Student Solutions Manual to accompany Vector Calculus

by Lovric, Miroslav

• ISBN13: 9780471725718
• ISBN10: 0471725714
• Edition: 1st
• Format: Paperback
• Copyright: 2007-02-28
• Publisher: Wiley

Summary

This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem.

Author Biography

Miroslav Lovric, Ph.D, is Associate Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada.

Table of Contents

Vectors, Matrices, and Applications	p. 1
Vectors	p. 1
Applications in Geometry and Physics	p. 10
The Dot Product	p. 20
Matrices and Determinants	p. 30
The Cross Product	p. 39
Chapter Review	p. 48
Calculus of Functions of Several Variables	p. 52
Real-Valued and Vector-Valued Functions of Several Variables	p. 52
Graph of a Function of Several Variables	p. 62
Limits and Continuity	p. 76
Derivatives	p. 93
Paths and Curves in R[superscript 2]-and R[superscript 3]	p. 112
Properties of Derivatives	p. 123
Gradient and Directional Derivative	p. 135
Cylindrical and Spherical Coordinate Systems	p. 151
Chapter Review	p. 159
Vector-Valued Functions of One Variable	p. 164
World of Curves	p. 164
Tangents, Velocity, and Acceleration	p. 181
Length of a Curve	p. 191
Acceleration and Curvature	p. 200
Introduction to Differential Geometry of Curves	p. 209
Chapter Review	p. 215
Scalar and Vector Fields	p. 219
Higher-Order Partial Derivatives	p. 219
Taylor's Formula	p. 230
Extreme Values of Real-Valued Functions	p. 242
Optimization with Constraints and Lagrange Multipliers	p. 261
Flow Lines	p. 272
Divergence and Curl of a Vector Field	p. 278
Implicit Function Theorem	p. 292
Appendix: Some Identities of Vector Calculus	p. 298
Chapter Review	p. 302
Integration Along Paths	p. 306
Paths and Parametrizations	p. 306
Path Integrals of Real-Valued Functions	p. 316
Path Integrals of Vector Fields	p. 325
Path Integrals Independent of Path	p. 341
Chapter Review	p. 360
Double and Triple Integrals	p. 363
Double Integrals: Definition and Properties	p. 363
Double Integrals Over General Regions	p. 375
Examples and Techniques of Evaluation of Double Integrals	p. 394
Change of Variables in a Double Integral	p. 401
Triple Integrals	p. 417
Chapter Review	p. 427
Integration Over Surfaces, Properties, and Applications of Integrals	p. 431
Parametrized Surfaces	p. 431
World of Surfaces	p. 448
Surface Integrals of Real-Valued Functions	p. 462
Surface Integrals of Vector Fields	p. 474
Integrals: Properties and Applications	p. 484
Chapter Review	p. 495
Classical Integration Theorems of Vector Calculus	p. 499
Green's Theorem	p. 499
The Divergence Theorem	p. 511
Stokes' Theorem	p. 524
Differential Forms and Classical Integration Theorems	p. 536
Vector Calculus in Electromagnetism	p. 553
Vector Calculus in Fluid How	p. 566
Chapter Review	p. 576
Various Results Used in This Book and Proofs of Differentiation Theorems	p. 581
Answers to Odd-Numbered Exercises	p. 590
Index	p. 615
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