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Textbook
Vector CalculusJanuary 2007, ©2007
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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.
Table of Contents
Chapter 1: Vectors, Matrices, and Applications.
Chapter 2: Calculus of Functions of Several Variables.
Chapter 3: Vector-Valued Functions of One Variable.
Chapter 4: Scalar and Vector Fields.
Chapter 5: Integration Along Paths.
Chapter 6: Double and Triple Integrals.
Chapter 7: Integrations Over Surfaces, Properties, and Applications of Integrals.
Chapter 8: Classical Integration Theorems of Vector Calculus.
Appendix A: Various Results Used in This Book and Proofs of Differentiation Theorems.
Appendix B: Answers to Odd-Numbered Exercises.
Index.
Hallmark Features
- Comprehensive review of relevant topics in linear algebra and calculus of real-valued functions of one and several variables.
- Geometric, numeric, analytic and applied approaches to presentation of mathematics promote better understanding of the material and help build intuition and experience.
- Detailed, step-by-step solutions to all examples; end of each section contains a large number of exercises, ranging from basic and routine to challenging and thought-provoking.
- Review section at the end of each chapter includes a number of review questions, a true/false quiz and additional problems.
- Several sections entirely devoted to applications; World of Curves and World of Surfaces sections study features of interesting curves and surfaces and introduce several new applications.
- Classical integration theorems of Green, Gauss and Stokes covered in depth, illustrated with numerous examples and applications.
Available Versions
Vector Calculus
ISBN 978-0-471-72569-5
January 2007, ©2007
Hardcover, 640 pages
Vector Calculus, Textbook and Student Solutions Manual
ISBN 978-0-470-14063-5
November 2006, ©2007
Hardcover
