Multivariable calculus, linear algebra, and differential equations

✍ Scribed by Stanley I Grossman

• Publisher: Academic Press, , Elsevier Inc
• Year: 1986
• Tongue: English
• Leaves: 984
• Edition: 2nd
• Category: Library

✦ Synopsis

The third edition combines coverage of multivariable calculus with linear algebra and differential equations. Grossman's unique approach provides maths, engineering, and physical science students with a continuity of level and style. The intuitive approach is stressed over a more rigorous/formal treatment of the topics. An abundance of examples, graded exercises, and numerous applications all contribute to student appeal. Features: * Historical notes and biographical sketches describe the development of an idea or identify an important person in mathematics. * Graphs and exercises sets are incorporated thoughout the text to help students visualize mathematics and better understand concepts. * An optional discussion of Newton's method for two variables is part of Section 3.12. * The Summing Up Theorem is used to tie together seemingly disparate topics in the study of linear algebra. * Section 10.3 contains an answer to the question ''When is a differential equation separable ?'' * Numerous examples throughout the text contain all the algebraic steps needed to complete the solution. * The text contains over 5,500 exercises graded according to difficulty, and there is a balance between technique and proof. New to this edition: * Solving Linear Systems Numerically: Gaussian Elimination with Divoting has been added to Chapter 6. * Coverage of Least Squares Approximation and Isomorphisms has been added to Chapter 8. * True/False and multiple choice ''Self-Quiz'' exercises now begin each problem set. Students can use these exercises to access their comprehension before tackling the exercise set. * Each chapter now ends with a review of the important results of that chapter. * Examples and figures are now titled so that students can easily grasp the essential concept each one illustrates

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Dedication, Page iv
Preface, Pages xi-xiv
1 - Vectors in the Plane, Pages 1-25
2 - Vector Functions, Vector Differentiation, and Parametric Equations in ℝ2, Pages 26-82
3 - Vectors in Space, Pages 83-152
4 - Differentiation of Functions of Two or More Variables, Pages 153-263
5 - Multiple Integration, Pages 264-321
6 - Introduction to Vector Analysis, Pages 322-397
7 - Matrices and Linear Systems of Equations, Pages 398-447
8 - Determinants, Pages 448-477
9 - Vector Spaces and Linear Transformations, Pages 478-575
10 - Calculus in ℝn, Pages 576-618
11 - Ordinary Differential Equations, Pages 619-718
12 - Matrices and Systems of Differential Equations, Pages 719-783
13 - Taylor Polynomials, Sequences, and Series, Pages 784-876
Appendix 1 - Mathematical Induction, Pages A1-A5
Appendix 2 - The Binomial Theorem, Pages A6-A9
Appendix 3 - Complex Numbers, Pages A10-A18
Appendix 4 - Proof of the Basic Theorem About Determinants, Pages A19-A22
Appendix 5 - Existence and Uniqueness for First-Order Initial Value Problems, Pages A23-A36
Tables of Integrals, Pages A37-A47
Answers to Odd-Numbered Problems and Review Exercises, Pages A49-A92
Index, Pages I-1-I-10