MULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS


 Bertram Allen
 1 years ago
 Views:
Transcription
1 T H I R D E D I T I O N MULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS STANLEY I. GROSSMAN University of Montana and University College London SAUNDERS COLLEGE PUBLISHING HARCOURT BRACE COLLEGE PUBLISHERS Fort Worth Philadelphia San Diego New York Orlando Austin San Antonio Toronto Montreal London Sydney Tokyo
2 TABLE OF CONTENTS MULTIVARIABLE CALCULUS VECTORS IN THE PLANE AND IN SPACE, 3 Vectors and Vector Operations, 4 The Dot Product, 14 The Rectangular Coordinate System in Space, 24 Vectors in U\ 28 Lines in IR 3, 36 The Cross Product of Two Vectors, 42 Planes, 52 Quadric Surfaces, 59 Cylindrical and Spherical Coordinates, 66 The Space W and the Scalar Product (Optional), 72 Summary Outline, 80 Review Exercises, 83 2 VECTOR FUNCTIONS AND PARAMETRIC EQUATIONS, Vector Functions and Parametric Equations, The Equation of the Tangent Line to a Plane Curve and Smoothness, The Differentiation and Integration of a Vector Function, Some Differentiation Formulas, Arc Length Revisited, Curvature and the Acceleration Vector (Optional), 120 Summary Outline, 131 Review Exercises, 133 Computer Exercises, DIFFERENTIATION OF FUNCTIONS OF TWO OR MORE VARIABLES, 1 35 Functions of Two or More Variables, 136 Limits and Continuity, 147 Partial Derivatives, 162 HigherOrder Partial Derivatives, 170 Differentiability and the Gradient, 178 The Chain Rule, 186 Tangent Planes, Normal Lines, and Gradients, 197 Directional Derivatives and the Gradient, 201 The Total Differential and Approximation, 210 Maxima and Minima for a Function of Two Variables, 212 Constrained Maxima and Minima Lagrange Multipliers, 222 Newton's Method for Functions of Two Variables (Optional), 232 Summary Outline, 236 Review Exercises, 240 Computer Exercises, 242 MULTIPLE INTEGRATION, 243 Volume Under a Surface and the Double Integral, 243 The Calculation of Double Integrals, 253 Density, Mass, and Center of Mass (Optional), 265 Double Integrals in Polar Coordinates, 269 The Triple Integral, 275 The Triple Integral in Cylindrical and Spherical Coordinates, 282 Summary Outline, 287 Review Exercises, 289 Computer Exercises, 290 XIII
3 XIV TABLE OF CONTENTS 5 INTRODUCTION TO VECTOR ANALYSIS, Vector Fields, Work and Line Integrals, Exact Vector Fields and Independence of Path, Green's Theorem in the Plane, The Parametric Representation of a Surface and Surface Area, Surface Integrals, Divergence and Curl, Stokes's Theorem, The Divergence Theorem, Changing Variables in Multiple Integrals and the Jacobian, 356 Summary Outline, 364 Review Exercises, 367 LINEAR ALGEBRA SYSTEMS OF LINEAR EQUATIONS AND MATRICES, 371 Introduction, 371 Two Linear Equations in Two Unknowns, 372 m Equations in n Unknowns: GaussJordan and Gaussian Elimination, 376 Homogeneous Systems of Equations, 390 Matrices, 393 Matrix Products, 400 Matrices and Linear Systems of Equations, 410 The Inverse of a Square Matrix, 415 The Transpose of a Matrix, 432 Elementary Matrices and Matrix Inverses, 436 Summary Outline, 444 Review Exercises, 446 DETERMINANTS, 448 Definitions, 448 Properties of Determinants, 457 Determinants and Inverses, 473 Cramer's Rule (Optional), 479 Summary Outline, 483 Review Exercises, VECTOR SPACES AND LINEAR TRANSFORMATIONS, Vector Spaces, Subspaces, Linear Combination and Span, Linear Independence, Basis and Dimension, The Rank, Nullity, Row Space, and Column Space of a Matrix, Orthonormal Bases and Projections in W Least Squares Approximation, Linear Transformations, Properties of Linear Transformations: Range and Kernel, The Matrix Representation of a Linear Transformation, Isomorphisms, Eigenvalues and Eigenvectors, A Model of Population Growth (Optional), Similar Matrices and Diagonalization, Symmetric Matrices and Orthogonal Diagonalization, Quadratic Forms and Conic Sections, 615 Summary Outline, 624 Review Exercises, 628
4 TABLE OF CONTENTS XV PART III INTRODUCTION TO INTERMEDIATE CALCULUS CALCULUS IN U n, 632 Taylor's Theorem in n Variables, 632 Inverse Functions and the Implicit Function Theorem: I, 642 Functions from W to W, Derivatives and the Jacobian Matrix, Inverse Functions and the Implicit Function Theorem: II, 663 Summary Outline, 674 Review Exercises, 676 PART IV DIFFERENTIAL EQUATIONS 10 ORDINARY DIFFERENTIAL EQUATIONS, Introduction, Review of the Differential Equation of Exponential Growth, FirstOrder Equations Separation of Variables, Linear First Order Differential Equations, Exact Differential Equations (Optional), Simple Electric Circuits, Theory of Linear Differential Equations, Using One Solution to Find Another: Reduction of Order, Homogeneous Equations with Constant Coefficients: Real Roots, Homogeneous Equations with Constant Coefficients: Complex Roots, Nonhomogeneous Equations I: Variation of Parameters, Nonhomogeneous Equations II: The Method of Undetermined Coefficients, Euler Equations, Vibratory Motion (Optional), More on Electric Circuits (Optional), HigherOrder Linear Differential Equations (Optional), ' Numerical Solution of Differential Equations: Euler's Methods, 797 Summary Outline, 803 Review Exercises, SYSTEMS OF DIFFERENTIAL EQUATIONS, 8O The Method of Elimination for Linear Systems with Constant Coefficients, Linear Systems: Theory, The Solution of Homogeneous Linear Systems with Constant Coefficients: The Method of Determinants, Electric Circuits with Several Loops (Optional), Mechanical Systems, A Model for Epidemics (Optional), Matrices and Systems of Linear FirstOrder Equations Fundamental Sets and Fundamental Matrix Solutions of a Homogeneous System of Differential Equations, The Computation of the Principal Matrix Solution to a Homogeneous System of Equations with Constant Coefficients, Nonhomogeneous Systems, An Application of Nonhomogeneous Systems: Forced Oscillations (Optional), 880
5 XVI TABLE OF CONTENTS Computing e At : An Application of the Cayley Hamilton Theorem (Optional), 884 Summary Outline, 893 Review Exercises, 897 PART V SEQUENCES AND SERIES 12 TAYLOR POLYNOMIALS, SEQUENCES, AND SERIES, Taylor's Theorem and Taylor Polynomials, Approximation Using Taylor Polynomials, Sequences of Real Numbers, Bounded and Monotonic Sequences, Geometric Series, Infinite Series, Series with Nonnegative Terms I: Two Comparison Tests and the Integral Test, Series with Nonnegative Terms II: The Ratio and Root Tests, Absolute and Conditional Convergence: Alternating Series, Power Series, Differentiation and Integration of Power Series, Taylor and Maclaurin Series, Using Power Series to Solve Ordinary Differential Equations (Optional), 994 Summary Outline, 1002 Review Exercises, 1006 Computer Exercises, 1008 APPENDIX 1 MATHEMATICAL INDUCTION, A1 APPENDIX 2 THE BINOMIAL THEOREM, A6 APPENDIX 3 COMPLEX NUMBERS, A14 APPENDIX 4 PROOF OF THE BASIC THEOREM ABOUT DETERMINANTS, A21 APPENDIX 5 EXISTENCE AND UNIQUENESS FOR FIRST ORDER INITIALVALUE PROBLEMS, A24 APPENDIX 6 THE FOUNDATIONS OF VECTOR SPACE THEORY: THE EXISTENCE OF A BASIS, A37 TABLE OF INTEGRALS, A43 ANSWERS TO ODDNUMBERED PROBLEMS AND REVIEW EXERCISES, A51 INDEX, 11
DENNIS D. BERKEY. Boston University PAUL BLANCHARD. Boston University
i Calculus T H I R D E D I T I O N DENNIS D. BERKEY Boston University PAUL BLANCHARD Boston University SAUNDERS COLLEGE PUBLISHING Harcourt Brace Jovanovich College Publishers Fort Worth Philadelphia San
More informationMATHEMATICS COMPREHENSIVE EXAM: INCLASS COMPONENT
MATHEMATICS COMPREHENSIVE EXAM: INCLASS COMPONENT The following is the list of questions for the oral exam. At the same time, these questions represent all topics for the written exam. The procedure for
More informationUpon successful completion of MATH 220, the student will be able to:
MATH 220 Matrices Upon successful completion of MATH 220, the student will be able to: 1. Identify a system of linear equations (or linear system) and describe its solution set 2. Write down the coefficient
More informationMath 302 Outcome Statements Winter 2013
Math 302 Outcome Statements Winter 2013 1 Rectangular Space Coordinates; Vectors in the ThreeDimensional Space (a) Cartesian coordinates of a point (b) sphere (c) symmetry about a point, a line, and a
More informationRobert Seeley. University of Massachusetts at Boston. ini HARCOURT BRACE JOVANOVICH, PUBLISHERS. and its subsidiary, Academic Press
L MMH^^S^^^K Robert Seeley University of Massachusetts at Boston ini Qf HARCOURT BRACE JOVANOVICH, PUBLISHERS and its subsidiary, Academic Press San Diego New York Chicago Austin Washington, D.C. London
More informationCALCULUS GARRET J. ETGEN SALAS AND HILLE'S. ' MiIIIIIIH. I '////I! li II ii: ONE AND SEVERAL VARIABLES SEVENTH EDITION REVISED BY \
/ / / ' ' ' / / ' '' '  '/' yy xy xy' y y/ /:  y/ yy y /'}' / >' // yy,y' 'y '/' /y , I '////I! li II ii: ' MiIIIIIIH IIIIII!l ii ri: V / A' /; // ;.1 " SALAS AND HILLE'S
More informationCalculus from Graphical, Numerical, and Symbolic Points of View, 2e Arnold Ostebee & Paul Zorn
Calculus from Graphical, Numerical, and Symbolic Points of View, 2e Arnold Ostebee & Paul Zorn Chapter 1: Functions and Derivatives: The Graphical View 1. Functions, Calculus Style 2. Graphs 3. A Field
More informationVarberg 8e9eET Version Table of Contents Comparisons
Varberg 8e9eET Version Table of Contents Comparisons 8th Edition 9th Edition Early Transcendentals 9 Ch Sec Title Ch Sec Title Ch Sec Title 1 PRELIMINARIES 0 PRELIMINARIES 0 PRELIMINARIES 1.1 The Real
More informationMA3025 Course Prerequisites
MA3025 Course Prerequisites MA 3025 (41) MA3025 (41) Logic and Discrete Mathematics: Provides a rigorous foundation in logic and elementary discrete mathematics. Topics from logic include modeling English
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWSKENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More information9TH EDITION. George B. Thomas, Jr. Massachusetts Institute of Technology. Ross L. Finney. With the collaboration of Maurice D.
9TH EDITION Calculus and Analytic Geometry George B. Thomas, Jr. Massachusetts Institute of Technology Ross L. Finney With the collaboration of Maurice D. Weir Naval Postgraduate School ^ AddisonWesley
More informationMathematical Methods for Engineers and Scientists 1
K.T. Tang Mathematical Methods for Engineers and Scientists 1 Complex Analysis, Determinants and Matrices With 49 Figures and 2 Tables fyj Springer Part I Complex Analysis 1 Complex Numbers 3 1.1 Our Number
More informationNORCO COLLEGE SLO to PLO MATRIX
SLO to PLO MATRI CERTIFICATE/PROGRAM: Math ADT COURSE: MAT1A Calculus I Calculate the limit of a function. SLO 2 Determine the continuity of a function. Find the derivatives of algebraic and transcendental
More informationELEMENTARY MATRIX ALGEBRA
ELEMENTARY MATRIX ALGEBRA Third Edition FRANZ E. HOHN DOVER PUBLICATIONS, INC. Mineola, New York CONTENTS CHAPTER \ Introduction to Matrix Algebra 1.1 Matrices 1 1.2 Equality of Matrices 2 13 Addition
More informationUNIVERSITY OF NORTH ALABAMA MA 110 FINITE MATHEMATICS
MA 110 FINITE MATHEMATICS Course Description. This course is intended to give an overview of topics in finite mathematics together with their applications and is taken primarily by students who are not
More informationGATE Engineering Mathematics SAMPLE STUDY MATERIAL. Postal Correspondence Course GATE. Engineering. Mathematics GATE ENGINEERING MATHEMATICS
SAMPLE STUDY MATERIAL Postal Correspondence Course GATE Engineering Mathematics GATE ENGINEERING MATHEMATICS ENGINEERING MATHEMATICS GATE Syllabus CIVIL ENGINEERING CE CHEMICAL ENGINEERING CH MECHANICAL
More informationFINITEDIMENSIONAL LINEAR ALGEBRA
DISCRETE MATHEMATICS AND ITS APPLICATIONS Series Editor KENNETH H ROSEN FINITEDIMENSIONAL LINEAR ALGEBRA Mark S Gockenbach Michigan Technological University Houghton, USA CRC Press Taylor & Francis Croup
More informationENGINEERING MATHEMATICS I. CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 PARTA
ENGINEERING MATHEMATICS I CODE: 10 MAT 11 IA Marks: 25 Hrs/Week: 04 Exam Hrs: 03 Total Hrs: 52 Exam Marks:100 PARTA UnitI: DIFFERENTIAL CALCULUS  1 Determination of n th derivative of standard functionsillustrative
More informationHarbor Creek School District
Unit 1 Days 19 Evaluate onesided twosided limits, given the graph of a function. Limits, Evaluate limits using tables calculators. Continuity Evaluate limits using direct substitution. Differentiability
More informationReduction to the associated homogeneous system via a particular solution
June PURDUE UNIVERSITY Study Guide for the Credit Exam in (MA 5) Linear Algebra This study guide describes briefly the course materials to be covered in MA 5. In order to be qualified for the credit, one
More informationMEAN VALUE THEOREMS FUNCTIONS OF SINGLE & SEVERAL VARIABLES
MATHEMATICSI MEAN VALUE THEOREMS FUNCTIONS OF SINGLE & SEVERAL VARIABLES I YEAR B.TECH By Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam, Hyderabad. Name
More informationCALCULUS. C. HENRY EDWARDS The University of Georgia, Athens. DAVID E. PENNEY The University of Georgia, Athens. Prentice Hall
CALCULUS C. HENRY EDWARDS The University of Georgia, Athens DAVID E. PENNEY The University of Georgia, Athens Prentice Hall Pearson Education International CONTENTS ABOUT THE AUTHORS PREFACE XI xiii CHAPTER
More informationLinear Algebra I for Science (NYC)
Element No. 1: To express concrete problems as linear equations. To solve systems of linear equations using matrices. Topic: MATRICES 1.1 Give the definition of a matrix, identify the elements and the
More informationENGINEERINGMATHEMATICSI. Hrs/Week:04 Exam Hrs: 03 Total Hrs:50 Exam Marks :100
ENGINEERINGMATHEMATICSI CODE: 14MAT11 IA Marks:25 Hrs/Week:04 Exam Hrs: 03 Total Hrs:50 Exam Marks :100 UNIT I Differential Calculus 1 Determination of n th order derivatives of Standard functions 
More informationhomogeneous 71 hyperplane 10 hyperplane 34 hyperplane 69 identity map 171 identity map 186 identity map 206 identity matrix 110 identity matrix 45
address 12 adjoint matrix 118 alternating 112 alternating 203 angle 159 angle 33 angle 60 area 120 associative 180 augmented matrix 11 axes 5 Axiom of Choice 153 basis 178 basis 210 basis 74 basis test
More informationMathematics (MAT) MAT 051 PreAlgebra. 4 Hours. Prerequisites: None. 4 hours weekly (40)
Mathematics (MAT) MAT 051 PreAlgebra 4 Hours Prerequisites: None 4 hours weekly (40) MAT 051 is designed as a review of the basic operations of arithmetic and an introduction to algebra. The student
More informationGlossary of Linear Algebra Terms. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB
Glossary of Linear Algebra Terms Basis (for a subspace) A linearly independent set of vectors that spans the space Basic Variable A variable in a linear system that corresponds to a pivot column in the
More informationDepartment: Course Description: Course Competencies: MAT 201 Calculus III Prerequisite: MAT Credit Hours (Lecture) Mathematics
Department: Mathematics Course Description: Calculus III is the final course in the threesemester sequence of calculus courses. This course is designed to prepare students to be successful in Differential
More informationSCIENCE PROGRAM CALCULUS III
SCIENCE PROGRAM CALCULUS III Discipline: Mathematics Semester: Winter 2002 Course Code: 201DDB05 Instructor: R.A.G. Seely Objectives: 00UV, 00UU Office: H 204 Ponderation: 323 Tel.: 4576610 Credits:
More informationCalculus. reparation for Calculus, Limits and Their Properties, and Differentiation. Gorman Learning Center (052344) Basic Course Information
Calculus Gorman Learning Center (052344) Basic Course Information Title: Calculus Transcript abbreviations: calcag / calc Length of course: Full Year Subject area: Mathematics ("c") / Calculus UC honors
More informationCourse Code: MTHS101 Breakup: 3 1 0 4 Course Name: MathematicsI Course Details: UnitI: Sequences & Series: Definition, Monotonic sequences, Bounded sequences, Convergent and Divergent Sequences Infinite
More informationLAKELAND COMMUNITY COLLEGE COURSE OUTLINE FORM
LAKELAND COMMUNITY COLLEGE COURSE OUTLINE FORM ORIGINATION DATE: 8/2/99 APPROVAL DATE: 3/22/12 LAST MODIFICATION DATE: 3/28/12 EFFECTIVE TERM/YEAR: FALL/ 12 COURSE ID: COURSE TITLE: MATH2800 Linear Algebra
More informationMathematica for Rogawski's 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 Copyright 2010 Table of
More informationAdvanced. Engineering Mathematics
Advanced Engineering Mathematics A new edition of Further Engineering Mathematics K. A. Stroud Formerly Principal Lecturer Department of Mathematics, Coventry University with additions by Dexter j. Booth
More informationThe value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver I.N.
Math 410 Homework Problems In the following pages you will find all of the homework problems for the semester. Homework should be written out neatly and stapled and turned in at the beginning of class
More informationSCIENCE PROGRAM CALCULUS III
SCIENCE PROGRAM CALCULUS III Discipline: Mathematics Semester: Fall 2003 Course Code: 201DDB05 Instructor: R.A.G. Seely Objectives: 00UV, 00UU Office: H 204 Ponderation: 323 Tel.: 4576610 Credits:
More informationLinear Algebra Practice Problems
Linear Algebra Practice Problems Page of 7 Linear Algebra Practice Problems These problems cover Chapters 4, 5, 6, and 7 of Elementary Linear Algebra, 6th ed, by Ron Larson and David Falvo (ISBN3 = 97868783762,
More informationWest WindsorPlainsboro Regional School District AP Calculus BC Grades 912
West WindsorPlainsboro Regional School District AP Calculus BC Grades 912 Unit 1: Limits and Continuity What is a limit? Definition of limit, continuous, Sandwich Theorem, Intermediate Value Theorem
More informationSCIENCE PROGRAM CALCULUS III
SCIENCE PROGRAM CALCULUS III Discipline: Mathematics Semester: Winter 2005 Course Code: 201DDB05 Instructor: Objectives: 00UV, 00UU Office: Ponderation: 323 Tel.: 4576610 Credits: 2 2/3 Local: Course
More informationAS and A level Further mathematics contents lists
AS and A level Further mathematics contents lists Contents Core Pure Mathematics Book 1/AS... 2 Core Pure Mathematics Book 2... 4 Further Pure Mathematics 1... 6 Further Pure Mathematics 2... 8 Further
More informationMobile Robotics 1. A Compact Course on Linear Algebra. Giorgio Grisetti
Mobile Robotics 1 A Compact Course on Linear Algebra Giorgio Grisetti SA1 Vectors Arrays of numbers They represent a point in a n dimensional space 2 Vectors: Scalar Product ScalarVector Product Changes
More informationConceptual Questions for Review
Conceptual Questions for Review Chapter 1 1.1 Which vectors are linear combinations of v = (3, 1) and w = (4, 3)? 1.2 Compare the dot product of v = (3, 1) and w = (4, 3) to the product of their lengths.
More informationMATHEMATICS FOR ECONOMISTS. An Introductory Textbook. Third Edition. Malcolm Pemberton and Nicholas Rau. UNIVERSITY OF TORONTO PRESS Toronto Buffalo
MATHEMATICS FOR ECONOMISTS An Introductory Textbook Third Edition Malcolm Pemberton and Nicholas Rau UNIVERSITY OF TORONTO PRESS Toronto Buffalo Contents Preface Dependence of Chapters Answers and Solutions
More informationSemester I. Mathematics I (Calculus with applications in Chemistry I) Code: MM
University of Kerala Complementary Course in Mathematics for First Degree Programme in Chemistry Semester I Mathematics I (Calculus with applications in Chemistry I) Code: MM 1131.2 Instructional hours
More informationAnalytical Mechanics for Relativity and Quantum Mechanics
Analytical Mechanics for Relativity and Quantum Mechanics Oliver Davis Johns San Francisco State University OXPORD UNIVERSITY PRESS CONTENTS Dedication Preface Acknowledgments v vii ix PART I INTRODUCTION:
More informationMULTIVARIABLE CALCULUS 61
MULTIVARIABLE CALCULUS 61 Description Multivariable Calculus is a rigorous second year course in college level calculus. This course provides an indepth study of vectors and the calculus of several variables
More informationBASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA
1 BASIC EXAM ADVANCED CALCULUS/LINEAR ALGEBRA This part of the Basic Exam covers topics at the undergraduate level, most of which might be encountered in courses here such as Math 233, 235, 425, 523, 545.
More informationTABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiplechoice test 7 Problem set 9
TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1 Chapter 01.01 Introduction to numerical methods 1 Multiplechoice test 7 Problem set 9 Chapter 01.02 Measuring errors 11 True error 11 Relative
More information1 9/5 Matrices, vectors, and their applications
1 9/5 Matrices, vectors, and their applications Algebra: study of objects and operations on them. Linear algebra: object: matrices and vectors. operations: addition, multiplication etc. Algorithms/Geometric
More informationMathematics for Chemists
Mathematics for Chemists MATHEMATICS FOR CHEMISTS D. M. Hirst Department of Molecular Sciences, university of Warwick, Coventry M D. M. Hirst 1976 All rights reserved. No part of this publication may be
More informationGAME PHYSICS SECOND EDITION. дяййтаййг 1 *
GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers
More informationMATHEMATICAL FORMULAS AND INTEGRALS
HANDBOOK OF MATHEMATICAL FORMULAS AND INTEGRALS Second Edition ALAN JEFFREY Department of Engineering Mathematics University of Newcastle upon Tyne Newcastle upon Tyne United Kingdom ACADEMIC PRESS A Harcourt
More informationContents. Part I Vector Analysis
Contents Part I Vector Analysis 1 Vectors... 3 1.1 BoundandFreeVectors... 4 1.2 Vector Operations....................................... 4 1.2.1 Multiplication by a Scalar.......................... 5 1.2.2
More informationTABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1. Chapter Introduction to numerical methods 1 Multiplechoice test 7 Problem set 9
TABLE OF CONTENTS INTRODUCTION, APPROXIMATION & ERRORS 1 Chapter 01.01 Introduction to numerical methods 1 Multiplechoice test 7 Problem set 9 Chapter 01.02 Measuring errors 11 True error 11 Relative
More informationLinear Algebra: Matrix Eigenvalue Problems
CHAPTER8 Linear Algebra: Matrix Eigenvalue Problems Chapter 8 p1 A matrix eigenvalue problem considers the vector equation (1) Ax = λx. 8.0 Linear Algebra: Matrix Eigenvalue Problems Here A is a given
More informationCourse Outline. 2. Vectors in V 3.
1. Vectors in V 2. Course Outline a. Vectors and scalars. The magnitude and direction of a vector. The zero vector. b. Graphical vector algebra. c. Vectors in component form. Vector algebra with components.
More informationCHAPTER 1 Prerequisites for Calculus 2. CHAPTER 2 Limits and Continuity 58
CHAPTER 1 Prerequisites for Calculus 2 1.1 Lines 3 Increments Slope of a Line Parallel and Perpendicular Lines Equations of Lines Applications 1.2 Functions and Graphs 12 Functions Domains and Ranges Viewing
More informationContents. Preface for the Instructor. Preface for the Student. xvii. Acknowledgments. 1 Vector Spaces 1 1.A R n and C n 2
Contents Preface for the Instructor xi Preface for the Student xv Acknowledgments xvii 1 Vector Spaces 1 1.A R n and C n 2 Complex Numbers 2 Lists 5 F n 6 Digression on Fields 10 Exercises 1.A 11 1.B Definition
More informationHOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS
HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 217 Linear Algebra CREDIT HOURS: 4.0 EQUATED HOURS: 4.0 CLASS HOURS: 4.0 PREREQUISITE: PRE/COREQUISITE: MAT 210 Calculus I MAT 220 Calculus II RECOMMENDED
More informationUNIVERSITY OF PUNE, PUNE BOARD OF STUDIES IN MATHEMATICS S.Y. B. Sc. (MATHEMATICS) SYLLABUS. S.Y.B.Sc. MT:211 Linear Algebra MT:221
UNIVERSITY OF PUNE, PUNE 411007 BOARD OF STUDIES IN MATHEMATICS S.Y. B. Sc. (MATHEMATICS) SYLLABUS S.Y.B.Sc Paper I Paper II SemesterI Calculus of Several Variables A) : Differential Equations SemesterII
More informationA geometric proof of the spectral theorem for real symmetric matrices
0 0 0 A geometric proof of the spectral theorem for real symmetric matrices Robert Sachs Department of Mathematical Sciences George Mason University Fairfax, Virginia 22030 rsachs@gmu.edu January 6, 2011
More informationCalculus Early Transcendentals
Calculus Early Transcendentals 9781635451016 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts
More informationMath 1553, Introduction to Linear Algebra
Learning goals articulate what students are expected to be able to do in a course that can be measured. This course has courselevel learning goals that pertain to the entire course, and sectionlevel
More informationSTATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING TNCF DRAFT SYLLABUS.
STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING TNCF 2017  DRAFT SYLLABUS Subject :Mathematics Class : XI TOPIC CONTENT Unit 1 : Real Numbers  Revision : Rational, Irrational Numbers, Basic Algebra
More informationApplied Linear Algebra
Applied Linear Algebra Peter J. Olver School of Mathematics University of Minnesota Minneapolis, MN 55455 olver@math.umn.edu http://www.math.umn.edu/ olver Chehrzad Shakiban Department of Mathematics University
More informationMATHEMATICS. Units Topics Marks I Relations and Functions 10
MATHEMATICS Course Structure Units Topics Marks I Relations and Functions 10 II Algebra 13 III Calculus 44 IV Vectors and 3D Geometry 17 V Linear Programming 6 VI Probability 10 Total 100 Course Syllabus
More informationCalculus Early Transcendentals
Calculus Early Transcendentals 9781635451016 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts
More informationCalculus Early Transcendentals
Calculus Early Transcendentals 9781635451016 To learn more about all our offerings Visit Knewton.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Gilbert Strang, Massachusetts
More informationChap 3. Linear Algebra
Chap 3. Linear Algebra Outlines 1. Introduction 2. Basis, Representation, and Orthonormalization 3. Linear Algebraic Equations 4. Similarity Transformation 5. Diagonal Form and Jordan Form 6. Functions
More informationCalculus III SCIENCE PROGRAM COURSE OUTLINE WINTER 2019
Calculus III SCIENCE PROGRAM COURSE OUTLINE WINTER 2019 General Information. Discipline: Mathematics Course code: 201DDB05 Ponderation: 323 Credits: 2 2 3 Prerequisite: 201NYB05 (grade> 65%) Objectives:
More information2. TRIGONOMETRY 3. COORDINATEGEOMETRY: TWO DIMENSIONS
1 TEACHERS RECRUITMENT BOARD, TRIPURA (TRBT) EDUCATION (SCHOOL) DEPARTMENT, GOVT. OF TRIPURA SYLLABUS: MATHEMATICS (MCQs OF 150 MARKS) SELECTION TEST FOR POST GRADUATE TEACHER(STPGT): 2016 1. ALGEBRA Sets:
More information8. Diagonalization.
8. Diagonalization 8.1. Matrix Representations of Linear Transformations Matrix of A Linear Operator with Respect to A Basis We know that every linear transformation T: R n R m has an associated standard
More informationTakeHome Exam 1: pick up on Thursday, June 8, return Monday,
SYLLABUS FOR 18.089 1. Overview This course is a review of calculus. We will start with a weeklong review of single variable calculus, and move on for the remaining five weeks to multivariable calculus.
More information2. Every linear system with the same number of equations as unknowns has a unique solution.
1. For matrices A, B, C, A + B = A + C if and only if A = B. 2. Every linear system with the same number of equations as unknowns has a unique solution. 3. Every linear system with the same number of equations
More informationAP Calculus BC Syllabus Course Overview
AP Calculus BC Syllabus Course Overview Textbook Anton, Bivens, and Davis. Calculus: Early Transcendentals, Combined version with Wiley PLUS. 9 th edition. Hoboken, NJ: John Wiley & Sons, Inc. 2009. Course
More informationMaple in Calculus. by Harald Pleym. Maple Worksheets Supplementing. Edwards and Penney. CALCULUS 6th Edition Early Transcendentals  Matrix Version
Maple in Calculus by Harald Pleym Maple Worksheets Supplementing Preface Edwards and Penney CALCULUS 6th Edition Early Transcendentals  Matrix Version These worksheets provide a comprehensive Maple supplement
More informationABSTRACT ALGEBRA WITH APPLICATIONS
ABSTRACT ALGEBRA WITH APPLICATIONS IN TWO VOLUMES VOLUME I VECTOR SPACES AND GROUPS KARLHEINZ SPINDLER Darmstadt, Germany Marcel Dekker, Inc. New York Basel Hong Kong Contents f Volume I Preface v VECTOR
More informationANSWERS. E k E 2 E 1 A = B
MATH 7 Final Exam Spring ANSWERS Essay Questions points Define an Elementary Matrix Display the fundamental matrix multiply equation which summarizes a sequence of swap, combination and multiply operations,
More informationWe wish the reader success in future encounters with the concepts of linear algebra.
Afterword Our path through linear algebra has emphasized spaces of vectors in dimension 2, 3, and 4 as a means of introducing concepts which go forward to IRn for arbitrary n. But linear algebra does not
More informationspring, math 204 (mitchell) list of theorems 1 Linear Systems Linear Transformations Matrix Algebra
spring, 2016. math 204 (mitchell) list of theorems 1 Linear Systems THEOREM 1.0.1 (Theorem 1.1). Uniqueness of Reduced RowEchelon Form THEOREM 1.0.2 (Theorem 1.2). Existence and Uniqueness Theorem THEOREM
More informationxvi xxiii xxvi Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7
About the Author v Preface to the Instructor xvi WileyPLUS xxii Acknowledgments xxiii Preface to the Student xxvi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real
More informationCourse Code: MTHS101 Breakup: 3 1 0 4 Course Name: MathematicsI Course Details: UnitI: Sequences & Series: Definition, Monotonic sequences, Bounded sequences, Convergent and Divergent Sequences Infinite
More informationMATH 2083 FINAL EXAM REVIEW The final exam will be on Wednesday, May 4 from 10:00am12:00pm.
MATH 2083 FINAL EXAM REVIEW The final exam will be on Wednesday, May 4 from 10:00am12:00pm. Bring a calculator and something to write with. Also, you will be allowed to bring in one 8.5 11 sheet of paper
More informationMaths for Map Makers
SUB Gottingen 7 210 050 861 99 A 2003 Maths for Map Makers by Arthur Allan Whittles Publishing Contents /v Chapter 1 Numbers and Calculation 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14
More informationSingle and Multivariable Calculus. Early Transcendentals
Single and Multivariable Calculus Early Transcendentals This work is licensed under the Creative Commons AttributionNonCommercialShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/byncsa/3.0/
More informationMATHEMATICS (MATH) Calendar
MATHEMATICS (MATH) This is a list of the Mathematics (MATH) courses available at KPU. For information about transfer of credit amongst institutions in B.C. and to see how individual courses transfer, go
More informationSaxon Calculus Scope and Sequence
Saxon Calculus Scope and Sequence Foundations Real Numbers Identify the subsets of the real numbers Identify the order properties of the real numbers Identify the properties of the real number field Discuss
More informationADVANCED ENGINEERING MATHEMATICS MATLAB
ADVANCED ENGINEERING MATHEMATICS WITH MATLAB THIRD EDITION Dean G. Duffy Contents Dedication Contents Acknowledgments Author Introduction List of Definitions Chapter 1: Complex Variables 1.1 Complex Numbers
More informationMathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS
Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS (i) Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams;
More informationPreface. Figures Figures appearing in the text were prepared using MATLAB R. For product information, please contact:
Linear algebra forms the basis for much of modern mathematics theoretical, applied, and computational. The purpose of this book is to provide a broad and solid foundation for the study of advanced mathematics.
More informationSingle and Multivariable Calculus. Late Transcendentals
Single and Multivariable Calculus Late Transcendentals This work is licensed under the Creative Commons AttributionNonCommercialShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/byncsa/3.0/
More informationCOURSE OUTLINE. Course Number Course Title Credits MAT251 Calculus III 4
COURSE OUTLINE Course Number Course Title Credits MAT251 Calculus III 4 Hours: Lecture/Lab/Other 4 Lecture Co or Prerequisite MAT152 with a minimum C grade or better, successful completion of an equivalent
More informationCALCULUS SALAS AND HILLE'S REVISED BY GARRET J. ETGEI ONE VARIABLE SEVENTH EDITION ' ' ' ' i! I! I! 11 ' ;' 1 ::: T.
' ' ' ' i! I! I! 11 ' SALAS AND HILLE'S CALCULUS I ;' 1 1 ONE VARIABLE SEVENTH EDITION REVISED BY GARRET J. ETGEI y.'' ' / ' ' ' / / // X / / / /..,
More informationENGINEERING MATHEMATICS
A TEXTBOOK OF ENGINEERING MATHEMATICS For B.Sc. (Engg.), B.E., B. Tech., M.E. and Equivalent Professional Examinations By N.P. BALI Formerly Principal S.B. College, Gurgaon Haryana Dr. MANISH GOYAL M.Sc.
More informationCourse Contents. Prerequisite : MATH 140
Course Contents MATH 140 : Introduction to Mathematics (E) 2 (2+0+0) credit hours Linear equations and applications, linear inequalities, absolute value in equations and inequalities, complex numbers,
More informationFundamentals of Engineering (FE) Exam Mathematics Review
Fundamentals of Engineering (FE) Exam Mathematics Review Dr. Garey Fox Professor and Buchanan Endowed Chair Biosystems and Agricultural Engineering October 16, 2014 Reference Material from FE Review Instructor
More informationNotes Prepared PREETHA VARGHESE
Notes Prepared by PREETHA VARGHESE Syllabus for  S1 & S2  Engineering Mathematics MODULE 1 Matrix: Elementary transformation  finding inverse and rank using elementary transformation  solution of linear
More informationMATH 102 Calculus II (404)
MATH 101 Calculus I (404) (Old 101) Limits and continuity of functions of a single variable. Differentiability. Techniques of differentiation. Implicit differentiation. Local extrema, first and second
More informationPreface. 2 Linear Equations and Eigenvalue Problem 22
Contents Preface xv 1 Errors in Computation 1 1.1 Introduction 1 1.2 Floating Point Representation of Number 1 1.3 Binary Numbers 2 1.3.1 Binary number representation in computer 3 1.4 Significant Digits
More informationUNDERSTANDING ENGINEERING MATHEMATICS
UNDERSTANDING ENGINEERING MATHEMATICS JOHN BIRD WORKED SOLUTIONS TO EXERCISES 1 INTRODUCTION In Understanding Engineering Mathematic there are over 750 further problems arranged regularly throughout the
More information