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School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 2 Solutions 1. ( Chapter 2, Problem 3) a) Denote the steady state by N . Then N N = N er(1 K ) The trivial N steady state that holds for the above equation is N = 0. To nd the nontrivial steady states we div
School: Rutgers
% Math 250 Matlab Lab Assignment #2 rand('seed',2573) %Question 1 (a) A = rmat(3,5), rank(A(:,1:3) A = 7 5 3 5 8 8 8 9 4 9 5 8 0 8 5 ans = 3 b = rvect(3), R=rref([A b]) b = 2 6 9 R = 1.0000 0 0 0.4638 1.2319 0.9130 0 1.0000 0 0.7101 0.1449 1.69
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #4 Revised 5/16/12 LAB 4: General Solution to Ax = b In this lab you will use Matlab to study the following topics: The column space Col(A) of a matrix A The null space Null(A) of a matrix A. Particular solutions to an in
School: Rutgers
Course: Calculus
Econ 103  Review Sheet I Chapter 4: 1. Determine through calculation, which has a higher present value: An annual payment of $100 received over 3 years or an annual payment of $50 received 7 years. In both cases the discount rate is 7% (0.07). 2. To
School: Rutgers
PRECALCULUS Recitation 9a (EXAM 2 REVIEW) NONCALCULATOR PART: 1. Graph the function . State the domain, range, and the asymptote. 2. Graph the function . State the domain, range, and the asymptote. 3. Evaluate the following exactly: a. b. c. 4. A bacteri
School: Rutgers
Pre Calc 111 Review Sheet Intervals Notation (a,b) [a,b] [a,b) (a,b] (a,) [a,) (,b) (,b] (,) Set description {x a<x<b} {x a<=x<=b} {x a<=x<b} {x a<x<=b} {x a<x} {x a<=x} {x x<b} {x x<=b} All Real Numbers Laws of Exponents (A/b)n = (b/a)
School: Rutgers
Course: CALCULUS 2 MATH/PHYS
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School: Rutgers
Course: High Frequency Finance
Lecture 1 Introduction Math 627 High Frequency Trading: Market Microstructure and Optimal Control Essential Information Doug Borden 6464164875 dborden@knight.com TA: Nader Rahman Books Hasbrouck, Empirical Market Microstructure Kissell & Glantz, Optimal
School: Rutgers
Course: Crytography
Lecture 12  The PohligHellman attack and Chinese Remainder Theorem In the last lecture we saw how discrete logarithms could be efficiently solved if p1 was a power of 2. Today we generalize this to the case when p1 is smooth, meaning that it is a prod
School: Rutgers
Course: Linear Algebra
Text 1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 1 2 2 x1 7
School: Rutgers
Course: Numerical Analysis
74 MATH 573 LECTURE NOTES 13.8. Predictorcorrector methods. We consider the Adams methods, obtained from the formula xn+1 xn+1 f (x, y (x) dx y (x) dx = y (xn+1 y (xn ) = xn xn by replacing f by an interpolating polynomial. If we use the points xn , xn1
School: Rutgers
Course: Numerical Analysis
MATH 573 LECTURE NOTES 71 13.7. Strong, weak, absolute and relative stability. To formalize the stability problem discussed above, we now dene several concepts of stability that seek to dierentiate between methods which exhibit numerical instability and t
School: Rutgers
Course: Numerical Analysis
68 MATH 573 LECTURE NOTES 13.6. Stability of linear multistep methods. Denition: 1st and 2nd characteristic polynomial of a multistep method: p (z ) = z p+1 p ai z pi , bi z pi . (z ) = i=0 i=1 The linear multistep method is consistent if (1) = 0 and (1)
School: Rutgers
Course: Precalc 2
1. Let 2 x 7 g(x) = and h(x) = 3 + 4x x2 a. Find (g o h)(x) (don't forget to simplify). b. Find the inverse of g. Label your answer clearly either as "the inverse of g" or with "g1(x) = . . 2. a. Find the domain of the function k defined by k (t) = (5 
School: Rutgers
Course: Basic Calculus
Basic Calculus/Exam #1/Spring 2012 NAME: Calculators may be used. For full credit, you must show your work. You do not need to simplify your answers. Answer all questions. Total points: 100. 1. (10 points) Let f (x) = x2  4x + 2, g(x) = (x2 + 1)2 . Find
School: Rutgers
Course: CALCULUS 135
1A [10) 1. Suppose = 5:2. Use the denition of derivative to nd .1: 3 3 . .3   K : hPU h. 1H0 h. . + 2) +171. + 2) . 3h = 11111 = 11111 iii>0 M3: + h + + 2) iii>0 M3: + h. + + 2] 3 3 :1. =_ 1113; (3: +11+ 2(.1:+ 2) (.7: + 2)? 43: at the oint where
School: Rutgers
Course: CALCULUS 135
(10) (9) (12) 1A 1. Suppose f(3:) : 23:2 3:1,". Use the denition of derivative to nd f(3t). f(:r: + h.) f(:) 2(3: + h.)2 3(5'? +31 (23:2 3:1?) f _ . _ . f (3) _ lilIih h. _ IiiIii: h. 23:2 + 4.1:; + 2.33.2 3h. 213':2 + 3:3: 2 hm hm it 4, 2F.2Z', =li
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 3 2 3 2 3 2 3 2 3 2 = sin() ( + ) = sin() sin() + sin() = 3 2 sin() (3 2 + sin() = 3 2 sin() 3 2 sin() = 3 2 + sin() 0 + 2sin(0) = =0 12 + 0 Equation
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 Equation of the tangent: (y (2) = 0(x 0) y+2=0 y = 2 b) at (2,1) Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) Equ
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 2 Solutions 1. ( Chapter 2, Problem 3) a) Denote the steady state by N . Then N N = N er(1 K ) The trivial N steady state that holds for the above equation is N = 0. To nd the nontrivial steady states we div
School: Rutgers
640:423 Partial Dierential Equations, Autumn 2012 Department of Mathematics, Rutgers University Problem Set 0 Most of the following exercises are from Strauss [Str] and Rogawski [Rog]. For every exercise, be sure to justify your answer completely, stating
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 5 (Solutions) 1. MMB Chapter 5, Problem 13. We begin with the equations dN dt dC dt C N N 1+C C = N C + 2 1+C = 1 (a) Obvious. (b) If we let x = N + 1 2 then the equation reduces to dx = 1 2 x dt Using separ
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 3A (Covering material from 3.1 3.4) [Warmup problems in the book: #15, 17] 1. Martha and Nick share the rights to use a certain store location, but they have separate busi nesses, and only one can use the space at a time. To minimize the costs
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 4 (Covering material from 4.1 4.5 + ME1) 1. The Placerville General Hospital has a nursing staff of 225 nurses working in four shifts A (7am to 1 pm), B (1pm to 7pm), C (7pm to 1am), and D (1am to 7am). The number of nurses apportioned to each
School: Rutgers
% Math 250 Matlab Lab Assignment #2 rand('seed',2573) %Question 1 (a) A = rmat(3,5), rank(A(:,1:3) A = 7 5 3 5 8 8 8 9 4 9 5 8 0 8 5 ans = 3 b = rvect(3), R=rref([A b]) b = 2 6 9 R = 1.0000 0 0 0.4638 1.2319 0.9130 0 1.0000 0 0.7101 0.1449 1.69
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #4 Revised 5/16/12 LAB 4: General Solution to Ax = b In this lab you will use Matlab to study the following topics: The column space Col(A) of a matrix A The null space Null(A) of a matrix A. Particular solutions to an in
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #3 Revised 5/14/12 LAB 3: LU Decomposition and Determinants In this lab you will use Matlab to study the following topics: The LU decomposition of an invertible square matrix A. How to use the LU decomposition to solve the
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #2 1 Revised 9/30/12 LAB 2: Linear Equations and Matrix Algebra In this lab you will use Matlab to study the following topics: Solving a system of linear equations by using the reduced row echelon form of the augmented matrix
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #5 1 Revised 12/06/12 LAB 5: Eigenvalues and Eigenvectors In this lab you will use Matlab to study these topics: The geometric meaning of eigenvalues and eigenvectors of a matrix Determination of eigenvalues and eigenvectors
School: Rutgers
Math 250C Matlab Assignment #1 1 Revised 1/18/13 LAB 1: Matrix and Vector Computations in Matlab In this lab you will use Matlab to study the following topics: How to create matrices and vectors in Matlab. How to manipulate matrices in Matlab and creat
School: Rutgers
Course: Linear Algebra
Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax y Ay 0 z b b Az b 0 0 Contents Preface iv 1 . . . . . . . . 1 1 4 13 21 36 50 66 72 . . . . . . . 77 77 86 103 115 128 140 154 . . . . . . 159 159 171 180 195 211 221 2 3 Matrices
School: Rutgers
Course: MULTIVARIABLE CALCULUS
Calc III Study Guide Exam I 1. ReRead Notes 2. Do all of these problems 12.1: 5, 9, 11, 15, 21, 40, 47 12.2: 11, 13, 19, 25, 27, 31, 51 12.3: 1, 13, 21, 29, 31, 52, 57, 63 12.4: 1, 5, 13, 20, 25, 26, 43, 44 12.5: 1, 9, 11, 15, 25, 31, 53 13.1: 5, 13, 15,
School: Rutgers
Course: Calculus 1
Prof. Jose Sosa Math 135 Sections 84, 85 and 86 Fall 2013 email: jsosa@math.rutgers.edu Oce Hours: Mondays, Thursdays, 10:0010:45 am Heldrich SB (Douglass) Room 203 Thursdays, 1:503:10 pm Lucy Stone H (Livingston) Room B102C Classes: Tuesdays, Thursday
School: Rutgers
Course: Basic Calculus
21:640:119:07/Basic Calculus/Spring 2012 Class meetings: MW 1011:20, Smith B26 Instructor: John Randall Smith 305, (973)3533919, randall@rutgers.edu Office hours: M 910, WTh 11:301 Course web site: http:/pegasus.rutgers.edu/~randall/119/ and Rutgers Blac
School: Rutgers
Course: Math 103
Math 103: Topics in Math for the Liberal Arts, Section 11, Spring 2011 CourseOverviewSheet Prerequisite: Elementary Algebra at the level of Rutgers Math 025, or equivalent. Elementary algebra and other basic skills are helpful. Text: Excursions in Modern
School: Rutgers
SYLLABUS MULTIVARIABLE CALCULUS 251 SUMMER 2008 PREREQUISITE: Calc 152 or the equivalent. TEXT: Calculus with Early Transcendentals, Custom Edition for Rutgers University. Author: Jon Rogawski. Publisher: Freeman Custom Publishing. Note 1: You may
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 2 Solutions 1. ( Chapter 2, Problem 3) a) Denote the steady state by N . Then N N = N er(1 K ) The trivial N steady state that holds for the above equation is N = 0. To nd the nontrivial steady states we div
School: Rutgers
% Math 250 Matlab Lab Assignment #2 rand('seed',2573) %Question 1 (a) A = rmat(3,5), rank(A(:,1:3) A = 7 5 3 5 8 8 8 9 4 9 5 8 0 8 5 ans = 3 b = rvect(3), R=rref([A b]) b = 2 6 9 R = 1.0000 0 0 0.4638 1.2319 0.9130 0 1.0000 0 0.7101 0.1449 1.69
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #4 Revised 5/16/12 LAB 4: General Solution to Ax = b In this lab you will use Matlab to study the following topics: The column space Col(A) of a matrix A The null space Null(A) of a matrix A. Particular solutions to an in
School: Rutgers
640:423 Partial Dierential Equations, Autumn 2012 Department of Mathematics, Rutgers University Problem Set 0 Most of the following exercises are from Strauss [Str] and Rogawski [Rog]. For every exercise, be sure to justify your answer completely, stating
School: Rutgers
Course: High Frequency Finance
Lecture 1 Introduction Math 627 High Frequency Trading: Market Microstructure and Optimal Control Essential Information Doug Borden 6464164875 dborden@knight.com TA: Nader Rahman Books Hasbrouck, Empirical Market Microstructure Kissell & Glantz, Optimal
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #3 Revised 5/14/12 LAB 3: LU Decomposition and Determinants In this lab you will use Matlab to study the following topics: The LU decomposition of an invertible square matrix A. How to use the LU decomposition to solve the
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #2 1 Revised 9/30/12 LAB 2: Linear Equations and Matrix Algebra In this lab you will use Matlab to study the following topics: Solving a system of linear equations by using the reduced row echelon form of the augmented matrix
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #5 1 Revised 12/06/12 LAB 5: Eigenvalues and Eigenvectors In this lab you will use Matlab to study these topics: The geometric meaning of eigenvalues and eigenvectors of a matrix Determination of eigenvalues and eigenvectors
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 5 (Solutions) 1. MMB Chapter 5, Problem 13. We begin with the equations dN dt dC dt C N N 1+C C = N C + 2 1+C = 1 (a) Obvious. (b) If we let x = N + 1 2 then the equation reduces to dx = 1 2 x dt Using separ
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 3A (Covering material from 3.1 3.4) [Warmup problems in the book: #15, 17] 1. Martha and Nick share the rights to use a certain store location, but they have separate busi nesses, and only one can use the space at a time. To minimize the costs
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 4 (Covering material from 4.1 4.5 + ME1) 1. The Placerville General Hospital has a nursing staff of 225 nurses working in four shifts A (7am to 1 pm), B (1pm to 7pm), C (7pm to 1am), and D (1am to 7am). The number of nurses apportioned to each
School: Rutgers
Course: Calculus 2
1) Find the Volume of the Solid generated by revolving about yaxis, circle x^2+y^2=16, by line x=4, y=4. V=2pi integral(4,0) x. (4Square root of (x^2+16) dx< let U=x^2+16. 2) use shell method, about yaxis, Y=8X^2, y=x^2, x=0 8X^2=X^2, 82X^2 V= 2pi
School: Rutgers
Course: Precalc 2
1. Let 2 x 7 g(x) = and h(x) = 3 + 4x x2 a. Find (g o h)(x) (don't forget to simplify). b. Find the inverse of g. Label your answer clearly either as "the inverse of g" or with "g1(x) = . . 2. a. Find the domain of the function k defined by k (t) = (5 
School: Rutgers
Course: Precalc 2
Formulas and Identities Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that p 0 < q < or 0 < q < 90 . 2 Unit circle definition For this definition q is any angle. y ( x, y ) hypotenuse y opposite
School: Rutgers
Formula Sheet for Math 152, Exam 1 The solutions of ax2 + bx + c = 0 are x =  b b2  4ac /(2a). ea+b = ea eb , ln(ab) = (ln a) + (ln b) , ln(ab ) = b(ln a) , ln(1) = 0 , ln(e) = 1 d d du eln x = x , ln(ex ) = x , dx (ex ) = ex , dx (ln x) = 1/x ,
School: Rutgers
Course: Calculus
Econ 103  Review Sheet I Chapter 4: 1. Determine through calculation, which has a higher present value: An annual payment of $100 received over 3 years or an annual payment of $50 received 7 years. In both cases the discount rate is 7% (0.07). 2. To
School: Rutgers
Course: Basic Calculus
Basic Calculus/Exam #1/Spring 2012 NAME: Calculators may be used. For full credit, you must show your work. You do not need to simplify your answers. Answer all questions. Total points: 100. 1. (10 points) Let f (x) = x2  4x + 2, g(x) = (x2 + 1)2 . Find
School: Rutgers
PRECALCULUS Recitation 9a (EXAM 2 REVIEW) NONCALCULATOR PART: 1. Graph the function . State the domain, range, and the asymptote. 2. Graph the function . State the domain, range, and the asymptote. 3. Evaluate the following exactly: a. b. c. 4. A bacteri
School: Rutgers
Course: Crytography
Lecture 12  The PohligHellman attack and Chinese Remainder Theorem In the last lecture we saw how discrete logarithms could be efficiently solved if p1 was a power of 2. Today we generalize this to the case when p1 is smooth, meaning that it is a prod
School: Rutgers
Pre Calc 111 Review Sheet Intervals Notation (a,b) [a,b] [a,b) (a,b] (a,) [a,) (,b) (,b] (,) Set description {x a<x<b} {x a<=x<=b} {x a<=x<b} {x a<x<=b} {x a<x} {x a<=x} {x x<b} {x x<=b} All Real Numbers Laws of Exponents (A/b)n = (b/a)
School: Rutgers
Course: CALCULUS 2 MATH/PHYS
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School: Rutgers
Course: CALCULUS 135
1A [10) 1. Suppose = 5:2. Use the denition of derivative to nd .1: 3 3 . .3   K : hPU h. 1H0 h. . + 2) +171. + 2) . 3h = 11111 = 11111 iii>0 M3: + h + + 2) iii>0 M3: + h. + + 2] 3 3 :1. =_ 1113; (3: +11+ 2(.1:+ 2) (.7: + 2)? 43: at the oint where
School: Rutgers
Course: CALCULUS 135
(10) (9) (12) 1A 1. Suppose f(3:) : 23:2 3:1,". Use the denition of derivative to nd f(3t). f(:r: + h.) f(:) 2(3: + h.)2 3(5'? +31 (23:2 3:1?) f _ . _ . f (3) _ lilIih h. _ IiiIii: h. 23:2 + 4.1:; + 2.33.2 3h. 213':2 + 3:3: 2 hm hm it 4, 2F.2Z', =li
School: Rutgers
Course: Mathematics, Advanced Calculus I
Annuities Your Name: _ Topic 4. Annuities and Amortization Many contracts use a series of small, equal payments, at equal time intervals, to repay a large sum. For example, a series of fixed payments, monthly for 30 years, can pay off the $300,000 mortgag
School: Rutgers
Course: Mathematics, Advanced Calculus I
Simple Discount Your Name: _ The Simple Discount Formula is: DiscAmt = M d T where: the ending (future) value is M, such as $500 . the discount rate is d, such as 2% or 0.02 (per year) the length of time is T, such as 3 years the starting value is M minus
School: Rutgers
Course: Mathematics, Advanced Calculus I
Time Series Prepared by: _ Growth Factor = NewValue / OldValue Stock market DIA weekly price JanApr 2015 Jan 2 Jan 9 Jan 16 Jan 23 Jan 30 Feb 6 Feb 13 Feb 20 Feb 27 Mar 6 Mar 13 Mar 20 Mar 27 $ / share value 178 177 174 growth factor this / previous 0.9
School: Rutgers
Course: Mathematics, Advanced Calculus I
Arithmetric Series An Arithmetic Series has "n" terms. It starts with "a", adds a constant difference "d" for each term, and ends with "z". The first term is a. The second term is a + d . The third term is a + d(2) . The kth term is a + d(k1) for any k=
School: Rutgers
Course: Mathematics, Advanced Calculus I
Simple Interest Your Name: _ The Simple Interest Formula is: FV = P ( 1 + R T ) where: the starting value is P (Principal) or PV (Present Value), such as $100 . the interest rate is R, such as 1.4% or 0.014 (per year) the length of time is T, such as 3 ye
School: Rutgers
Course: Mathematics, Advanced Calculus I
Spreadsheets Your Name: _ For an annuity, the Future Value Factor is: s(n,i) = [(1+i)n 1] / i where i is the effective interest rate and the annuity is n payments of pmt dollars (at end of month or year). The Present Value Factor is: a(n,i) = s(n,i) / (1
School: Rutgers
Course: Mathematics, Advanced Calculus I
Geometric Series [There was a typographical error in HW9: Adding a constant "d" to find the next term is called an Arithmetic Series] A Geometric Series has "n" terms, starting with "a". Multiply by a constant ratio "r" to find the next term. The first te
School: Rutgers
Course: Mathematics, Advanced Calculus I
Income Statement Prepared by: _ Profit = Income  Expense Sam Client Income Statement Year ending Dec 31 actual 2014 estimated 2015 Income Salary Interest Income Dividends Capital Gain Other Income Comments 43,000 ? ? subtotal Expense Income Tax (20%) She
School: Rutgers
Course: Mathematics, Advanced Calculus I
Time Series Prepared by: _ Growth Factor = NewValue / OldValue Stock market DIA weekly price JanApr 2015 Jan 2 Jan 9 Jan 16 Jan 23 Jan 30 Feb 6 Feb 13 Feb 20 Feb 27 Mar 6 Mar 13 Mar 20 Mar 27 $ / share value 178 177 174 growth factor this / previous 0.9
School: Rutgers
Course: Mathematics, Advanced Calculus I
Net Worth Statement Prepared by: _ Net Worth = Assets  Liabilities Sam Client Net Worth Statement As of Dec 31 Assets Checking Account Savings Account Bonds Stocks Real Estate Car Other Assets subtotal Liabilities Home Mortgage Auto Loan Student Loan Oth
School: Rutgers
Course: Calc
f(x) = x2 12 10 8 6 4 2 0 0 2 4 6 8 10 12 f(x) = x2 We want to find the equation of the line 12 that is tangent to f(x) at (1,1) so that we 10 can describe the rate of change at (1,1). The slope of 8 the curve at (1,1) is 6 the slope of the tangent line a
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 3 2 3 2 3 2 3 2 3 2 = sin() ( + ) = sin() sin() + sin() = 3 2 sin() (3 2 + sin() = 3 2 sin() 3 2 sin() = 3 2 + sin() 0 + 2sin(0) = =0 12 + 0 Equation
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 Equation of the tangent: (y (2) = 0(x 0) y+2=0 y = 2 b) at (2,1) Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) Equ
School: Rutgers
Course: Intermediate Algebra
Homework Assignments Math 026 Intermediate Algebra Spring 2014 Chapter 5 Review Exercises P 314316 Due Date Monday 3/10 2, 6. 8, 10, 14, 16, 28, 32, 42, 50, 55, 56, 60, 66, 70, 73, 78, 80, 84, 85. Chapter 6 Review Exercises P 376379 Due Date Thursday 3/
School: Rutgers
Solutions to Dr. Z.s Math 421(1), Exam #1 1. (15 points) Using the denition nd the Laplace transform Lcfw_f (t) (alias F (s) of 1, if 0 t 2; 3, if t 2. f (t) = Sol.: = est 2 est +3 s 0 s Ans. to 1: 1 s = 2 est (3) est (1) + 2 0 0 2 est f (t) dt = Lcfw_f
School: Rutgers
Solutions to Dr. Z.s Math 421(2), Exam #1 1. (15 points) Use any method to compute Lcfw_f (t) if f (t) = (et + 1)(e2t + 1) + t3 (t + 1) . Sol. First use algebra to expand: f (t) = e3t + et + e2t + 1 + t4 + t3 . Now use the table to get Lcfw_f (t) = Lcfw_e
School: Rutgers
640:421:06 REVIEW PROBLEMS FOR EXAM 1 SPRING 2013 Note that no books, notes, or calculators may used during the exam. You will be given a table of the Laplace transform, based on Table III in our text. Some unneeded formulas will be omitted, and the formu
School: Rutgers
Course: Linear Algebra
Wednesday, September 3, 2014 6:16 PM New Section 3 Page 1 New Section 3 Page 2 New Section 3 Page 3 New Section 3 Page 4 New Section 3 Page 5 New Section 3 Page 6 New Section 3 Page 7 Monday, September 8, 2014 6:07 PM New Section 7 Page 8 New Section 7 Pa
School: Rutgers
Course: SET THEORY
Math 361Homework Set 7Solutions End of Part 1 Exercise 1. Let r R. Show that there is a unique pair n, s with n Z and s [0, 1) such that r =n+s Proof. Let Z(r) = (, r) Z. Then Z(r) is a nonempty subset of R which is bounded above by r. By an earlier resul
School: Rutgers
Course: SET THEORY
Part II Higher Set TheoryOrdinals, Cardinals, and the Cumulative Hierarchy 14 Cardinality When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to meanneither more nor less. (Lewis Carroll, Through the Looking Gl
School: Rutgers
Course: Linear Algebra
INTRODUCTION TO LINEAR ALGEBRA Third Edition MANUAL FOR INSTRUCTORS Gilbert Strang gs@math.mit.edu Massachusetts Institute of Technology http:/web.mit.edu/18.06/www http:/math.mit.edu/~gs http:/www.wellesleycambridge.com WellesleyCambridge Press Box 8120
School: Rutgers
Course: Linear Algebra
Text 1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 1 2 2 x1 7
School: Rutgers
Course: Linear Algebra
Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax y Ay 0 z b b Az b 0 0 Contents Preface iv 1 . . . . . . . . 1 1 4 13 21 36 50 66 72 . . . . . . . 77 77 86 103 115 128 140 154 . . . . . . 159 159 171 180 195 211 221 2 3 Matrices
School: Rutgers
Course: Linear Algebra
Assignment 4 Math 573, Numerical Analysis I, Fall 2014 Due : 5PM Tuesday, October 21 Justify your answer and provide the necessary explanations to get full credit. 1 Problem 1.(15 points.) Derive the NewtonCotes formula for 0 f (x) dx based on the nodes
School: Rutgers
Course: Linear Algebra
Math 550A 1 MATLAB Assignment #2 Revised 8/14/10 LAB 2: Orthogonal Projections, the Four Fundamental Subspaces, QR Factorization, and Inconsistent Linear Systems In this lab you will use Matlab to study the following topics: Geometric aspects of vectors:
School: Rutgers
Course: Calculus 1
5" ldti tus F y. a/at\/v I Math r. 135 (L2 pts.) For this problem, you do not need to simplify your answers. Find the derivative of /(r) if: (a) /(r) :2trScos r .# t' (A= ,o x4wx+2x'('s)*x)+ (b) /(") : ta,nr cfw_"+*' s.oLL ['(*) 4 tLt') = L + rc,)  t*t
School: Rutgers
Course: Calculus 1
Prof. Jose Sosa Math 135 Sections 84, 85 and 86 Fall 2013 email: jsosa@math.rutgers.edu Oce Hours: Mondays, Thursdays, 10:0010:45 am Heldrich SB (Douglass) Room 203 Thursdays, 1:503:10 pm Lucy Stone H (Livingston) Room B102C Classes: Tuesdays, Thursday
School: Rutgers
Course: Calculus II
5 o lrli o, s Math Second ExamA 135 1. (10 pts.) Find the equation of the normal (perpendicular to tangent) line to the curve scribed by 2r lny* .1_ .)? r,u, : de g 1 at the point (2,L). Any correct equation specifying this line is acceptable. L ()*V+
School: Rutgers
Course: CALC
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School: Rutgers
Course: Calculus
Econ 103  Review Sheet I Chapter 4: 1. Determine through calculation, which has a higher present value: An annual payment of $100 received over 3 years or an annual payment of $50 received 7 years. In both cases the discount rate is 7% (0.07). 2. To
School: Rutgers
PRECALCULUS Recitation 9a (EXAM 2 REVIEW) NONCALCULATOR PART: 1. Graph the function . State the domain, range, and the asymptote. 2. Graph the function . State the domain, range, and the asymptote. 3. Evaluate the following exactly: a. b. c. 4. A bacteri
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Pre Calc 111 Review Sheet Intervals Notation (a,b) [a,b] [a,b) (a,b] (a,) [a,) (,b) (,b] (,) Set description {x a<x<b} {x a<=x<=b} {x a<=x<b} {x a<x<=b} {x a<x} {x a<=x} {x x<b} {x x<=b} All Real Numbers Laws of Exponents (A/b)n = (b/a)
School: Rutgers
Course: CALCULUS 2 MATH/PHYS
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School: Rutgers
Course: Calc
f(x) = x2 12 10 8 6 4 2 0 0 2 4 6 8 10 12 f(x) = x2 We want to find the equation of the line 12 that is tangent to f(x) at (1,1) so that we 10 can describe the rate of change at (1,1). The slope of 8 the curve at (1,1) is 6 the slope of the tangent line a
School: Rutgers
Course: Linear Algebra
Wednesday, September 3, 2014 6:16 PM New Section 3 Page 1 New Section 3 Page 2 New Section 3 Page 3 New Section 3 Page 4 New Section 3 Page 5 New Section 3 Page 6 New Section 3 Page 7 Monday, September 8, 2014 6:07 PM New Section 7 Page 8 New Section 7 Pa
School: Rutgers
Course: SET THEORY
Math 361Homework Set 7Solutions End of Part 1 Exercise 1. Let r R. Show that there is a unique pair n, s with n Z and s [0, 1) such that r =n+s Proof. Let Z(r) = (, r) Z. Then Z(r) is a nonempty subset of R which is bounded above by r. By an earlier resul
School: Rutgers
Course: SET THEORY
Part II Higher Set TheoryOrdinals, Cardinals, and the Cumulative Hierarchy 14 Cardinality When I use a word, Humpty Dumpty said, in rather a scornful tone, it means just what I choose it to meanneither more nor less. (Lewis Carroll, Through the Looking Gl
School: Rutgers
Course: Real Analysis
A result for 8.6 in Rudin, Real Analysis II, Spring, 2011. (Rudin 8.6) (Polar coordinates in Rk ). Let Sk1 the unit sphere in R , i.e., the set of all u Rk whose distance from the origin 0 is 1. Show that every x Rk , except for x = 0, has a unique repres
School: Rutgers
Course: Real Analysis
Some notes on completions The completion of a metric space (X, d) is a complete metric space (Y, D) together with an injective isometry X Y so that the closure X = Y . Recall a map h : X Y is an isometry if for all x, y X , d(x, y ) = D(h(x), h(y ). We wi
School: Rutgers
Course: Real Analysis
Mollifiers and Smooth Functions We say a function f from R C is C (or simply smooth ) if all its derivatives to every order exist at every point of R. For f : Rk C, we say f is C if all partial derivatives to every order exist and are continuous. Proposit
School: Rutgers
Course: Real Analysis
Outline of Material for Qualifying Test, Real Analysis, 2011 Sections of Rudin and the notes (with exceptions noted below). (1) (2) (3) (4) (5) Rudin chapters 1,2,3,4,6,8 Notes on molliers notes of completions of metric spaces course notes, chapters 1,2,4
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #13.5 (2nd ed.) [Motion in ThreeSpace] By Doron Zeilberger Problem Type 13.5a: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = x(t) i + y (t) j + z (t) k . Example Problem 13.5a: Fi
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #13.3 (2nd ed.) [Arc Length and Speed] By Doron Zeilberger Problem Type 13.3a: Find the length of the curve r(t) = x(t)i + y (t)j + z (t)k , t0 t t1 . Example Problem 13.3a: Find the length of the curve r(t) = t2 i + 2t j + ln t k ,
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #13.4 (2nd ed.) [Curvature] By Doron Zeilberger Problem Type 13.4a: Find the curvature for r(t) = x(t) i + y (t) j + z (t) k . Example Problem 13.4a: Find the curvature for r(t) = t i + 2t j + t2 k . Steps Example 1. Compute r (t) a
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #13.2 (2nd ed.) [Calculus of VectorValued Functions] By Doron Zeilberger Problem Type 13.2a: Find a parametric equation for the tangent line to the curve with the given parametric equation at the specied point x = f1 (t) , y = f2 (
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #13.1 (2nd ed.) [VectorValued Functions] By Doron Zeilberger Problem Type 13.1a: Find a vector equation and a parametric equation for the line segment joining P (p1 , p2 , p3 ) and Q(q1 , q2 , q3 ) Example Problem 13.1a: Find a vec
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #12.5 (2nd ed.) [Planes in Three Space] By Doron Zeilberger Problem Type 12.5a: Find an equation of the plane that passes through three given points Example Problem 12.5a: Find an equation of the plane that passes through the points
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout #12.4 (2nd ed.) [The Cross Product] By Doron Zeilberger Problem Type 12.4a: Find the cross product a b and verify that it is orthogonal to both a and b. a = a1 , a2 , a3 , b = b1 , b 2 , b 3 . Example Problem 12.4a: Find the cross p
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout (2nd ed.) #12.2 [Vectors in three dimensions] By Doron Zeilberger Problem Type 12.2a: Show that the triangle with vertices P = (p1 , p2 , p3 ), Q = (q1 , q2 , q3 ), R = (r1 , r2 , r3 ) is an equilateral triangle. Example Problem 12.
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout (2nd ed.) #12.3 [Dot Product and the Angle Between Two Vectors] By Doron Zeilberger Problem Type 12.3a : Use vectors to decide whether the triangle with P (p1 , p2 , p3 ), Q(q1 , q2 , q3 ), R(r1 , r2 , r3 ), is rightangled. Example
School: Rutgers
Course: Calculus 13
Dr. Zs Math251 Handout (2nd ed.) #12.1 [Vectors in the Plane] By Doron Zeilberger Problem Type 12.1a: A person walks due west (or east) on the deck of a ship at a mi/h. This ship is moving north (or south, or whatever) at b mi/h. Find the speed and direct
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Chapters 1,2,4 Review Sheet Note: This only represents a sampling of questions and does not represent all possible questions. It is strongly advised that you study all examples in notes, odd numbers from the textbook, and homework as well. CHAPTER 1 Part
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Chapters 1,2,4 Review  ANSWERS CHAPTER 1 1. 2. 27 + 19 + 9 + 15 + 2 = 72 voters. There were 72 voters in the election. Under the extended Plurality with Elimination Method, C ranked in 1 st place, B ranked in 2nd place, C ranked in 3rd place, and D ranke
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
CHAPTERS 57 REVIEW ANSWER KEY Chapter 5 1. a) Graph 1 Euler Path (Two odd vertices C and D) b) c) Graph 2 Neither (Four odd vertices B,D,E,G) Graph 3 Euler Circuit (No odd vertices) 2. 3a. 3b. (2 x 4) + (2 x 3) + (2 x 2) = 18 To avoid edges we double cou
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Chapters 57 Review Chapter 5 1. Answer the questions regarding the graphs below. a) State whether the graph contains an Euler circuit, Euler path, or neither. b) Give an optimal eulerization of Graph 1. c) Give an optimal semieurlerzation of Graph 2. 2.
School: Rutgers
Course: CALCULUS 2 MATH/PHYS
640:152 Calculus II Review Exercises, Spring 2012 Department of Mathematics, Rutgers University This course covers selected sections from Chapters 612 in your textbook. Please note that the exercises listed are intended to assist you in reviewing the mai
School: Rutgers
Course: Calculus 1
Math 135, Section C7 Review problems for Exam #2  July 2, 2010 Exam #2 is on Monday, July 12, from 6:00 to 7:20. A review session will be held on: Saturday, July 10, 2:00  4:30 PM in HILL525 (BUSCH) #1 Find dy dx if 2x + exy = 0. #2 Find an equation of
School: Rutgers
Course: Calculus 1
CHAPTER 4 Review of Trigonometry One of the prerequisites for calculus is trigonometry. You are reminded of this fact in Section 1.1 of your textbook. In this chapter, we provide a brief summary and review of ideas from trigonometry that are needed as you
School: Rutgers
Course: Calculus 1
John Kerrigan Final Exam Practice These problems were taken directly from the nal exam given to the students in Math 135 in the Fall of 2007. This is not a graded assignment and is only here for your benet in checking the answers that you get while doing
School: Rutgers
Course: Differential Equations For Engineering And Physics
School: Rutgers
Course: Differential Equations For Engineering And Physics
= u1(t) = u(t) 2
School: Rutgers
Course: Differential Equations For Engineering And Physics
e r initial any partial IC
School: Rutgers
Course: Differential Equations For Engineering And Physics
h h We move along the directional or the vector field. s
School: Rutgers
Course: Differential Equations For Engineering And Physics
School: Rutgers
Course: Differential Equations For Engineering And Physics
School: Rutgers
Course: Differential Equations For Engineering And Physics
School: Rutgers
Course: Differential Equations For Engineering And Physics
School: Rutgers
Course: Differential Equations For Engineering And Physics
(The integral curve is unique, but corresponds to many solutions)
School: Rutgers
Course: Differential Equations For Engineering And Physics
(the analytical formula) (this is a very important result for PDE)
School: Rutgers
Course: High Frequency Finance
Lecture 1 Introduction Math 627 High Frequency Trading: Market Microstructure and Optimal Control Essential Information Doug Borden 6464164875 dborden@knight.com TA: Nader Rahman Books Hasbrouck, Empirical Market Microstructure Kissell & Glantz, Optimal
School: Rutgers
Course: Crytography
Lecture 12  The PohligHellman attack and Chinese Remainder Theorem In the last lecture we saw how discrete logarithms could be efficiently solved if p1 was a power of 2. Today we generalize this to the case when p1 is smooth, meaning that it is a prod
School: Rutgers
Course: Linear Algebra
Text 1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12), 1922, and 25. For brevity, the symbols R1, R2, stand for row 1 (or equation 1), row 2 (or equation 2), and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 1 2 2 x1 7
School: Rutgers
Course: Numerical Analysis
74 MATH 573 LECTURE NOTES 13.8. Predictorcorrector methods. We consider the Adams methods, obtained from the formula xn+1 xn+1 f (x, y (x) dx y (x) dx = y (xn+1 y (xn ) = xn xn by replacing f by an interpolating polynomial. If we use the points xn , xn1
School: Rutgers
Course: Numerical Analysis
MATH 573 LECTURE NOTES 71 13.7. Strong, weak, absolute and relative stability. To formalize the stability problem discussed above, we now dene several concepts of stability that seek to dierentiate between methods which exhibit numerical instability and t
School: Rutgers
Course: Numerical Analysis
68 MATH 573 LECTURE NOTES 13.6. Stability of linear multistep methods. Denition: 1st and 2nd characteristic polynomial of a multistep method: p (z ) = z p+1 p ai z pi , bi z pi . (z ) = i=0 i=1 The linear multistep method is consistent if (1) = 0 and (1)
School: Rutgers
Course: Numerical Analysis
0.1. Linear multistep methods. The general linear (p + 1) step method has the form p yn+1 = p ai yni + h bi fni , i=1 i=0 where fni = f (xni , yni ) and the ai and bi are constants. Remarks: Any of the ai s and bi s may be zero, but we assume either ap or
School: Rutgers
Course: Numerical Analysis
MATH 573 LECTURE NOTES 57 13.4. Estimation of local error. In practice, we not only want to produce an approximation to the solution at each step of the algorithm, we also want to produce an estimate of the local error. If this error is too big, we will r
School: Rutgers
Course: Numerical Analysis
1. The Finite Fourier Transform We consider the approximation of a periodic function f with period 2 , i.e., f (t + 2 ) = f (t). Note that a function with a more general period can be reduced to this case in the following simple way. If g (t + ) = g (t),
School: Rutgers
Course: Numerical Analysis
1. Cubic spline approximation 1.1. Cubic spline interpolation. We consider the problem of nding a C 2 piecewise cubic function S (x) that satises S (xi ) = f (xi ), i = 0, . . . , n plus two additional conditions. These are usually taken to be either S (x
School: Rutgers
Course: High Frequency Finance
Lecture 9 The Flash Crash Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: Week 14: Introduction Simple Mi
School: Rutgers
Course: High Frequency Finance
Lecture 10 Regulation and U.S Equity Market Structure Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: Wee
School: Rutgers
Course: High Frequency Finance
Lecture 7 Calculus of Variations and Stochastic Control Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: I
School: Rutgers
Course: High Frequency Finance
Lecture 6 Execution Strategies Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: Introduction Simple Micros
School: Rutgers
Course: High Frequency Finance
Lecture 6 Execution Strategies Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: Introduction Simple Micros
School: Rutgers
Course: High Frequency Finance
Lecture 5 HFT in Practice Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week 13: Introduction Simple Microstruct
School: Rutgers
Course: High Frequency Finance
Lecture 4 Predictive Modeling Predictive Modeling Forecasting prices can lead to protable trading strategies Variety of techniques can be used over different horizons Focus on intraday data and modeling Ultra high frequency: simpler, mechanical models Lon
School: Rutgers
Course: High Frequency Finance
Lecture 3 Market Microstructure Models II Math 627 High Frequency Trading: Market Microstructure and Optimal Control Course Outline (subject to change) Week 1: Week 2: Week 3: Week 4: Week 5: Week 6: Week 7: Week 8: Week 9: Week 10: Week 11: Week 12: Week
School: Rutgers
Course: High Frequency Finance
Lecture 2 Microstructure Models Contents What/why microstructure? Auctions Roll model Sequential trade models Strategic trade models Market Microstructure Study of how trading actually occurs Many economic and nancial models assume that price is kn
School: Rutgers
Course: Crytography
Recap of the first day' s lecture on Substitution Ciphers At its core, cryptography is about making encryption systems that can keep secrets away from smart and wise attackers who try to crack them. A famous NSA maxim states that attacks never get worse,
School: Rutgers
Course: Crytography
Recap of the lecture on the Civil War Vigenere discovery Recently a Civil War encrypted message was discovered (see http:/www.aolnews.com/2010/12/25/civilwarmessageinabottleopeneddecoded/). We will now decode it, using just a little knowledge of the
School: Rutgers
Course: Crytography
Lecture 4  Vigenere Cipher and the Kasiski Attack Let us review the Vigenere encryption method that we discussed in the last class. Recall that it is a polyalphabetic substitution cipher, in that it does not necessarily always encrypt the same letter the
School: Rutgers
Course: Crytography
Lecture 5  Vigenere Cipher, Index of Coincidence, and the Friedman Attack In the last lecture we discussed the Kasiski attack, which finds the key length of a Vigenere text based on the pattern of repeated trigraphs (that is, 3 letter combinations). Toda
School: Rutgers
Course: Crytography
Lecture 14  The Miller  Rabin primality test Recall last time that we spoke about Fermat ' s primality test, which rules out primes rather than showing numbers are primes. If n is a prime, then Fermat ' s little theorem asserts that an is congruent to a
School: Rutgers
Course: Crytography
Lecture 17  Pollards factoring algorithms This lecture actually 2 in class concern two clever factoring algorithms introduced by J. Pollard. The first, Pollard ' s algorithm for integer factorization as distinct from his algorithm for discrete logarithms
School: Rutgers
Course: COMPT&GRAPH APPSTAT
When to use regression analysis Goodnessoffit: how well does the model fit the data? Es#ma#on example Es#ma#on example This example concerning the number of species of tortoise on the various Galapagos Islands. There are 30 case
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Lecture One Before you start Statistics starts with a problem, continues with the collection of data, proceeds with the data analysis and finishes with conclusions. It is a common mistake of inexperienced Statisticians to plunge into a complex analysis wi
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Parameter Estimation Here is a data set concerning the number of species of tortoise on the various Galapagos Islands. There are 30 cases (Islands) and 7 variables in the data set. We start by reading the data into R. > gala < read.table("gala.data") # r
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Diagnostics 2 Residual Plots We still use the saving data as an example again: > savings < read.table("saving.txt") # read the data into R > g < lm(sav ~ p15 + p75 + inc + gro, data=savings) # fit the model with sav as the response and the rest variable
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Diagnostics 1 Residual We'll use the saving data (with country name) as an example here. ? First fit the model and make an index plot of the residuals: > saving.x < read.table("saving.txt",header=T) # read the data into R > p15 < saving.x[,1]; > p75 <
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Identifiability? Now, consider the saving data we analyzed in previous lab: > saving.x < read.table("saving.txt",header=T) # read the data into R > p15 < saving.x[,1]; > p75 < saving.x[,2]; > inc < saving.x[,3]; > gro < saving.x[,4]; > sav < saving.
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Generalized least square ? We'll use a builtin R dataset called Longley's regression data where the response is number of people employed, yearly from 1947 to 1962, and the predictors are o GNP implicit price deflator (1954=100), o GNP, o unemployed, o a
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Confidence Interval and Region Now, consider the savings data we analyzed in previous lab: > saving.x < read.table("saving.x", header=T) # read the data into R > p15 < saving.x[,1]; p75 < saving.x[,2]; inc < saving.x[,3]; gro < saving.x[,4]; sav < s
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Hypothesis Test We will illustrate a dataset called "saving.txt". Savings Rates for Countries SUMMARY: The saving data set is originally from unpublished data of Arlie Sterling. It is a matrix with 50 rows representing countries and 5 columns representing
School: Rutgers
Course: COMPT&GRAPH APPSTAT
Introduction to R > 2+3 # R can be used as a simple calculator > exp(1) # All the usual calculator functions are available > pnorm(1.645) # the normal probability function The assignment operator is "<" > x < 2 # assign the value 2 to x > y < 3 # y is
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IN PRAISE OF LECTURES T. W. KORNER The Ibis was a sacred bird to the Egyptians and worshippers acquired merit by burying them with due ceremony. Unfortunately the number of worshippers greatly exceeded the number of birds dying of natural causes so the t
School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
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School: Rutgers
vb Qt OQ  r 1 L&i t5 & ()j) az 1 Cc)?K  3j i4 i Tccx: x : ok Jr: 1 (2 )IL F L (c H jr 4 + 1K ( &4 Ld GALj tc A rrL W5 L _ (t  A+  y c  y C  2 Ih L v 4L f III \ < aU) / L () 7 y c( Cw  2   C  * L\   IA V\ I N 4 N I ci / WOc C I A ) 4 1 o(k y
School: Rutgers
22 6. Piecewise polynomial approximation in two dimensions We consider the approximation of a function u(x, y), where u is dened on a convex polygon . For each 0 < h < 1, we let T be a triangulation of with the following properties: i: = i Ti ,
School: Rutgers
Course: Precalc 2
1. Let 2 x 7 g(x) = and h(x) = 3 + 4x x2 a. Find (g o h)(x) (don't forget to simplify). b. Find the inverse of g. Label your answer clearly either as "the inverse of g" or with "g1(x) = . . 2. a. Find the domain of the function k defined by k (t) = (5 
School: Rutgers
Course: Basic Calculus
Basic Calculus/Exam #1/Spring 2012 NAME: Calculators may be used. For full credit, you must show your work. You do not need to simplify your answers. Answer all questions. Total points: 100. 1. (10 points) Let f (x) = x2  4x + 2, g(x) = (x2 + 1)2 . Find
School: Rutgers
Course: CALCULUS 135
1A [10) 1. Suppose = 5:2. Use the denition of derivative to nd .1: 3 3 . .3   K : hPU h. 1H0 h. . + 2) +171. + 2) . 3h = 11111 = 11111 iii>0 M3: + h + + 2) iii>0 M3: + h. + + 2] 3 3 :1. =_ 1113; (3: +11+ 2(.1:+ 2) (.7: + 2)? 43: at the oint where
School: Rutgers
Course: CALCULUS 135
(10) (9) (12) 1A 1. Suppose f(3:) : 23:2 3:1,". Use the denition of derivative to nd f(3t). f(:r: + h.) f(:) 2(3: + h.)2 3(5'? +31 (23:2 3:1?) f _ . _ . f (3) _ lilIih h. _ IiiIii: h. 23:2 + 4.1:; + 2.33.2 3h. 213':2 + 3:3: 2 hm hm it 4, 2F.2Z', =li
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 3 2 3 2 3 2 3 2 3 2 = sin() ( + ) = sin() sin() + sin() = 3 2 sin() (3 2 + sin() = 3 2 sin() 3 2 sin() = 3 2 + sin() 0 + 2sin(0) = =0 12 + 0 Equation
School: Rutgers
Course: Calc
Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) 1. a) x3 y3 = cos (xy) + 7 Equation of the tangent: (y (2) = 0(x 0) y+2=0 y = 2 b) at (2,1) Answers to Midterm Exam 2 Review Problems prepared by S. Sofer (W. Miervaldis) Equ
School: Rutgers
Solutions to Dr. Z.s Math 421(1), Exam #1 1. (15 points) Using the denition nd the Laplace transform Lcfw_f (t) (alias F (s) of 1, if 0 t 2; 3, if t 2. f (t) = Sol.: = est 2 est +3 s 0 s Ans. to 1: 1 s = 2 est (3) est (1) + 2 0 0 2 est f (t) dt = Lcfw_f
School: Rutgers
Solutions to Dr. Z.s Math 421(2), Exam #1 1. (15 points) Use any method to compute Lcfw_f (t) if f (t) = (et + 1)(e2t + 1) + t3 (t + 1) . Sol. First use algebra to expand: f (t) = e3t + et + e2t + 1 + t4 + t3 . Now use the table to get Lcfw_f (t) = Lcfw_e
School: Rutgers
640:421:06 REVIEW PROBLEMS FOR EXAM 1 SPRING 2013 Note that no books, notes, or calculators may used during the exam. You will be given a table of the Laplace transform, based on Table III in our text. Some unneeded formulas will be omitted, and the formu
School: Rutgers
Course: Calculus 1
5" ldti tus F y. a/at\/v I Math r. 135 (L2 pts.) For this problem, you do not need to simplify your answers. Find the derivative of /(r) if: (a) /(r) :2trScos r .# t' (A= ,o x4wx+2x'('s)*x)+ (b) /(") : ta,nr cfw_"+*' s.oLL ['(*) 4 tLt') = L + rc,)  t*t
School: Rutgers
Course: Calculus II
5 o lrli o, s Math Second ExamA 135 1. (10 pts.) Find the equation of the normal (perpendicular to tangent) line to the curve scribed by 2r lny* .1_ .)? r,u, : de g 1 at the point (2,L). Any correct equation specifying this line is acceptable. L ()*V+
School: Rutgers
Course: CALC
This is eTeX, Version 3.1415922.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 3 DEC 2008 08:42 entering extended mode *report1.tex (report1.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, ge rma
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document Classroom Observation Report I Course: Mathematics 135  Calculus for Liberal Arts Students I (01:640:135) Instructo
School: Rutgers
Course: CALC
#;# TeX output 2008.12.03:0842#y#? #M#src:8report1.tex#K`y# # #cmr10ClassroG#om#SObservqationReport#SI#SCourse:#nM athematics135Calculusfor #>#LibG#eral#UUArtsStudentsI(01:640:135)Instructor'sname: #qBrentY*oungM#src:12report1.texDescription#of#th ecours
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 9 \authorcfw_11/25/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 9 \authorcfw_11/25/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 24 NOV 2008 10:21 entering extended mode *quiz9.tex (quiz9.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
#;# TeX output 2008.11.24:1021#y#? #`#src:15quiz9.tex#Dt#G#G#cmr17Math#7t135Quiz9 # #X Q# # #cmr1211/25/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz9.texPlease#shorwallyourworkn otjusttheanswer.#9>#src:22quiz9.tex(T#Votal#10pSoin rts)F
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 7 \authorcfw_11/13/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 8 \authorcfw_11/20/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
#;# TeX output 2008.11.19:1753#y#? #`#src:15quiz8.tex#Dt#G#G#cmr17Math#7t135Quiz8 # #X Q# # #cmr1211/20/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz8.texPlease#shorwallyourworkn otjusttheanswer.#9>#src:22quiz8.tex(T#Votal#10pSoin rts)F
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 19 NOV 2008 17:53 entering extended mode *quiz8.tex (quiz8.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 7 \authorcfw_11/13/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 7 \authorcfw_11/13/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 12 NOV 2008 17:29 entering extended mode *quiz7.tex (quiz7.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
#;# TeX output 2008.11.12:1729#y#? #`#src:15quiz7.tex#Dt#G#G#cmr17Math#7t135Quiz7 # #X Q# # #cmr1211/13/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz7.texPlease#shorwallyourworkn otjusttheanswer.#9>#src:22quiz7.tex(T#Votal#^10#]pS oinrt
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 6 \authorcfw_11/6/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[7
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 6 \authorcfw_11/6/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[7
School: Rutgers
Course: CALC
#;# TeX output 2008.11.05:2211#y#? #`#src:15quiz6.tex#Dt#G#G#cmr17Math#7t135Quiz6 # #X Q# # #cmr1211/6/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz6.texT#Votal#10pSoinrts.#8P leaseshowallyourworknotjusttheanswer.#9>#src:23quiz 6.texCon
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 5 NOV 2008 22:12 entering extended mode *quiz6.tex (quiz6.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, ge
School: Rutgers
Course: CALC
#;# TeX output 2008.10.30:1810#y#? #`#src:15quiz5.tex#Dt#G#G#cmr17Math#7t135Quiz5 # #X Q# # #cmr1210/30/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz5.texPlease#shorwallyourworkn otjusttheanswer.#9>#src:22quiz5.tex(T#Votal#O10pSoin rts)
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 5 \authorcfw_10/30/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 30 OCT 2008 18:11 entering extended mode *quiz5.tex (quiz5.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 4 \authorcfw_10/23/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 4 \authorcfw_10/23/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 22 OCT 2008 15:28 entering extended mode *quiz4.tex (quiz4.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
#;# TeX output 2008.10.22:1528#y#? #`#src:15quiz4.tex#Dt#G#G#cmr17Math#7t135Quiz4 # #X Q# # #cmr1210/23/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz4.texPlease#shorwallyourworkn otjusttheanswer.#9>#src:22quiz4.tex(T#Votal#10pSoin rts)C
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 2 \authorcfw_10/2/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[7
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 3 \authorcfw_10/2/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[7
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 2 \authorcfw_09/25/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 2 \authorcfw_09/25/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 1 OCT 2008 15:31 entering extended mode *quiz3.tex (quiz3.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, ge
School: Rutgers
Course: CALC
#;# TeX output 2008.10.01:1530#y#? #`#src:15quiz3.tex#Dt#G#G#cmr17Math#7t135Quiz3 # #X Q# # #cmr1210/2/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz3.texPlease#shorw#allyourwo rks#notjusttheanswer.#I+Partial#creditswill#>#bS e#givrenacc
School: Rutgers
Course: CALC
This is eTeX, Version 3.1415922.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 10 FEB 2009 13:33 entering extended mode *quiz2.tex (quiz2.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, ge rman,
School: Rutgers
Course: CALC
#;# TeX output 2009.02.10:1333#y#? #`#src:15quiz2.tex#Dt#G#G#cmr17Math#7t135Quiz2 # #X Q# # #cmr1209/25/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz2.texPlease#shorw#allyourwo rks#notjusttheanswer.#I+Partial#creditswill#>#bS e#givrenac
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 1 \authorcfw_09/18/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
\documentclasscfw_article \usepackagecfw_amsfonts \usepackagecfw_amsmath \usepackagecfw_amssymb \usepackagecfw_mathrsfs \begincfw_document \large \titlecfw_Math 135 Quiz 1 \authorcfw_09/18/2008 \datecfw_\makebox[3.4em][l]cfw_Section\underlinecfw_\makebox[
School: Rutgers
Course: CALC
This is pdfeTeX, Version 3.1415921.21a2.2 (MiKTeX 2.4) (preloaded format=latex 2005.12.13) 16 SEP 2008 22:28 entering extended mode *quiz1.tex (quiz1.tex LaTeX2e <2003/12/01> Babel <v3.8g> and hyphenation patterns for english, dumylang, nohyphenation, g
School: Rutgers
Course: CALC
#;# TeX output 2008.09.16:2228#y#? #`#src:15quiz1.tex#Dt#G#G#cmr17Math#7t135Quiz1 # #X Q# # #cmr1209/18/2008 #O4Sectionw'#?#z#R? #R5Name(prinrt)#K# ? #z#u)>#src:17quiz1.texPlease#shorw#allyourwo rks#notjusttheanswer.#I+Partial#creditswill#>#bS e#givrenac
School: Rutgers
Course: CALC
Math 135 Quiz 9 11/25/2008 Section Name(print) Please show all your work not just the answer. (Total 10 points) Find the following indenite integral (1 + x)(1 1 1 ) dx. x2
School: Rutgers
Course: CALC
Math 135 Quiz 8 11/20/2008 Section Name(print) Please show all your work not just the answer. (Total 10 points) Find the following indenite integral 3 1 (u 2 u 2 + u10 )du. 1
School: Rutgers
Course: CALC
Math 135 Quiz 7 11/13/2008 Section Name(print) Please show all your work not just the answer. (Total 10 points) Find all the vertical and horizontal asymptotes of the function f (x) = x24 . 9 1
School: Rutgers
Course: CALC
Math 135 Quiz 6 11/6/2008 Section Name(print) Total 10 points. Please show all your work not just the answer. Consider the function f (x) = x3 + 3x2 + 2. (a) Find the critical points of the function. (b) Find where the function is decreasing and increasin
School: Rutgers
Course: CALC
Math 135 Quiz 5 10/30/2008 Section Name(print) Please show all your work not just the answer. (Total 10 points) A farmer like to use 120 ft of fence to enclose a maximal area rectangle pen along a river. Find the area of the pen. 1
School: Rutgers
Course: CALC
Math 135 Quiz 4 10/23/2008 Section Name(print) Please show all your work not just the answer. (Total 10 points) Consider the following function f (x), x2 + A if x > 3 B if x = 3 f (x) = 5x 2 if x < 3, (a) (6 points) Find the value of A and B such that th
School: Rutgers
Course: CALC
Math 135 Quiz 3 10/2/2008 Section Name(print) Please show all your works not just the answer. Partial credits will be given accordingly. (10 points) Find constants a and b such that f (2) + 3 = f (0) and f is continuous at x = 1, where f (x) is given by i
School: Rutgers
Course: CALC
Math 135 Quiz 2 09/25/2008 Section Name(print) Please show all your works not just the answer. Partial credits will be given accordingly. (10 points) Find the following limit. x2 cos 2x lim . x0 1 cos x 1
School: Rutgers
Course: CALC
Math 135 Quiz 1 09/18/2008 Section Name(print) Please show all your works not just the answer. Partial credits will be given accordingly. (10 points) Find the equation of the line which is passing through the midpoint of the line segment connecting (3, 7)
School: Rutgers
Course: Elementary Differential Equations II
Happy and Joyous (and Joyous and Happy) Practice Midterm Answers Math 320, Spring 2007 1. 23 27 35 14 15 29 +=+= + = . 57 57 75 35 35 35 23 6 = . 57 35 2 5 3 7 = 14 27 = . 53 15 7 18 5 18 = 7 18 7 =. 18 5 5 2 3 + 4 5 2 + 6 3 = 2 3 + 4 10 + 18 = 11 Note: A
School: Rutgers
Course: Elementary Differential Equations II
Happy and Joyous (and Joyous and Happy) Practice Midterm Answers Math 320, Spring 2007 1. State the quadratic formula and state when it applies! If ax2 + bx + c = 0, and a = 0, then b b2 4ac . x= 2a A few comments are in order. (You dont need to write the
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 2 Solutions 1. ( Chapter 2, Problem 3) a) Denote the steady state by N . Then N N = N er(1 K ) The trivial N steady state that holds for the above equation is N = 0. To nd the nontrivial steady states we div
School: Rutgers
640:423 Partial Dierential Equations, Autumn 2012 Department of Mathematics, Rutgers University Problem Set 0 Most of the following exercises are from Strauss [Str] and Rogawski [Rog]. For every exercise, be sure to justify your answer completely, stating
School: Rutgers
Course: Dynamic Models In Biology
Math 640:336 Dynamic Models in Biology Homework 5 (Solutions) 1. MMB Chapter 5, Problem 13. We begin with the equations dN dt dC dt C N N 1+C C = N C + 2 1+C = 1 (a) Obvious. (b) If we let x = N + 1 2 then the equation reduces to dx = 1 2 x dt Using separ
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 3A (Covering material from 3.1 3.4) [Warmup problems in the book: #15, 17] 1. Martha and Nick share the rights to use a certain store location, but they have separate busi nesses, and only one can use the space at a time. To minimize the costs
School: Rutgers
Course: Topics In Math For The Liberal Arts
Assignment 4 (Covering material from 4.1 4.5 + ME1) 1. The Placerville General Hospital has a nursing staff of 225 nurses working in four shifts A (7am to 1 pm), B (1pm to 7pm), C (7pm to 1am), and D (1am to 7am). The number of nurses apportioned to each
School: Rutgers
Course: Intermediate Algebra
Homework Assignments Math 026 Intermediate Algebra Spring 2014 Chapter 5 Review Exercises P 314316 Due Date Monday 3/10 2, 6. 8, 10, 14, 16, 28, 32, 42, 50, 55, 56, 60, 66, 70, 73, 78, 80, 84, 85. Chapter 6 Review Exercises P 376379 Due Date Thursday 3/
School: Rutgers
Course: Linear Algebra
INTRODUCTION TO LINEAR ALGEBRA Third Edition MANUAL FOR INSTRUCTORS Gilbert Strang gs@math.mit.edu Massachusetts Institute of Technology http:/web.mit.edu/18.06/www http:/math.mit.edu/~gs http:/www.wellesleycambridge.com WellesleyCambridge Press Box 8120
School: Rutgers
Course: Linear Algebra
Assignment 4 Math 573, Numerical Analysis I, Fall 2014 Due : 5PM Tuesday, October 21 Justify your answer and provide the necessary explanations to get full credit. 1 Problem 1.(15 points.) Derive the NewtonCotes formula for 0 f (x) dx based on the nodes
School: Rutgers
Course: Linear Algebra
Math 550A 1 MATLAB Assignment #2 Revised 8/14/10 LAB 2: Orthogonal Projections, the Four Fundamental Subspaces, QR Factorization, and Inconsistent Linear Systems In this lab you will use Matlab to study the following topics: Geometric aspects of vectors:
School: Rutgers
Course: Honors Calc 2
HOMEWORK #9 DUE FRIDAY APRIL 16TH (1) Determine whether the following series converges and whether it converges absolutely. n (a) (1!i) n=1 n (b) (1/3 + 2/3i)n n=1 (2) Use the ratio test to nd the radius of convergence of the following power series. Justi
School: Rutgers
Course: Honors Calc 2
HOMEWORK #4 DUE WEDNESDAY FEBRUARY 3RD (1) Give example of the following types of sequences. (a) An unbounded sequence that has a convergent subsequence. (b) A bounded sequence that has two dierent convergent subsequences which converge to distinct values
School: Rutgers
Course: Honors Calc 2
HOMEWORK #6 DUE MONDAY MARCH 8TH (1) Write down matrix representations of the following linear transformations. Also explain as well as you can what this linear transformation does geometrically. Fix an orthonormal basis u, v for R2 and an orthonormal bas
School: Rutgers
Course: Honors Calc 2
HOMEWORK #7 DUE FRIDAY MARCH 19TH (1) Fix u, v R2 to be a basis. Find the eigvalues and describe the eigenvectors of the following linear transformations. (a) The map T : R2 R2 dened in the following way. T (u) = v and T (v) = 2v. 10 (b) The map T : R2 R2
School: Rutgers
Course: Honors Calc 2
HOMEWORK #8 DUE FRIDAY MARCH 26TH (1) Are the following matrices diagonalizable? If so, nd a diagonal matrix similar to them. If not, justify why they arent diagonalizable. 13 (a) 02 13 (b) 01 12 (c) (Hint, look at the solutions to an old worksheet) 34 (2
School: Rutgers
Course: Honors Calc 2
HOMEWORK #3 MATH 1861 WINTER 2010 DUE WEDNESDAY JANUARY 27TH (1) Suppose that f exists. (a) Show that f (a + h) + f (a h) 2f (a) h0 h2 Hint: Use the Taylor polynomial P2,a (x) with x = a + h and with x = a h. (b) Let x2 , x0 f (x) = x2 , x < 0 f (a) = lim
School: Rutgers
Course: Honors Calc 2
SYLLABUS Math 186 Section 1 Winter 2010 Instructor: Karl Schwede Class web page: http:/wwwpersonal.umich.edu/kschwede/math186 Text: Calculus by Michael Spivak Suggested Text: Calculus and Linear Algebra by Wilfred Kaplan and Donald Lewis Contacting
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Solutions to Chapter 5 Homework on the Mathematics of Getting Around Problem 20: Comment: Each block which has houses on both sides of the street is represented by a pair of edges (since the mail carrier must make two passes on such
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Homework for chapter 4: Mathematics of Apportionment 1. (Based on chapter 4 problem #4 in the textbook) The Placerville General Hospital has a nursing staff of 225 nurses working in four shifts: A (7am 1pm) B (1pm 7pm) C (7pm 1am) D
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, homework SOLUTIONS for chapter 3 (Mathematics of Sharing) 1. Martha and Nick share the rights to use a certain store location, but they have separate businesses, and only one can use the space at a time. To minimize the costs and ha
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Homework on Weighted Voting Systems Solutions 1. [Suggested warmups from the textbook for this homework problem are #11, 13, 15, and 17] Consider the weighted voting system [12: 9, 4, 3, 2]. 1a. Write out all winning coalitions for
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Solutions to Chapter 6 Homework Assignment on the Mathematics of Touring Problem 24: (a) There are 25! Hamilton circuits in the complete graph K26, which is approximately 1.5511 x 1025. Dividing by a trillion, which equals 1012, we
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Solutions to Chapter 7 Homework on the Mathematics of Networks Please note that the problem numbers indicated here correspond to the color editions of the textbook. In the black and white edition, in this chapter, each problem numbe
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math of Money Problems 1. Over the period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday it went up 3.2% On Tuesday it went down 1.9% On Wednesday it went up 0.9% On Thursday it went up 4.3% On Friday it went down 2.7% W
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math of Sharing Problems 1. Four partners (Adkins, Bennington, Collins, and Dunn) own a company with a market value of $200,000. The company is being broken up into four pieces: s 1, s2, s3, and s4. Each partner will get one of the four pieces. The follow
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Spring 2013, Homework for chapter 10 (Mathematics of Money) 1. [Warmup problems from the book: #13, 15, 17] (4 points) Over a period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday the DJIA went up by 3.1%, on T
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103 Spring 2013, homework for chapter 1 Please remember to use complete English sentences when writing your solutions. See the document How to submit assignments in Sakai in the Resources folder of your Math 103 sections Sakai site. 1. The following
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Fall 2009, questions for final exam televised review, with solutions An election is held, in which there are four candidates Ann (A), Bob (B), Claire (C), and Dave (D), and the following preference schedule is obtained: 10 7 6 2 1 place A D B C
School: Rutgers
Course: Math 103 Topics In Math For The Liberal Arts
Math 103, Fall 2009, questions for final exam televised review An election is held, in which there are four candidates Ann (A), Bob (B), Claire (C), and Dave (D), and the following preference schedule is obtained: 10 7 6 2 st A D B C nd 2 place D C D B 3r
School: Rutgers
Math 250 Matlab Lab Assignment #2 PEILIN YANG 2573 rand('seed',2573) %Question 1 (a) A = rmat(3,5), rank(A(:,1:3) A= 75358 88949 58085 ans = 3 b = rvect(3), R=rref([A b]) b= 2 6 9 R= 1.0000 0 0 0.4638 1.2319 0.9130 0 1.0000 0 0.7101 0.1449 1.6957 0 0 1.
School: Rutgers
Course: Numerical Analysis
MATLAB FOR NUMERICAL ANALYSIS Home Exercises: (Submit the printed figures and necessary commands for the following two exercises next week.) Question1. For each of the following functions, find an interval a, b , so that f a and f b have opposite signs, b
School: Rutgers
Course: Numerical Analysis
Linear Algebra and Numerical Analysis: Matlab Martin Mensik 1 Martin Mensik Linear Algebra and Numerical Analysis : Matlab Basic routines Write a script le (not a function) that will do following tasks in order. All vectors should be of dimension 5 unless
School: Rutgers
Course: Numerical Analysis
Assignment 3 Problem 1 a. The function L1 (x, y ) satises L1 (1/2, 0) = 1, L1 (0, 1/2) = 0, L1 (1/2, 1/2) = 0 If L1 (x, y ) = ax + by = c, this implies 1 2a + c = 1 1 b+c=0 2 1 a + 1b + c = 0 2 2 which can be solved to obtain L1 (x, y ) = 1 2y Similarly L
School: Rutgers
Course: Numerical Analysis
Assignment 3 Problem 1 a. Since Qi (x) and Qi (x) are continuous, Qi (xi1 ) = Qi (xi1 ) = 0 and Qi (xi+2 ) = Qi (xi+2 ) = 0. First nd a function Q with the required properties in the interval [1, 2], with xj = i j . Since Q(1) = Q (1) = 0, in the subinter
School: Rutgers
Course: Numerical Analysis
Assignment 2 Problem 1a. i) The divided dierences table is: x f (x) f [, ] f [, , ] f [, , , ] f [, , , , ] 1 1 2 4 3 1 2 5 5 2 1 0 1 5 5 1 2 1 4 5 1 2 2 5 3 5 4 5 1 5 2 5 2 5 2 5 So P (x) = 1 1 2 1 2 1 1 13 + (x + 1) (x + 1)(x + ) (x + 1)(x + )x + (x + 1
School: Rutgers
Course: Numerical Analysis
Assignment 1 Problem 4 a. Since P3 (0) = P3 (1/3) = P3 (2/3) = 0, we must have 2 1 P3 (x) = Ax(x )(x ) 3 3 for some constant A. Now evaluating P3 (x) at x = 1 and using the condition P3 (1) = 1, we get P3 (1) = A (1/3) (2/3), from which we obtain A = 9/2.
School: Rutgers
Course: Calculus 1
135, F2013, Sara N Soffer HW if you use the Pearson textbook The problems with numbers in parentheses are somewhat similar to other problems in the list. However, this is a subject that rewards practice, so solving all of the listed problems is a wise use
School: Rutgers
Course: Calculus I
Statistics 285 Solutions to HW #3 Problems 4.16 a. = E(x) = xp( x ) = 10(.05) + 20(.20) + 30(.30) + 40(.25) + 50(.10) + 60(.10) = .5 + 4 + 9 + 10 + 5 + 6 = 34.5 2 = E(x )2 = ( x )2 p( x ) = (10 34.5)2(.05) + (20 34.5)2(.20) + (30 34.5)2(.30) + (40 34.5)2
School: Rutgers
Course: Calculus I
Statistics 285 Solutions to HW #2 Problems 3.2 a. This is a Venn Diagram. b. If the sample points are equally likely, then P(1) = P(2) = P(3) = = P(10) = 1 10 Therefore, 1 1 1 3 + += 10 10 10 10 1 1 2 + = = .2 10 10 10 P(A) = P(4) + P(5) + P(6) = P(B) = P
School: Rutgers
640:421:06 ASSIGNMENT 7 SPRING 2013 Turn in the starred problems, and only the starred problems, at the beginning of the class on Friday 3/15/2013. If your homework contains several sheets it must be stapled. All problems are from Zill and Wright. Section
School: Rutgers
640:421:06 ASSIGNMENT 4 SPRING 2013 Turn in the starred problems, and only the starred problems, at the beginning of the class on Friday 2/22/2013. If your homework contains several sheets it must be stapled. All problems are from Zill and Wright, and the
School: Rutgers
ASSIGNMENT 1 SPRING 2013 Turn in the starred problems, and only the starred problems, at the beginning of the class on Friday 02/01/2013. If your homework contains several sheets it must be stapled. All problems are from Zill and Wright. Section 4.1: 1, 3
School: Rutgers
ASSIGNMENT 3 SPRING 2013 Turn in the starred problems, and only the starred problems, at the beginning of the class on Friday 02/15/2013. If your homework contains several sheets it must be stapled. Note the additional problems 3.A and 3.B, which are to b
School: Rutgers
Course: Financial Mathematics
640:495 Mathematical Finance, Problem Solutions and Hints. 45. In class we stated the following special case of a fundamental fact about expectations and conditional expectations. Consider the binomial tree model with N periods and some (arbitrary) assign
School: Rutgers
Course: Financial Mathematics
640:495 Mathematical Finance, Problems. In class we discussed the fact that if (Y1 , . . . , Yn ) and (Y1 , . . . , Yn ) are functions of Y1 , . . . , Yn , then, abbreviating them by and , we have the identity E [ + X  Y1 , . . . , Yn ] = + E [X  Y1 , .
School: Rutgers
Course: Financial Mathematics
640:495 Mathematical Finance, Problems. 58. Show that if X N (m, 2 ), then aX +b N (am+b, a2 2 ). (See, online notes on Normal random variables and the Central Limit Theorem, http:/www.math.rutgers.edu/courses/495/lect18notes.pdf, page 2.) 59. Show that i
School: Rutgers
Course: Financial Mathematics
640:495 Mathematical Finance, Problems Itos rule. In class we gave a prescription called Itos rule for nding d[f (Xt , t)] if dXt = t dt + t dBt , where B is a standard Brownian motion. This rule had to do with using Taylor polynomial approximations, and
School: Rutgers
Course: Financial Mathematics
640:495 Mathematical Finance, Problems 88. Consider an option that pays $1 if ST > X and 0 otherwise, where S is the price of an underlying stock. This is the cash or nothing option. For notation, let 1(X,) (x) = 1, if x > X; 0, otherwise, denote its payo
School: Rutgers
Course: Crytography
Homework #1, due February 5 Exercise 1. Decrypt the following message which was created using the Caesar cipher: LORYHWKHQDPHRIKRQRU Exercise 2. Eve has intercepted the following ciphertext which was created by using a shift cipher: CNMNBYQLIHANLIOMYLM De
School: Rutgers
Course: Linear Algebra
MATH 35002 Solutions to problems from Chapter 6 #1 The four given vectors form an orthogonal set of nonzero vectors. Therefore this set is linearly independent and, hence, is a basis for R4 . Then if v = (5, 3, 7, 1), v1 = (1, 1, 1, 1), v2 = (1, 1, 1, 3)
School: Rutgers
The following is a graph of the first derivative f(x) of a function y = f(x). y 2 Use this graph of f(x) to answer the following questions about the graph of f(x). y = f(x) 1 7654321 123 4 5 6 7 8 x 2 a. On what interval(s) is the graph of f(x) con
School: Rutgers
The following is a graph of the first derivative f(x) of a function y = f(x). You may assume f(x) is defined for all real numbers. y 2 Use this graph of f(x) to answer the following questions about the graph of f(x). y = f(x) 1 7654321 123 4 5 6 7 8
School: Rutgers
Course: History Of Mathematics
v& 3 ` W Fug F 6 W 8 5 3 5 ug W 3 3 14)P#dt#u 96 iiq#@(4&#S#u dq& 4Q@18 X y W FD 6FX 6F y 6 T Fuu 6Fy 6 W F 6&8 F 6 3& F 6 3& T F 6&8 F 6&8 W F 6& m# #g a2 mD d#D # ivE92id15%2945%929pv2ia 8 b& 3&8 ) 45%ta1k vChEiE4&q4%qI#9h#E4&q4%qSA4Qqq#m# Fgy ` 6 u 3 x
School: Rutgers
Course: Honors Calculus 4
RUTGERS UNIVERSITY SPRING 2006 Due Date: Jan/30/06 Homework 2 Calculus VI  Math 292 Honors Section Eduardo V. Teixeira Department of Mathematics Hill 440 Phone: 7324452473 Email: teixeira@math.rutgers.edu www.math.rutgers.edu/~eteixeir/ Problem 1 Show
School: Rutgers
Course: Multivariable Calculus
Maple assignment 1 Here is some help for the first Maple assignment. The assignment requests several pictures. Pictures are very important. Not many people can get much information from vast tables of numbers, but humans possess a large capacity to receiv
School: Rutgers
Course: Multivariable Calculus
Maple assignment 5 Background Here is the problem: Theoretical results imply that x+3yz has a maximum and a minimum on the sphere x2+y2+z2=1. Use Lagrange multipliers to find these maximum and minimum values. The constraint in this problem is x2+y2+z2=1,
School: Rutgers
% Math 250 Matlab Lab Assignment #2 rand('seed',2573) %Question 1 (a) A = rmat(3,5), rank(A(:,1:3) A = 7 5 3 5 8 8 8 9 4 9 5 8 0 8 5 ans = 3 b = rvect(3), R=rref([A b]) b = 2 6 9 R = 1.0000 0 0 0.4638 1.2319 0.9130 0 1.0000 0 0.7101 0.1449 1.69
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #4 Revised 5/16/12 LAB 4: General Solution to Ax = b In this lab you will use Matlab to study the following topics: The column space Col(A) of a matrix A The null space Null(A) of a matrix A. Particular solutions to an in
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C 1 Matlab Assignment #3 Revised 5/14/12 LAB 3: LU Decomposition and Determinants In this lab you will use Matlab to study the following topics: The LU decomposition of an invertible square matrix A. How to use the LU decomposition to solve the
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #2 1 Revised 9/30/12 LAB 2: Linear Equations and Matrix Algebra In this lab you will use Matlab to study the following topics: Solving a system of linear equations by using the reduced row echelon form of the augmented matrix
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #5 1 Revised 12/06/12 LAB 5: Eigenvalues and Eigenvectors In this lab you will use Matlab to study these topics: The geometric meaning of eigenvalues and eigenvectors of a matrix Determination of eigenvalues and eigenvectors
School: Rutgers
Math 250C Matlab Assignment #1 1 Revised 1/18/13 LAB 1: Matrix and Vector Computations in Matlab In this lab you will use Matlab to study the following topics: How to create matrices and vectors in Matlab. How to manipulate matrices in Matlab and creat
School: Rutgers
% Math 250 MATLAB Lab Assignment #1 % Question 1 (a) rand('seed',2573) R = rand(2,3) R= 0.7147 0.5673 0.8356 0.8247 0.5527 0.8622 R = rand(2,3) R= 0.3863 0.0877 0.4029 0.9119 0.5258 0.8089 R = rand(2,3) R= 0.8864 0.5908 0.6478 0.9908 0.2026 0.9370 % Quest
School: Rutgers
format compact % Math 250 MATLAB Lab Assignment #1 rand('seed',2573) % Question 1 (a) R = rand(2,3) R = 0.7147 0.5673 0.8356 0.8247 0.5527 0.8622 R = rand(2,3) R = 0.3863 0.0877 0.4029 0.9119 0.5258 0.8089 R = rand(2,3) R = 0.8864 0.5908 0.6478 0.99
School: Rutgers
A=fix(10*rand(3,4) A = 9 2 4 1 3 1 0 2 3 0 3 8 R=a; R(1,:)=R(1,:)/R(1,1) cfw_Undefined function or variable 'a'. R=A; R(1,:)=R(1,:)/R(1,1) R = 1 2/9 4/9 1/9 3 1 0 2 3 0 3 8 R(2,:)=R(2,:)R(2,1)*R(1,:) R = 1 2/9 4/9 1/9 0 1/3 4/3 5/3 3 0
School: Rutgers
Course: Numerical Analysis
Numerical Analysis Lab Note #2 Matlab Basic Matrix, Vector, Function, and Script MFile = Matrices and Vectors In Matlab, all variables can be viewed as matrices. You can use "[ ]" to define a matrix. Or, you can use functions "zeros", "ones", "rand", "ey
School: Rutgers
Course: Numerical Analysis
Numerical Analysis Lab Note #1 Matlab Basic = Variables Like most other programming languages, the MATLAB language provides mathematical expressions, but MATLAB does not require any type declarations or dimension statements. When MATLAB encounters a new v
School: Rutgers
Course: Intro To Linear Algebra With MATLAB
Math 250C Matlab Assignment #1 1 Revised 6/14/12 LAB 1: Matrix and Vector Computations in Matlab In this lab you will use Matlab to study the following topics: How to create matrices and vectors in Matlab. How to manipulate matrices in Matlab and creat
School: Rutgers
Course: Calc 4
<?xml version="1.0" encoding="UTF8"?> <Worksheet><Version major="6" minor="0"/><ViewProperties><Zoom percentage="100"/></ViewProperties><Styles><Layout alignment="left" bullet="none" name="Warning"/><Layout alignment="left" bullet="none" name="Heading
School: Rutgers
Course: Differential Eqns
640:244 Lab 3: The Pendulum SPRING 2011 This Maple lab is closely based on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab we use Maple to examine dierential equations modeling
School: Rutgers
Mathematics 251 Maple Lab 3 Maximum and Minimum Values Spring 2006 This project Please turn in only the printout of your Maple worksheet. Use the text feature of Maple to add a header containing your name at the top of the worksheet, and discussion i
School: Rutgers
Mathematics 244: Lab 2 Fall 2003 0. Introduction and Setup. In this lab, we shall use Maples ability to plot direction elds and approximate the solution of differential equations by numerical methods to understand the solutions of differential equati
School: Rutgers
640:244 Lab 1: Exact Solutions of Dierential Equations SPRING 2008 This Maple lab is closely based on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab we use Maple to nd e
School: Rutgers
Mathematics 251: Lab 1 INTRODUCTION TO MAPLE This lab contains ten problems intended to introduce you to some of the basic features of Maple and to give you practice preparing a Maple worksheet. Most of the Maple commands you need are in the seed
School: Rutgers
640:244 Lab 1: Exact Solutions of Differential Equations FALL 2007 This Maple lab is closely based on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab we use Maple to find
School: Rutgers
640:244 Lab 4: Linear Systems Fall 2007 This Maple lab is based in part on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab we use Maple to find eigenvalues and eigenvecto
School: Rutgers
Mathematics 244: Lab 5 Trajectories in the Phase Plane In this lab, we shall use Maple to study the qualitative properties of autonomous systems of two dierential equations. Please turn in only the printout of your Maple worksheet. Include explicit
School: Rutgers
Mathematics 244: Lab 3 Second Order Differential Equations In this lab, we use Maple to examine differential equations modeling forced and unforced oscillations. In particular, we shall consider linear and nonlinear models of a pendulum and also ex
School: Rutgers
Mathematics 244: Lab 1 Exact Solutions of Differential Equations In this lab we use Maple to find exact solutions of differential equations and initial value problems and to help visualize solutions in cases when the solutions are only defined impl
School: Rutgers
Mathematics 244: Lab 0 INTRODUCTION TO MAPLE FOR DIFFERENTIAL EQUATIONS This lab is intended to introduce you to some of the features of Maple that are useful in solving differential equations and to give you practice preparing a Maple worksheet. Mos
School: Rutgers
640:244 Lab 4: Linear Systems SPRING 2009 This Maple lab is based in part on earlier versions prepared by Professors R. Falk and R. Bumby of the Rutgers Mathematics department. Introduction. In this lab we use Maple to find eigenvalues and eigenvec
School: Rutgers
Course: Linear Algebra
Linear Algebra and Its Applications Fourth Edition Gilbert Strang x y z Ax y Ay 0 z b b Az b 0 0 Contents Preface iv 1 . . . . . . . . 1 1 4 13 21 36 50 66 72 . . . . . . . 77 77 86 103 115 128 140 154 . . . . . . 159 159 171 180 195 211 221 2 3 Matrices
School: Rutgers
Course: MULTIVARIABLE CALCULUS
Calc III Study Guide Exam I 1. ReRead Notes 2. Do all of these problems 12.1: 5, 9, 11, 15, 21, 40, 47 12.2: 11, 13, 19, 25, 27, 31, 51 12.3: 1, 13, 21, 29, 31, 52, 57, 63 12.4: 1, 5, 13, 20, 25, 26, 43, 44 12.5: 1, 9, 11, 15, 25, 31, 53 13.1: 5, 13, 15,
School: Rutgers
Course: Calculus 1
Prof. Jose Sosa Math 135 Sections 84, 85 and 86 Fall 2013 email: jsosa@math.rutgers.edu Oce Hours: Mondays, Thursdays, 10:0010:45 am Heldrich SB (Douglass) Room 203 Thursdays, 1:503:10 pm Lucy Stone H (Livingston) Room B102C Classes: Tuesdays, Thursday
School: Rutgers
Course: Basic Calculus
21:640:119:07/Basic Calculus/Spring 2012 Class meetings: MW 1011:20, Smith B26 Instructor: John Randall Smith 305, (973)3533919, randall@rutgers.edu Office hours: M 910, WTh 11:301 Course web site: http:/pegasus.rutgers.edu/~randall/119/ and Rutgers Blac
School: Rutgers
Course: Math 103
Math 103: Topics in Math for the Liberal Arts, Section 11, Spring 2011 CourseOverviewSheet Prerequisite: Elementary Algebra at the level of Rutgers Math 025, or equivalent. Elementary algebra and other basic skills are helpful. Text: Excursions in Modern
School: Rutgers
SYLLABUS MULTIVARIABLE CALCULUS 251 SUMMER 2008 PREREQUISITE: Calc 152 or the equivalent. TEXT: Calculus with Early Transcendentals, Custom Edition for Rutgers University. Author: Jon Rogawski. Publisher: Freeman Custom Publishing. Note 1: You may