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School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Chapter Review Exercises SOLUTION 811 The function whose value we want to approximate is f (x, y, z) = x 2 + y2 + z We use the linear approximation at the point (7, 5, 70), hence h = 7.1 - 7 = 0.1, k = 4.9 - 5 = -0.1, and l = 70.1 - 70 = 0.1. We g
School: UCLA
MULTIVARIABLE CALCULUS (MATH 32A) FALL 2004 LECTURE NOTES 10/1/04 Office Hours: MS 7344, 11:00 12:40 Mon., Wed., Fri. E-mail: lchayes@math.ucla.edu Homework: 20% (each problem graded on a 2-pt. scale). PRINT OUT HOMEWORK FROM COURSE WEBPAGE Midterm
School: UCLA
Course: CALCULUS FOR LIFE SCIENCES STUDENTS
Lectuie I l-1-t3 I r.ivrew ] ?rnr ttxr-lr\ h-)0 - F(I] tx\ -> d.Y\uqtwo f h 6v(V(\q( [fite of chan4e f(xJ La,tl J(b)-f(d) b-a L rl rrne t'lturrl cfw_'un[i'cfw_on5 ' Llllcfw_-fii funrnpnt ' Powc( ] f(xl cfw_(xl * x " furn (-tt17t1(, Ro0l f Ut\(,flon j ro l
School: UCLA
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Math 33B Time table: Lecture time Lecture 2 Lecture 3 Lecture location Midterm 1 Midterm 2 Final time 1111:50am MWF 4000A MS October 31st , Friday. November 24th , Wednesday lecture time, lecture room lecture time, lecture room December 13, 11:30am2:30pm
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
172C June 2013 AV, Asset Shares, Year by Year Financial Universal Life Account Values 1. For Universal Life UL policies in particular, the Account Value AV functions like a policy holder "bank account that is periodically updated Even though premium
School: UCLA
School: UCLA
Tom M. Apostol CALCULUS VOLUME 1 One-Variable Calculus, with an Introduction to Linear Algebra SECOND EDITION New York l John Wiley & Sons, Inc. Santa Barbara l London l Sydney l Toronto C O N S U L T I N G EDITOR George Springer, Indiana University XEROX
School: UCLA
Handout #11 Assignment 7 clarication Riemann integral review Assignment 8 Clarication of problem 34.1 The notation in the problem is simply awful. Here is a better treatment. We want to use the second FTC to prove the rst FTC. i.e.,If f (x) is continuous
School: UCLA
Handout # 14 Review for Final watch for stupid errors Review Session Friday 4-5:30 (usual room unless I notify you) Answers to some second hour exam questions Suppose that an R is Cauchy. Then we showed it is bounded, i.e., there is a number M such that
School: UCLA
Handout #12 Norms on vector spaces This is an informal introduction to the modern norm approach to real analysis. We want to take seriously the notion that one can treat functions the same way that deals with numbers. We know how to add functions and mult
School: UCLA
Handout 8 Exam information (watch for silly errors) Reminder: The second hour exam is on Monday May 16. Review Session: Friday 4-5:30 (May 13) Things you should know for the exam. Note there wont be any questions about derivatives. Also we wont bother wit
School: UCLA
Handout 6 Review and Assignment 5 (due Friday, May 6) Some key results you should know how to prove. (1) An increasing sequence an R converges if and only if it is bounded above. (2) Any sequence an R has a monotone subsequence ank . (3) A bounded sequenc
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular
School: UCLA
(a) (5 points) State the Comparison :L Denition 2. The function f is said in he continuum; in 3 i Hunk", (b) (5 points) is the series E convergent? Justify you VT" 5 3 V5 > u 35 > 0 V1, 5 S Ii 7 ml < ,5 :5 Ix) , ru) < EL Fu- 1 ire-qu'nru' Inn}. 'll. wail:
School: UCLA
Course: Math32A
Remarks and a trick for the osculating plane Remark. Note that there is an error on Professor Taylors solution to Problem 5. The error occurs when he computes aN (1). The correct computation of aN (1) is aN (1) = (2, 1, 3) (2, 2, 1) = (0, 1, 2) NOT aN (1)
School: UCLA
Course: Math32A
About the 32A Final Location and Time Lecture #1 (the 10AM lecture) will be held in Moore 100 on Sunday, June 7th from 3:00PM until 6:00PM Lecture #2 (the 12PM lecture) will be held in Lakretz 110 on Sunday, June 7th from 3:00PM until 6:00PM Sections Co
School: UCLA
Course: Math32A
Math 21a: Multivariable calculus Distances overview DISTANCE POINT-POINT (3D). If P and Q are two points, then d(P, Q) = |P Q| is the distance between P and Q. We use the notation |v| instaed of |v| in this handout. DISTANCE POINT-PLANE (3D). If P is a po
School: UCLA
Course: Introduction Of Complex Analysis
Math 132: Complex Analysis for Applications INSTRUCTOR: Kefeng Liu TIME and LOCATION: MWF 9:00-9:50AM, MS5117. OFFICE HOURS: TT 9:00-10:00AM in MS 6330 (Or by appointment) SYLLABUS: Official Syllabus Text: Complex Analysis by Tom Gamelin TA: Wenjian Liu,
School: UCLA
Course: Linear Algebra
Math 33A, Sec. 2 Linear Algebra and Applications Spring 2012 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 2:00 p.m. 2:50 p.m.; Rolfe 1200 Office
School: UCLA
Course: Algebra-applicatns
v P y V ` V ` x G ~ y | G V | ` ` F G G y V F F GI | V U )HoASY2dddI)dY)2vdG u !A)w u zAdA)YV y V ` V ` x G ~ | G V | ` ` G V F GI X y V G ` ` FI ` ` 6 8 4 8 1 HAa92ddd!I dY)2vdG u F AHWdYaHa2 9!4 20 P U b U y b q b Uv b pv b gv b i tAACttAAmYACt7t
School: UCLA
Course: Math32A
UCLA Math 32A, Lecture 1 (Spring Quarter 2015) Calculus of Several Variables Instructor: David Wihr Taylor Time/Location: MWF 10:00am-10:50am in Rolfe 1200. Text: Calculus (2nd edition) by Jon Rogawski ISBN: 9781429294904 (Contact the UCLA Store in Ackerm
School: UCLA
Course: Math 31A
Dierential and Integral Calculus, Math 31a, Fall 2013, Lec 1 - Course Info Instructor: Tonci Antunovic, 6156 Math Sciences Building, tantunovic@math.ucla.edu, www.math.ucla.edu/tantunovic Instructor Oce Hours: Monday 11-12:30 and Thursday 5-6:30 in 6156 M
School: UCLA
Course: Sftwr-scntfc Cmpttn
Environment12: SustainabilityandtheEnvironment Summer2015 UCLAInstituteoftheEnvironment AndSustainability Page 1 of 5 SustainabilityandtheEnvironment Summer2015 Synopsis: There are a number of social, demographic, and ecological changes concurrently affec
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Sule Ozler Economics 12 Fall 2011 READ THE EXPLANATIONS IN BOLD LETTERS CAREFULLY! MID-TERM EXAM - GOOD LUCK! WRITE YOUR NAME AND ID# You will not be allowed to ask questions during the exam. This exam has three sections. Each section has multiple questio
School: UCLA
Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Name: Student ID: Prof. Alan J. Laub Section: 2 May 4, 2012 Math 33A/2 MIDTERM EXAMINATION Spring 2012 Instructions: (a) The exam is closed-book (except for one page of notes) and will last 50 minutes. No calculators, cell phones, or other electronic devi
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Solutions for assignment 2 1 of 2 Section 2.2 Question 9: (a) (z-5i)^2 is a polynomial, hence continuous everywhere, and thus on e can simply substitute in the limit to obtain (2+3i)^2 - 5i)^2 = -8i. (c) This is an indeterminate form; one can either use L
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the
School: UCLA
Course: Introduction To Discrete Structures
MATH 61: HOMEWORK 2 3.3 25. not reexive, not symmetric, antisymmetric, transitive, not a partial order 26. reexive, not symmetric, antisymmetric, transitive, partial order 28. reexive, symmetric, not antisymmetric, transitive, not a partial order (this is
School: UCLA
Course: MATH20F
Hector Ordorica Section: B51 / B02 TA: Matthew Cecil Exercise 3.1 Answer: D can be: 1. D = 0 0 00 2. D = 1 0 01 3. D = 0 1 10 Exercise 3.2 (a) Input: A = [1, 2, 0; 2, 1, 2; 0, 2, 1] B = [3, 0, 3; 1, 5, 1; 1, 1, 3] x = [1; 2; 3] C = (5*A^2*B - 3*A')^2 Outp
School: UCLA
Course: Discrete Structures
Math 115A Section 3 Final Exam Info There will be 10 questions on the exam. Anything discussed in lecture or on the homework is fair game for the exam. Relevant sections in the book are 1.2-1.6, 2.1-2.5, 4.4, 5.1-5.2, 6.1-6.4. Roughly half of the exam
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the monotonicit
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 2/14/13 Homework #5 Due: Thursday Feb 21 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 1/8/13 Homework #1 Due: Thursday Jan 17 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the H
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =
School: UCLA
Spring 2011- Professor Sule Ozler Name Economics 121 ID# FINAL EXAM WRITE YOUR NAME AND ID# No questions will be answered during the exam There will not be any bathroom breaks during the exam You are permitted to have only your writing equipment on your d
School: UCLA
Course: LINEAR ALGEBRA
1 Math 110 Homework 7 Partial Solutions If you have any questions about these solutions, or about any problem not solved, please ask via email or in oce hours, etc. 3.1.4 This is a sketch of the ideas: The elementary matrix that represents switching rows
School: UCLA
Course: Probability Theory
T. Liggett Mathematics 170B Midterm 2 Solutions May 23, 2012 (20) 1. (a) State Markovs inequality. Solution: If X 0, then P (X a) EX/a for a > 0. (b) Prove Markovs inequality. Solution: a1cfw_X a X . Taking expected values gives aP (X a) EX . (c) Suppose
School: UCLA
Chapter Review Exercises SOLUTION 811 The function whose value we want to approximate is f (x, y, z) = x 2 + y2 + z We use the linear approximation at the point (7, 5, 70), hence h = 7.1 - 7 = 0.1, k = 4.9 - 5 = -0.1, and l = 70.1 - 70 = 0.1. We g
School: UCLA
MULTIVARIABLE CALCULUS (MATH 32A) FALL 2004 LECTURE NOTES 10/1/04 Office Hours: MS 7344, 11:00 12:40 Mon., Wed., Fri. E-mail: lchayes@math.ucla.edu Homework: 20% (each problem graded on a 2-pt. scale). PRINT OUT HOMEWORK FROM COURSE WEBPAGE Midterm
School: UCLA
Course: CALCULUS FOR LIFE SCIENCES STUDENTS
Lectuie I l-1-t3 I r.ivrew ] ?rnr ttxr-lr\ h-)0 - F(I] tx\ -> d.Y\uqtwo f h 6v(V(\q( [fite of chan4e f(xJ La,tl J(b)-f(d) b-a L rl rrne t'lturrl cfw_'un[i'cfw_on5 ' Llllcfw_-fii funrnpnt ' Powc( ] f(xl cfw_(xl * x " furn (-tt17t1(, Ro0l f Ut\(,flon j ro l
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Math 33B Time table: Lecture time Lecture 2 Lecture 3 Lecture location Midterm 1 Midterm 2 Final time 1111:50am MWF 4000A MS October 31st , Friday. November 24th , Wednesday lecture time, lecture room lecture time, lecture room December 13, 11:30am2:30pm
School: UCLA
Course: MULTIVARIABLE CALCULUS
Mathematica for Rogawski's Calculus 2nd Edition 2010 Based on Mathematica Version 7 Abdul Hassen, Gary Itzkowitz, Hieu D. Nguyen, Jay Schiffman W. H. Freeman and Company New York 2 Mathematica for Rogawski's Calculus 2nd Editiion.nb Copyright 2010 Mathem
School: UCLA
172C June 2013 AV, Asset Shares, Year by Year Financial Universal Life Account Values 1. For Universal Life UL policies in particular, the Account Value AV functions like a policy holder "bank account that is periodically updated Even though premium
School: UCLA
School: UCLA
Tom M. Apostol CALCULUS VOLUME 1 One-Variable Calculus, with an Introduction to Linear Algebra SECOND EDITION New York l John Wiley & Sons, Inc. Santa Barbara l London l Sydney l Toronto C O N S U L T I N G EDITOR George Springer, Indiana University XEROX
School: UCLA
Handout #11 Assignment 7 clarication Riemann integral review Assignment 8 Clarication of problem 34.1 The notation in the problem is simply awful. Here is a better treatment. We want to use the second FTC to prove the rst FTC. i.e.,If f (x) is continuous
School: UCLA
Handout # 14 Review for Final watch for stupid errors Review Session Friday 4-5:30 (usual room unless I notify you) Answers to some second hour exam questions Suppose that an R is Cauchy. Then we showed it is bounded, i.e., there is a number M such that
School: UCLA
Handout #12 Norms on vector spaces This is an informal introduction to the modern norm approach to real analysis. We want to take seriously the notion that one can treat functions the same way that deals with numbers. We know how to add functions and mult
School: UCLA
Handout 8 Exam information (watch for silly errors) Reminder: The second hour exam is on Monday May 16. Review Session: Friday 4-5:30 (May 13) Things you should know for the exam. Note there wont be any questions about derivatives. Also we wont bother wit
School: UCLA
Handout 6 Review and Assignment 5 (due Friday, May 6) Some key results you should know how to prove. (1) An increasing sequence an R converges if and only if it is bounded above. (2) Any sequence an R has a monotone subsequence ank . (3) A bounded sequenc
School: UCLA
Handout #2 including Assignment 2 Remember that in contrast to the text, we proved the Principle of Induction. We used the fact that N is well-ordered, i.e., if S is a nonempty subset of N, then S has a least element. Here is the proof: Theorem 0.1. If P
School: UCLA
Math 131A/3 Spring 2011 MWF 2-2:50 MS5147 Recitation R 2:2:50 MS5147 Handout #1 Info and Assignment 1 Instructor: E. Eros, MS6931 Oce Hours Fri 4-5:30 (tentative) TA: Alden Waters, MS 3975 Oce Hours Mon 3:00-4:30 (tentative) Grading System: Homework 20%,
School: UCLA
Handout 4 Exam information, some proofs, and Assignment 3 (watch for stupid errors) Things you should know for the rst hour exam a) Assignments 1 and 2, and the rst problem on Assignment 3. b) The proof that the well-ordering principle for N implies the p
School: UCLA
Lemma 1. Let 0 x 1 then there is a sequence of integers, dn cfw_0, 1, 2, 3, ., 9 such that N dn (10n ) x = lim N n=1 Proof. Consider the case when x = 0. Then pick d1 to be the largest integer such that d1 (101 ) < x. Because x > 0, it follows that d1 0.
School: UCLA
Course: MATH 31B
a. a E - * -. 9er lgiatdtk v: and; 6* Z: (21: {1V :ei mat xix-Si ~ {9:1 + 3 at in £61: 93}; 1 -1: . _, ML :2 via "(that la + C =4 w (£23: R + C 7- (M S sim Lcsgmekx -: g 5mm) (Ausinztxli.os{><)rlx . (Lam 4M 5M _ Jun: mm in £3) E mnltx)» sag,5 (K) M : S
School: UCLA
Course: MATH 31B
MATH 31B - SECTION 1 PRACTICE MIDTERM #2 Problem 1. Evaluate the following integrals. x dx (a) e (b) (ln x)2 x2 dx Problem 2. Evaluate the following integrals. (a) sin2 (x) cos5 (x) dx (b) tan2 (x) sec3 (x) dx Problem 3. Evaluate the following integrals.
School: UCLA
Course: MATH 31B
MATH 31B - SECTION 1 MIDTERM #1 JANUARY 23, 2015 Full Name Student ID Discussion Section Problem 1 /20 Problem 2 /30 Problem 3 /20 Problem 4 /30 Total /100 Problem 1. Let f (x) = 1 1+x and g(x) = 1x x . (a) Show that g(x) is the inverse of f (x). (b) Comp
School: UCLA
Course: Math32A
Lecture 7 2 Page 1 Lecture 7 2 Page 2 Lecture 7 2 Page 3 Lecture 7 2 Page 4 From <http:/en.wikipedia.org/wiki/File:Corrientes-oceanicas.png> Lecture 7 2 Page 5 Lecture 7 2 Page 6 For example: (looks like this) spiral demo Lecture 7 2 Page 7 Or, (which loo
School: UCLA
Course: Math32A
Vectors in 3D We live in a world with 3 spatial dimensions (that we can see, anyway). Thus, it's useful to investigate 3D vectors. Three dimensional coordinate systems: Schematic diagram of Every point, , in Euclidean threedimensional space (denoted ) i
School: UCLA
Course: Math32A
Lecture 10: Curvature Intuitively, the curvature at some point belonging to a curve in (or ) is how much a curve bends at that point. Consider the following pictures: vs. Most of you intuitively know that at than does at . has greater curvature It seems t
School: UCLA
Course: Math32A
Lecture #6 (April 10 2015) Errata: I want clarify a typo I made in the 10 AM lecture. Consider the following diagram: distance between the point the plane The formula for the distance between a point in is: where and and a plane is a point on the plane. H
School: UCLA
Course: Sftwr-scntfc Cmpttn
UCLA Institute of the Environment and Sustainability Summer 2015 M. Nartey Myralyn Nartey= Interdisciplinarian! Environmental Biology Climate and Society African Studies Community Health Sciences (Comparative Education)
School: UCLA
Course: Sftwr-scntfc Cmpttn
UCLA Institute of the Environment and Sustainability Summer 2015 M. Nartey Key terms Environment Sustainable development Natural Resources Ecosystem Services Key concepts Ecological footprint Interdiscipli
School: UCLA
Course: Introduction Of Complex Analysis
. ~o~.~H~ ~ ~ Q(i\'1+ r \ .)' v ~rJ1 OJ\ o~ c.~- &t H~b @-~6\ H(~\ ( \-\ Lt.-& H-o, ~\ ~c- \ i ' .f t.o 1f" 61. 1 ~"' .,_ d i:o ~'(t) ~ ~. e-'! - (u:l- 4. f.! 0 \ ' ~ ~ ~. ~ r:f l:-: .b. ~ +. H(-tj ~ ~ ~ ~ tt;tn.~ . ~; t '(:t\.:o \II C't- ~.,)'" _, Hl't\
School: UCLA
Course: Introduction Of Complex Analysis
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School: UCLA
Course: Introduction Of Complex Analysis
- t, c Lcfw_ - R /~ /k.-. cfw_ > t) ,:,2- ~. ~ itMJ( -R 0 aJf i = l z = -1 ~ CZr;.fv,4 t re~ R/ 1 ~) _:_ J=b )-+i~ ~t wJ)_ < - - 1 - RL-\ ~ ~ ;, ~ a. lTK ~ul ~ct ~ k ~ )~Jj eM;~, ~:Jt tr~v)~t>~.f 1tr1>'fl-o ~ 4' 7tJ \ Jj :=. ~t;> _!. -. dlr~ f'(~) f,l ~ -
School: UCLA
Course: Introduction Of Complex Analysis
tr.hwrr . M~ I3d. )~JOI'-1 ~ t~)~ ~ j._ $' . It t(")'J) \l'~')1) ~ )l~)"'" cfw_lClt), 1 tt)\ -t f L-~J \'.et.<~ ~.J.e.' (t;: c. L ~ 'I . \ ~ Q. ;: Jl>v>-' ~ ) ~ '( 0 ~ CA~., "-~o.,.,1 \. ~ I X (-t) ; - ~1vvt - I 1 - "R(~iis,~vi) 'R (-:Sill+ f .\ em\ ., ~
School: UCLA
Course: Introduction Of Complex Analysis
:. -1i \t~o - 1-: ~ ~Vl-1-I.J.-l J d-t"'-\- h. d.~ 11\-\-cfw_a_:.-\ 7cfw_) OY "~ ~
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Course: ANALYSIS
Math 131a Lecture 2 Spring 2009 Midterm 1 Name: Instructions: There are 4 problems. Make sure you are not missing any pages. Unless stated otherwise (or unless it trivializes the problem), you may use without proof anything proven in the sections of the b
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Mathematics 131A Fall 2007 FINAL Your Name: Signature: INSTRUCTIONS: This is a closed-book test. Do all work on the sheets provided. If you need more space for your solution, use the back of the sheets and leave a pointer for the grader. Good luc
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Mathematics 131A - Final Examination Instructor : D. E. Weisbart June 12, 2012 NAME (please print legibly): Your University ID Number: Signature: There are SEVEN questions on this examination. Calculators, notes and books may not be used in this examina
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 2, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Probability Theory
Midterm 1 practice, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Name and student ID: Question Points 1 10 2 10 3 10 4 10 5 10 Total: 50 Score 1. (a) (2 points) If is a sample space, what is P(). Solution: P() = 1 (b) (2 points) If P(A) =
School: UCLA
Course: Probability Theory
T. Liggett Mathematics 170B Midterm 2 Solutions May 23, 2012 (20) 1. (a) State Markovs inequality. Solution: If X 0, then P (X a) EX/a for a > 0. (b) Prove Markovs inequality. Solution: a1cfw_X a X . Taking expected values gives aP (X a) EX . (c) Suppose
School: UCLA
Course: Introduction Of Complex Analysis
25 Solution. Consider r1 and r2 such that 0 < R1 < r1 < r2 < R2 . Then f (z) is holomorphic on the (closed) annulus cfw_z : r1 |z| r2 . Thus by Cauchy Integral Theorem, we have f (z) = 1 2i 2 1 f () d z 2i 1 f () d, z where 1 = cfw_z : |z| = r1 and 2
School: UCLA
Course: Probability Theory
Midterm 3, Math 170b - Lec 1, Winter 2013 Instructor: Toni Antunovi c c Printed name: Signed name: Student ID number: Instructions: Read problems very carefully. Please raise your hand if you have questions at any time. The correct nal answer alone is n
School: UCLA
Course: Discrete Math
Practice First Test Mathematics 61 Disclaimer: Listed here is a selection of the many possible sorts of problems. actual test is apt to make a different selection. 1. Let S5 be the set of all binary strings of length 5 (such as 11001). The Let E be
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Math 3C Midterm 1 Solutions Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and seven pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in o
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Course: Actuarial Math
MATH 115A - Practice Final Exam Paul Skoufranis November 19, 2011 Instructions: This is a practice exam for the nal examination of MATH 115A that would be similar to the nal examination I would give if I were teaching the course. This test may or may not
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Linear Algebra Math 115AH Midterm 1 Solutions Dominique Abdi 1. If W1 and W2 are subspaces of V and dim(W1 W2 ) = dim W1 what can you say about the relation between W1 and W2 ? Prove your answer. Solution. By the dimension theorem, dim(W1 + W2 ) = dim W1
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Math 32A: Practice Problems for Exam 2 Problem 1. A particle travels along a path r(t) with acceleration vector t4 , 4 t . Find r(t) if at t = 0, the particle is located at the origin and has initial velocity v0 = 2, 3 . Solution: We have r (t) = 1 1 t4 ,
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Math 3C Midterm 2 Name: BruinID: Section: Read the following information before starting the exam. This test has six questions and fourteen pages. It is your responsibility to ensure that you have all of the pages! Show all work, clearly and in order, i
School: UCLA
Course: Probability Theory
Mathematics Department, UCLA P. Caputo Fall 08, midterm 1 Oct 22, 2008 Midterm 1: Math 170A Probability, Sec. 2 Last name First and Middle Names Signature UCLA ID number (if you are an extension student, say so) Please note: 1. Provide the information ask
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Course: Linear Algebra
Name: Student ID: Prof. Alan J. Laub June 9, 2011 Math 33A/1 FINAL EXAMINATION Spring 2011 Instructions: (a) The exam is closed-book (except for one two-sided page of notes) and will last two and a half hours. No calculators, cell phones, or other electro
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Management 1A Summer 2004 Danny S. Litt EXAM 2 SOLUTION Name: _ Student ID No. _ I agree to have my grade posted by Student ID Number. _ (Signature) PROBLEM 1 2 3 4 5 6 7 8 TOTAL POINTS 20 25 20 20 30 30 30 25 200 SCORE MANAGEMENT 1A Problem 1
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Management 1A Winter 2004 Danny S. Litt Exam 3 Solutions Name: _ PROBLEM POINTS SCORE 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 TOTAL 100 Management 1A Problem 1 Winter 2004 (a) A company purchased a patent on January 1, 2002, for $1,000,
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MATH 32A FIRST MIDTERM EXAMINATION October, 18th, 20101 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sufficient explanations. If you have a question about any particular problem,
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MATH 33A/2 PRACTICE MIDTERM 2 Problem 1. (True/False) . 1 1 1 Problem 2. Let v1 = 1 , v2 = 0 , v3 = 1 . 0 1 1 3 (a) Show that B = 1 , v2 , v3 ) is a basis for R . (v 1 (b) Let u = 1 . Find the coordinates of u with respect to the basis B. 2 (c) Find the c
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MATH 32A FINAL EXAMINATION March 21th, 2012 Please show your work. You will receive little or no credit for a correct answer to a problem which is not accompanied by sucient explanations. If you have a question about any particular problem, please raise y
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Course: 31b
Math 31B, Lecture 4, Fall 2011 Exam #2, 9 November 2011 Name: ID Number: Section and TA: You have 50 minutes for the exam. No calculators, phones, notes, or books allowed. You must show your work for credit. Hint: n n=0 cr Question: 1 2 3 4 5 6 7 Tota
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Name: Student ID: Section: 2 Prof. Alan J. Laub Math 33A FINAL EXAMINATION Spring 2008 Instructions: June 9, 2008 (a) The exam is closed-book (except for one page of notes) and will last two and a half (2.5) hours. (b) Notation will conform as closely as
School: UCLA
Management 1A Summer 2004 Danny S. Litt EXAM 1 SOLUTION Name: _ Student ID No. _ I agree to have my grade posted by Student ID Number. _ (Signature) PROBLEM 1 2 3 4 5 6 7 8 9 10 TOTAL POINTS 20 20 20 20 20 20 20 20 20 20 200 SCORE MANAGEMENT 1A
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Math 31A Midterm 1 Solutions 1. [3 points] The derivative of (a) 1 (b) (c) x2 x)2 x3 Brent Nelson is: 1 x2 1 2 x3 (3x 1 1 + x2 + 8x2 x + 3) (d) None of the above. Solution. We rst apply the quotient rule d dx x2 x)2 x3 = d d x3 dx [(x2 x)2 ] (x2 x)2 dx (
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 solutions From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:/www.athenasc
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Mathemtcl Modeling
Math 142-2, Homework 1 Solutions April 7, 2014 Problem 34.4 Suppose the growth rate of a certain species is not constant, but depends in a known way on the temperature of its environment. If the temperature is known as a function of time, derive an expres
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi c c Homework 1 From the textbook solve the problems 1, 2, 3, 5, 6, 8, 11 and 14 at the end of the Chapter 4. And also the problems below: Problem 1. Give examples of (not independent) random variab
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 3 c c From the textbook solve the problems 29, 30, 31, 32 and 33 from the Chapter 4. Solve the problems 1, 2, 4, 5 and 6 from the Chapter 4 additional exercises at http:/www.athenasc.com
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
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Solutions for assignment 2 1 of 2 Section 2.2 Question 9: (a) (z-5i)^2 is a polynomial, hence continuous everywhere, and thus on e can simply substitute in the limit to obtain (2+3i)^2 - 5i)^2 = -8i. (c) This is an indeterminate form; one can either use L
School: UCLA
Course: Math 170
Probability Theory, Math 170b, Spring 2015, Toni Antunovi c c Homework 3 Due Friday, April 17th From the textbook solve the problems 17, 18 and 19 at the end of the Chapter 4. From the books supplementary problems, solve problem 30 in Chapter 4 (see http:
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a, Fall 2014 - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the
School: UCLA
Course: Introduction To Discrete Structures
MATH 61: HOMEWORK 2 3.3 25. not reexive, not symmetric, antisymmetric, transitive, not a partial order 26. reexive, not symmetric, antisymmetric, transitive, partial order 28. reexive, symmetric, not antisymmetric, transitive, not a partial order (this is
School: UCLA
Course: Probability Theory
Probability Theory, Math 170a - Homework 1 solutions Problem 1. Show that for any sets A and B P(A B) P(A) P(A B). Solution: One way to solve it is to notice that A B A and A A B and use the properties of the probability law (in particular the monotonicit
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 2/14/13 Homework #5 Due: Thursday Feb 21 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 1/8/13 Homework #1 Due: Thursday Jan 17 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the H
School: UCLA
Course: Introduction Of Complex Analysis
132 Homework 1 solutions Exercise 1 Suppose |z| = 1 and |a| < 1. Show that, za =1 1 az Solution. First, we must show that the left hand side is even dened, i.e. we are not dividing by zero. To show that 1 az = 0 is the same as to show that 1 = az. As |az|
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c solutions From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 addi
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 4 c c From the textbook solve the problems 42, 43 b) and 44 b), c) from the Chapter 4. Solve the problems 26, 27 and 29 from the Chapter 4 and problem 1 from the Chapter 7 additional exe
School: UCLA
Course: Mathemtcl Modeling
Math 142 Homework 1 Solution 34.5 (a) If the growth rate is 0, the discrete model becomes Nm+1 Nm = tfm , And the solution is Nm = N0 + t(f0 + f1 + fm1 ), which is analogous to integration, since let t = mt, then t t(f0 + f1 + fm1 ) f (s)ds 0 for t small
School: UCLA
Course: Probability Theory
Mathematics 170B Selected HW Solutions. F4 . Suppose Xn is B (n, p). (a) Find the moment generating function Mn (s) of (Xn np)/ np(1 p). Write q = 1 p. The MGF of Xn is (pes + q )n , since Xn can be written as the sum of n independent Bernoullis with para
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Course: Mathemtcl Modeling
Math 142 Homework 2 Solution 34.16 We will rstly proceed similarly as 34.14(c). We assume the theoretical growth has the form N0 eR0 t , and we hope to gure out which N0 and R0 t the data best. 34.14(b) suggests that N0 should be equal to the initial popu
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 2 c c From the textbook solve the problems 17, 18, 19, 22, 23 and 24 from the Chapter 4. Solve the problems 21, 22, 24, 30 from the Chapter 4 additional exercises at http:/www.athenasc.c
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 6 c c Solve the problems 18 a) c) d) e) and 19 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp.html And also the problems below: Problem 1. Denote points P0 ,
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Math32a HW1 Due on Monday, Jan 14 All the numbered problems are from the textbook Multivariable Calculus by Rogawski (2nd edition). Note: if your textbook is Early Transcendentals by Rogawski (2nd edition), then all your chapters are shifted by 1 down. Th
School: UCLA
Course: Introduction Of Complex Analysis
EE101 Engineering Electromagnetics Winter 2013 1/24/12 Homework #3 Due: Thursday Jan 31 10:00 AM Hand in to the TA at beginning of class. No late homework is accepted (see grading policy posted on eeweb). If you cannot make it to class, you must slip the
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Course: Mathematics OfFinance For Mathematics/Economics Students
Math 151A HW3 Solutions Will Feldman 1. (a) This is a translation of ln x (b) Noting that f (x) = ln (x + 2) is monotone and continuous we have that ln 2 x ln 4 for x [0, 2] and by the intermediate value theorem every value in [ln 2, ln 4] [0, 2] is obta
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Course: Real Analysis
Jerey Hellrung Wednesday, October 12, 2005 Math 245A, Homework 01 Chapter 1, # 3, 4, 5, 7, 8, 12, 14, 15 3. Let M be an innite -algebra. a. M contains an innite sequence of disjoint sets. b. card(M) c. Solution a. Construct the sequences cfw_En n=0 and c
School: UCLA
Course: Probability Theory
Probability Theory, Math 170b, Winter 2013, Toni Antunovi - Homework 5 c c From the textbook solve the problems 4 and 5 from the Chapter 5. Solve the problems 2, 4, 6, 7, 9 and 10 from the Chapter 7 additional exercises at http:/www.athenasc.com/prob-supp
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Math 172 B Class Project 1 Object: to download a specific mortality table from the Society of Actuaries website and utilize mortality rates to calculate life expectancies Steps: 1. Log onto www.soa.org 2. At the bottom of the opening page, select popular
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(a) (5 points) State the Comparison :L Denition 2. The function f is said in he continuum; in 3 i Hunk", (b) (5 points) is the series E convergent? Justify you VT" 5 3 V5 > u 35 > 0 V1, 5 S Ii 7 ml < ,5 :5 Ix) , ru) < EL Fu- 1 ire-qu'nru' Inn}. 'll. wail:
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Course: Math32A
Remarks and a trick for the osculating plane Remark. Note that there is an error on Professor Taylors solution to Problem 5. The error occurs when he computes aN (1). The correct computation of aN (1) is aN (1) = (2, 1, 3) (2, 2, 1) = (0, 1, 2) NOT aN (1)
School: UCLA
Course: Math32A
About the 32A Final Location and Time Lecture #1 (the 10AM lecture) will be held in Moore 100 on Sunday, June 7th from 3:00PM until 6:00PM Lecture #2 (the 12PM lecture) will be held in Lakretz 110 on Sunday, June 7th from 3:00PM until 6:00PM Sections Co
School: UCLA
Course: Math32A
Math 21a: Multivariable calculus Distances overview DISTANCE POINT-POINT (3D). If P and Q are two points, then d(P, Q) = |P Q| is the distance between P and Q. We use the notation |v| instaed of |v| in this handout. DISTANCE POINT-PLANE (3D). If P is a po
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Course: CALCULUS FOR LIFE SCIENCE STUDENTS
i Mod-h BRZZ fevgewg Fined exam : 3/ 511/10 3 wade? V g«:>m a? Fm? 8 Lag _.o/20\3;. «,McuwiL-ztuct mgnmicmmxmmnlm WWW : E i ; E g i i; 'Yilxnc Mum wk 56:. at "moat 21,5 x . buggy THom I W: MiAVerm Km? *6 K) thiem. ' . mm mm he. 1-71.-?Ec§k\em.(3'3. at:
School: UCLA
Course: CALCULUS FOR LIFE SCIENCE STUDENTS
YEAHEW 2 . = /:2.g~/ was Wm 3% f2 f MT 11 case-rs: 3A mans-t3 3n 2 Co Emmi/y 3. '3) Limrs (Kg :09 Q 4 Sandwmh eowm / "Triahmxts 3 S lnlrcrmeéle '- \que Theorem Bis-ecklom. Mei'hcsé make- SUgQL-f-J? 4r. 1. Degmttien .09. QXQKiVCWlVQ: : ' ' Ycu W "0 42
School: UCLA
Course: Calculus
31B Notes Sudesh Kalyanswamy 1 Exponential Functions (7.1) The following theorem pretty much summarizes section 7.1. Theorem 1.1. Rules for exponentials: (1) Exponential Rules (Algebra): (a) ax ay = ax+y (b) ax ay = x y axy (c) (a ) = axy (2) Derivatives
School: UCLA
School: UCLA
School: UCLA
The Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business, number of customers in waiting lines, number of defects in a given surface area, airplane arriv
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3C Notes Sudesh Kalyanswamy 1 Counting (12.1) 1.1 Guiding Questions for the Chapter Here are some questions for you to ask yourself as you read. If you can answer them all by the end, youre in pretty good shape as far as understanding the material. After
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3C Practice Problems for Midterm 1 Sudesh Kalyanswamy (1) Bills school schedule has four timeslots. Bill has 30 choices of classes for the rst timeslot, 20 for the second, 23 for the third, and 17 for the last. How many possible schedules are there? (2) C
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School: UCLA
Math 171 Spring 2013 Homework 8 (due Friday, June 7th at lecture time) (1) Read Sections 5.3 and 5.4. (2) Solve problems 2, 3, 4 and 6 from the end of chapter 5.
School: UCLA
School: UCLA
Course: INTEGRATION AND INFINITE SERIES
A dierential equation is an equation that relates the derivative of a function to that function (and possibly other functions). For example a dierential equation involving the function y (t) could look like dy (t) = ky (t) (1) dt for some constant k . Whe
School: UCLA
Course: Calculus
Answer Key B. Johnson Calculus AB Memory Quiz Important Relationships, Theorems, Rules, and Formulas Important Relationships 1. State the formal definition of derivative, include diagram. If y = f ( x ) then f ( x ) = lim h0 f ( x + h) f ( x) h 2. Where a
School: UCLA
Course: Introduction Of Complex Analysis
Math 132: Complex Analysis for Applications INSTRUCTOR: Kefeng Liu TIME and LOCATION: MWF 9:00-9:50AM, MS5117. OFFICE HOURS: TT 9:00-10:00AM in MS 6330 (Or by appointment) SYLLABUS: Official Syllabus Text: Complex Analysis by Tom Gamelin TA: Wenjian Liu,
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Course: Linear Algebra
Math 33A, Sec. 2 Linear Algebra and Applications Spring 2012 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 2:00 p.m. 2:50 p.m.; Rolfe 1200 Office
School: UCLA
Course: Algebra-applicatns
v P y V ` V ` x G ~ y | G V | ` ` F G G y V F F GI | V U )HoASY2dddI)dY)2vdG u !A)w u zAdA)YV y V ` V ` x G ~ | G V | ` ` G V F GI X y V G ` ` FI ` ` 6 8 4 8 1 HAa92ddd!I dY)2vdG u F AHWdYaHa2 9!4 20 P U b U y b q b Uv b pv b gv b i tAACttAAmYACt7t
School: UCLA
Course: Math32A
UCLA Math 32A, Lecture 1 (Spring Quarter 2015) Calculus of Several Variables Instructor: David Wihr Taylor Time/Location: MWF 10:00am-10:50am in Rolfe 1200. Text: Calculus (2nd edition) by Jon Rogawski ISBN: 9781429294904 (Contact the UCLA Store in Ackerm
School: UCLA
Course: Math 31A
Dierential and Integral Calculus, Math 31a, Fall 2013, Lec 1 - Course Info Instructor: Tonci Antunovic, 6156 Math Sciences Building, tantunovic@math.ucla.edu, www.math.ucla.edu/tantunovic Instructor Oce Hours: Monday 11-12:30 and Thursday 5-6:30 in 6156 M
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Course: Sftwr-scntfc Cmpttn
Environment12: SustainabilityandtheEnvironment Summer2015 UCLAInstituteoftheEnvironment AndSustainability Page 1 of 5 SustainabilityandtheEnvironment Summer2015 Synopsis: There are a number of social, demographic, and ecological changes concurrently affec
School: UCLA
Course: SYSTMS-DIFFNTL EQTN
Math 131 A/1: Analysis, UCLA, Spring 2015 Instructor name Dr. Roman Taranets, Department of Mathematics, UCLA E-mail: taranets @ math.ucla.edu Website: www.math.ucla.edu/~taranets Office Phone: (310) 825-4746 Office: MS 7360 Office Hours: MWF 9:00 am
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Course: SYSTMS-DIFFNTL EQTN
MATH 135-2 Instructor: Sungjin Kim, MS 6617A, E-mail: i707107@math.ucla.edu Meeting Time and Location: MWF 3:00 - 3:50 PM, Room: MS 5200 O ce Hours: MW 11:45 PM - 12:30 PM, Room: MS 6617A Textbook: G. Simmons, Dierential Equations (2nd) with Applications
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Course: Differential Equations
Math 33B, Differential Equations Lecture 1, Spring 2015 Instructor: Will Conley Email: wconley@ucla.edu Office: MS 6322 Office Hours: Tentatively Wednesdays 3:004:00 Thursdays 12:001:30 and 3:004:00, and by appointment Website: http:/www.math.ucla.edu/~wc
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Math 174E (Summer 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWR 11:00am-12:50pm in MS 5137. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: TBA Email Address
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Math 174E, Lecture 1 (Winter 2014) Mathematics of Finance Instructor: David W. Taylor Time/Location: MWF 3:00pm-3:50pm in MS 5127. Text: Options, Futures, and Other Derivatives (8th edition) by John C. Hull. Instructor: David W. Taylor Oce Hours: Monday a
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Math 3B Integral calculus and differential equations Prof. M. Roper Young Hall CS 76, MWF 2-2.50pm. All inquiries about this class should be posted to the class Piazza page. The only emails that I will respond to are questions about how to login to Piazza
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Course: Calculus
Sample Syllabus Philosophical Analysis of Contemporary Moral Issues Winter 2015, MW 8-9:50 Instructor: Robert Hughes (hughes@humnet.ucla.edu) Instructor office hours: Dodd 378, M 11-12 and W 10-11 or by appointment TAs: Kelsey Merrill (kmerrill@humnet.ucl
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Course: Math 170
Probability Theory, Math 170A, Winter 2015 - Course Info Instructor: Tonci Antunovic, 6156 Math Sciences Building, tantunovic@math.ucla.edu, www.math.ucla.edu/~tantunovic Instructor Oce Hours: Monday 10-12am and Wednesday 9-10am in 6156 Math Sciences Buil
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Course: Math 1
Math1 Fall2012 Lecture1(8am),Lecture2(10am)andLecture3(1pm) Instructor Paige Greene E-Mail: paige@math.ucla.edu Office Number: MS 6617 B Office Hours: Mon and Wed (copy from me in class) Course Goals: The purpose of Math 1 is to give you a strong preparat
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Math33BDifferentialEquations Winter2015,lecture3 Time:MWF3:003:50p.m. Room:MS4000A Discussionsections: 3A T3:00P3:50PGEOLOGY6704 3B R3:00P3:50PGEOLOGY4645 Instructor:YuZhang Office:MS6617F Officehours:Monday2:003:00p.m. Wednesday4:006:00p.m. Email:yuzhang
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Math 3B Integral calculus and differential equations Prof. M. Roper Young Hall CS 76, MWF 2-2.50pm. All inquiries about this class should be posted to the class Piazza page. The only emails that I will respond to are questions about how to login to Piazza
School: UCLA
Course: Actuarial Math
Math 172A: Syllabus, Structure, Details and Policies (Fall 2014) Introduction to Financial Mathematics This course is designed to provide an understanding of basic concepts of actuarial/financial mathematics. The course touches most (but not all) syllabus
School: UCLA
Course: Abstract Algebra
Math 32B (Calculus of several variables), Section 2 Fall 2013 MWF 2:00-2:50 pm, 1178 Franz Hall UCLA Instructor: William Simmons, MS 6617A, simmons@math.ucla.edu. Oce Hours (held in MS 6617A): M: 8:00-8:55 am T: 10:30-11:30 am W: 3:30-4:30 pm Teaching Ass
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Math 115A, Linear Algebra, Lecture 6, Fall 2014 Exterior Course Website: http:/www.math.ucla.edu/heilman/115af14.html Prerequisite: MATH 33A, Linear algebra and applications. Course Content: Linear independence, bases, orthogonality, the Gram-Schmidt proc
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Math 32A, Calculus of Several Variables Lecture 1, Winter 2014 Instructor: Will Conley Email: wconley@ucla.edu Office: MS 6322 Office Hours: Tentatively Wednesdays 11:3012:30, Thursdays 1:302:30, and any other time by appointment. Website: http:/www.math.
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Math 33A, Section 2 Linear Algebra and Applications Winter 2014 Instructor: Professor Alan J. Laub Dept. of Mathematics / Electrical Engineering Math Sciences 7945 phone: 310-825-4245 e-mail: laub@ucla.edu Lecture: MWF 1:00 p.m. 1:50 p.m. Math Sciences 40
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Math1 Fall2012 Lecture1(8am),Lecture2(10am)andLecture3(1pm) Instructor Paige Greene E-Mail: paige@math.ucla.edu Office Number: MS 6617 B Office Hours: Mon and Wed (copy from me in class) Course Goals: The purpose of Math 1 is to give you a strong preparat
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Differential Equations MATH 33B-1 Instructor Details: Lecture 1: Instructor: Office: Office hours: MWF 12PM-12:50PM in MOORE 100 Prof. Zachary Maddock MS 6236 (MS := Mathematical Sciences) Mondays 1:30PM-2:30PM Wednesdays 9:50AM-10:50AM, 1:30PM-2:30PM Tea
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Course: Linear Algebra
Course information and Policy, v. of Oct.1st, 2013 Marc-Hubert NICOLE Linear Algebra with Applications Math 33A-1, Lecture 1, Fall 2013. U.C.L.A. -Instructor Marc-Hubert NICOLE Lectures: MWF 8:00-8:50 AM in Rolfe 1200. Ofce: MS 5230 (see Ofce Hours belo
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Course: Linear Algebra
Winter 2011, UCLA Department of Economics Economics 106G: Introduction to Game Theory Instructor: Ichiro Obara Bunche 9381 E-mail: iobara@econ.ucla.edu Web: http:/www.econ.ucla.edu/iobara Office Hour: Tuesday 1:00pm - 2:30pm or by appointment. Time and Lo
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Course: Linear Algebra
Math 115A Fall 2012 Professor: David Gieseker Oce: Math Sciences 5636. Phone: 206-6321, email: dag at math ucla edu Oce Hours: M, W, F 9:30-10, 11-11:30. M,W 2-2:30 and by appointment. Text: Linear Algebra, Friedberg, Insel, Spence. Material to be covered
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S YLLABUS : P HYSICS 1B, L ECTURE 1, W INTER 2012 I NSTRUCTOR : Prof. Troy Carter 4-909 PAB (310) 825-4770 tcarter@physics.ucla.edu O FFICE H OURS : M 10-11AM, T 1PM-2PM, F 1-2PM, other times by appointment C OURSE A DMINISTRATOR : Elaine Dolalas (handles
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Math 3C, Probability for Life Sciences Students, Lecture 2, Spring 2012 Instructor: Thomas Sinclair E-mail: thomas.sinclair@math.ucla.edu Oce: Math Sciences (MS) 7304 Oce Hours: M 3:004:30, W 11:0012:30 TAs: 2a,b Theodore Gast Oce: MS 2961 Oce Hours: TBA
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Mathematics 31B: Integration and Innite Series. Fall 2012 Instructor: David Weisbart Email: dweisbar@math.ucla.edu Textbook: J. Rogawski, Single Variable Calculus, 2nd Ed., W.H. Freeman & Co. 31B Teaching Statement: Along with 31A, this course is the foun