Vector Calculus

ISBN-10: 0471725714
ISBN-13: 9780471725718
Edition: 2007 (Student Manual, Study Guide, etc.)
Authors: Miroslav Lovric
List price: $66.95
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Description: 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  More...

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Book details

List price: $66.95
Copyright year: 2007
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/15/2006
Binding: Paperback
Pages: 256
Size: 8.25" wide x 11.00" long x 0.75" tall
Weight: 1.276
Language: English

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.

Vectors, Matrices, and Applications
Vectors
Applications in Geometry and Physics
The Dot Product
Matrices and Determinants
The Cross Product
Chapter Review
Calculus of Functions of Several Variables
Real-Valued and Vector-Valued Functions of Several Variables
Graph of a Function of Several Variables
Limits and Continuity
Derivatives
Paths and Curves in R[superscript 2]-and R[superscript 3]
Properties of Derivatives
Gradient and Directional Derivative
Cylindrical and Spherical Coordinate Systems
Chapter Review
Vector-Valued Functions of One Variable
World of Curves
Tangents, Velocity, and Acceleration
Length of a Curve
Acceleration and Curvature
Introduction to Differential Geometry of Curves
Chapter Review
Scalar and Vector Fields
Higher-Order Partial Derivatives
Taylor's Formula
Extreme Values of Real-Valued Functions
Optimization with Constraints and Lagrange Multipliers
Flow Lines
Divergence and Curl of a Vector Field
Implicit Function Theorem
Appendix: Some Identities of Vector Calculus
Chapter Review
Integration Along Paths
Paths and Parametrizations
Path Integrals of Real-Valued Functions
Path Integrals of Vector Fields
Path Integrals Independent of Path
Chapter Review
Double and Triple Integrals
Double Integrals: Definition and Properties
Double Integrals Over General Regions
Examples and Techniques of Evaluation of Double Integrals
Change of Variables in a Double Integral
Triple Integrals
Chapter Review
Integration Over Surfaces, Properties, and Applications of Integrals
Parametrized Surfaces
World of Surfaces
Surface Integrals of Real-Valued Functions
Surface Integrals of Vector Fields
Integrals: Properties and Applications
Chapter Review
Classical Integration Theorems of Vector Calculus
Green's Theorem
The Divergence Theorem
Stokes' Theorem
Differential Forms and Classical Integration Theorems
Vector Calculus in Electromagnetism
Vector Calculus in Fluid How
Chapter Review
Various Results Used in This Book and Proofs of Differentiation Theorems
Answers to Odd-Numbered Exercises
Index

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