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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: 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: 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
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: 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: 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: 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
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: 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: 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: 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: 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: 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: 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: 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
% 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
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: 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: 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