Advanced Calculus Demystified

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McGraw Hill Professional, Jun 5, 2007 - Technology & Engineering - 274 pages
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Your INTEGRAL tool for mastering ADVANCED CALCULUS

Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn.

Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering.

This fast and easy guide offers:

  • Numerous detailed examples to illustrate basic concepts
  • Geometric interpretations of vector operations such as div, grad, and curl
  • Coverage of key integration theorems including Green's, Stokes', and Gauss'
  • Quizzes at the end of each chapter to reinforce learning
  • A time-saving approach to performing better on an exam or at work

Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without!

 

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Contents

Chapter 1 Functions of Multiple Variables
1
Chapter 2 Fundamentals of Advanced Calculus
17
Chapter 3 Derivatives
23
Chapter 4 Integration
33
Chapter 5 Cylindrical and Spherical Coordinates
49
Chapter 6 Parameterizations
59
Chapter 7 Vectors and Gradients
69
Chapter 8 Calculus with Parameterizations
95
Chapter 9 Vector Fields and Derivatives
125
Chapter 10 Integrating Vector Fields
133
Chapter 11 Integration Theorems
145
Final Exam
175
Answers to Problems
177
Index
265
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About the author (2007)

David Bachman, Ph.D., is an assistant professor of mathematics at Pitzer College in California. He currently teaches courses in multivariable calculus as well as mathematical logic games.

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