector basics: adding, subtracting, mu
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
VC.10 Problem 1 F = ex x sin y + 2y 2 z. We evaluate this at (0, 1, 5) to obtain e0 0 sin(1) + 2 5 = 1 + 10 = 11 > 0 so the point (0, 1, 5) is a source. VC.10 Problem 2 We want to calculate R F dA. First calculate the divergence F = 3x2 + 3y 2 + 3z 2 S
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
VC.05 Problem 1 Here we just compute F (x (t), y (t) and F (y (t), x (t) and check what matches. The answers are along, across, across, along. VC.05 Problem 2 The ow along the curve is 2 2 F (x (t), y (t) dt = 0 (3x(t)y(t), 2x(t) (2t 1, 5t) dt 0 2 3(t2 t)
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Math 241 C8 Quiz 9 12 April 2011 Name: Problem 1: Let C be the cone with vertex at (0, 0, 0), aperture of radians, axis aligned 2 with the z-axis, and 22 z 2 (see the picture below). The aperture of a cone is the angle between the two sides, therefore the
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
Section VC.05 Here are the concepts you should know. You should be able to do problems but also be able to answer true/false or short answer questions about these concepts. Flow across a curve: Flow along a curve: thigh tlow thigh tlow F normaldt, where
School: University Of Illinois, Urbana Champaign
Course: Mathmatica
1.2 We want to check the sign of (3, 1, 3)(t, 5, t+3). Positive means acute, negative means obtuse, and zero means perpendicular. 1.3 A vector tangent (10t, 4 sin(4t). This vector is also the velocity. For the acceleration: (10, 16 cos(4t). 1.4 Formula is
School: University Of Illinois, Urbana Champaign
Course: Calculus II Honors
Test Hypothesis Geometric Series an = arn p-series an = Conclusion 1 X a an = for |r| < 1 and diverges other1 r n=0 wise 1 X an converges for p > 1 and diverges othn=1 1 np Examples 1 X 1 n 5 5 = 2 1 n=0 n=0 Compute lim sn directly For erwise Telescoping
School: University Of Illinois, Urbana Champaign
Course: Actuarial Modeling
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 478 / 568 Actuarial Modeling Prof. Rick Gorvett Spring 2012 Project: Data Analysis and Write-Up Due At or Before the Final Exam at 1:30 pm, Wednesday, May
School: University Of Illinois, Urbana Champaign
Course: Differential Equations
Math 441 Syllabus - Spring 2014 Text: Elementary Dierential Equations and Boundary Value Problems, John Wiley & Sons, Inc., by Boyce and DiPrima 9th edition. Instructor: Nikolaos Tzirakis Introduction/Motivation/Terminology (2 Lectures) How dierential e
School: University Of Illinois, Urbana Champaign
Course: Calculus II
Math 231: Calculus II Study guide for midterm 2 (mastery exam) The second midterm will cover material from chapters 7 and 8. The goal of the exam is to test basic skills and problem solving WITHOUT THE USE OF A CALCULATOR. The following is a list of
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
Short study guide for nal, math 286, Fall 2008 Note that the nal is comprehensive, so study all your study guides and past exams and exam solution sheets. You may also be asked questions relating to the IODE project! Here are some sample solved probl
School: University Of Illinois, Urbana Champaign
Course: College Algebra
MATH 115 PREPARATION FOR CALCULUS FALL 2013 Instructor Office E-mail Lecture A1 8am 100 Gregory Hall Lecture D1 11am 114 DKH Jennifer McNeilly 121 Altgeld Hall jrmcneil@illinois.edu Lecture X1 Noon 217 Noyes Lab Theodore Molla 226 Illini Hall molla@illino
School: University Of Illinois, Urbana Champaign
Course: Applied Linear Algebra
Syllabus for the Midterm Exam on February 23 * Systems of linear equations and their applications (Sections 1.1, 1.2) * Gaussian elimination, row-echelon form (Section 1.2) * Matrix operations (Sections 1.3, 1.4, 1.5) * Nonsingular matrices, computing
School: University Of Illinois, Urbana Champaign
Course: Abstract Linear Algebra
MATH416AbstractLinearAlgebra I. GeneralInformation Instructor:BenjaminWyser ContactInfo: TimeandPlace:MWF9:00am 9:50am,141AltgeldHall Email:bwyser@illinois.edu OfficePhone:(217)3000363 OfficeLocation:222AIlliniHall OfficeHours:MWF1:002:00,orby appointment
School: University Of Illinois, Urbana Champaign
Course: Actuarial Theory II
MATH 472/567: ACTUARIAL THEORY II/ TOPICS IN ACTUARIAL THEORY I SPRING 2012 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohns
School: University Of Illinois, Urbana Champaign
Course: Intro To Differential Eq Plus
MATH 286 Sections D1 & X1 Introduction to Differential Equations Plus Spring 2014 Course Information Sheet INSTRUCTOR: Michael Brannan CONTACT INFORMATION: Ofce: 376 Altgeld Hall. Email: mbrannan@illinois.edu COURSE WEB PAGE: http:/www.math.uiuc.edu/~mbra
School: University Of Illinois, Urbana Champaign
Course: Actuarial Problem Solving
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Actuarial Science Program DEPARTMENT OF MATHEMATICS Math 370 (Section Z) Actuarial Problem Solving Spring 2014 245 Altgeld Hall 7:00-8:50 pm Tuesday Starting February 4, 2014 12 Lectures Sarah Manuel Office Hours
School: University Of Illinois, Urbana Champaign
Course: Actuarial Statistics I
STAT 408 / MATH 408 Spring 2014 Actuarial Statistics I Monday, Wednesday, Friday Instructor: 9:00 9:50 a.m. 101 Armory Alex Stepanov Office: 101-A Illini Hall E-mail: stepanov@illinois.edu Office hours: ph.: 265-6550 Monday 3:30 4:30 p.m., Thursday 1:30 2
School: University Of Illinois, Urbana Champaign
Course: Elementary Linear Algebra
MATH 125: Calculus with Analytic Geometry II Instructor: Farhan Abedin Email: abedinf@uw.edu Oce: Padelford C-404 Oce Hours: TA: Neil Goldberg Email: neilrg@uw.edu Oce: Padelford C-34 Oce Hours: Text: Calculus, James Stewart, 7th Edition. MATH 125 Materia
School: University Of Illinois, Urbana Champaign
Math 231 B1 Summer 2012 Instructor: Vyron Vellis Oce: B3 Coble Hall, 217-244-3288 Oce hours: M 2-2:50PM, W 3-3:50PM B3 Coble Hall or by appointment Homepage: http : /www.math.uiuc.edu/ vellis1/math 231 sum2012.html E-mail: vellis1@illinois.edu Textbook: C
School: University Of Illinois, Urbana Champaign
Course: Calculus III
Math 241 Calculus III Section AL1 at MWF 9:00-9:50 in 314 Altgeld Hall Section CL1 at MWF 2:00-2:50 in 314 Altgeld Hall Spring 2010 Instructor: Tom Carty Oce: 121 Altgeld Hall Oce Phone: 265-6205 email: carty@illinois.edu Oce Hours: To Be Determined Websi
School: University Of Illinois, Urbana Champaign
Syllabus of the course MATH 482 LINEAR PROGRAMMING AND COMBINATORIAL OPTIMIZATION This is a course on mathematical aspects of problems in linear and integral optimization that are relevant in computer science and operation research. It is based on the boo
School: University Of Illinois, Urbana Champaign
Math 482 (Linear Programming and Combinatorial Optimization): (Spring 2011) Instructor: Alexander Yong ayong@math.uiuc.edu Lectures: MWF 1:00-1:50pm 141 Altgeld Office Hours: By appointment only, but in particular, I'm free MF 2:00-3:00pm (right after cla
School: University Of Illinois, Urbana Champaign
Math 482 (Linear Programming and Combinatorial Optimization): (Spring 2011) Instructor: Alexander Yong ayong@math.uiuc.edu Lectures: MWF 1:00-1:50pm 141 Altgeld Office Hours: By appointment only, but in particular, I'm free MF 2:00-3:00pm (right after cla
School: University Of Illinois, Urbana Champaign
Course: Differential Geometry Of Curves And Surfaces
DEP 3053 Syllabus, 1/8/2012 DEP 3053 DEVELOPMENTAL PSYCHOLOGY, LIFESPAN, SPRING 2012 Section # 0069 Instructor: Office Hours: Office: Phone: Email: ILAN SHRIRA Wednesday, 3-5pm; also available by appointment Room 273, Psychology Building 273-0166 ilans@uf
School: University Of Illinois, Urbana Champaign
Course: MLC
MATH 471: ACTUARIAL THEORY I FALL 2010 -INSTRUCTOR: Name: Office: Office phone number: E-mail address: Paul H. Johnson, Jr. 361 Altgeld Hall (217)-244-5517 pjohnson@illinois.edu Website: http:/www.math.uiuc.edu/~pjohnson/ Office Hours: Monday 1:00-2:00pm,