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CITATION

Bachman, David. Advanced Calculus Demystified. US: McGraw-Hill Professional, 2007.

Advanced Calculus Demystified

Authors: David Bachman

Published:  June 2007

eISBN: 9780071511094 0071511091 | ISBN: 9780071481212
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  • Contents
  • Preface
  • Acknowledgments
  • Chapter 1 Functions of Multiple Variables
  • 1.1 Functions
  • 1.2 Three Dimensions
  • 1.3 Introduction to Graphing
  • 1.4 Graphing Level Curves
  • 1.5 Putting It All Together
  • 1.6 Functions of Three Variables
  • 1.7 Parameterized Curves
  • Quiz
  • Chapter 2 Fundamentals of Advanced Calculus
  • 2.1 Limits of Functions of Multiple Variables
  • 2.2 Continuity
  • Quiz
  • Chapter 3 Derivatives
  • 3.1 Partial Derivatives
  • 3.2 Composition and the Chain Rule
  • 3.3 Second Partials
  • Quiz
  • Chapter 4 Integration
  • 4.1 Integrals over Rectangular Domains
  • 4.2 Integrals over Nonrectangular Domains
  • 4.3 Computing Volume with Triple Integrals
  • Quiz
  • Chapter 5 Cylindrical and Spherical Coordinates
  • 5.1 Cylindrical Coordinates
  • 5.2 Graphing Cylindrical Equations
  • 5.3 Spherical Coordinates
  • 5.4 Graphing Spherical Equations
  • Quiz
  • Chapter 6 Parameterizations
  • 6.1 Parameterized Surfaces
  • 6.2 The Importance of the Domain
  • 6.3 This Stuff Can Be Hard!
  • 6.4 Parameterized Areas and Volumes
  • Quiz
  • Chapter 7 Vectors and Gradients
  • 7.1 Introduction to Vectors
  • 7.2 Dot Products
  • 7.3 Gradient Vectors and Directional Derivatives
  • 7.4 Maxima, Minima, and Saddles
  • 7.5 Application: Optimization Problems
  • 7.6 LaGrange Multipliers
  • 7.7 Determinants
  • 7.8 The Cross Product
  • Quiz
  • Chapter 8 Calculus with Parameterizations
  • 8.1 Differentiating Parameterizations
  • 8.2 Arc Length
  • 8.3 Line Integrals
  • 8.4 Surface Area
  • 8.5 Surface Integrals
  • 8.6 Volume
  • 8.7 Change of Variables
  • Quiz
  • Chapter 9 Vector Fields and Derivatives
  • 9.1 Definition
  • 9.2 Gradients, Revisited
  • 9.3 Divergence
  • 9.4 Curl
  • Quiz
  • Chapter 10 Integrating Vector Fields
  • 10.1 Line Integrals
  • 10.2 Surface Integrals
  • Quiz
  • Chapter 11 Integration Theorems
  • 11.1 Path Independence
  • 11.2 Green’s Theorem on Rectangular Domains
  • 11.3 Green’s Theorem over More General Domains
  • 11.4 Stokes’ Theorem
  • 11.5 Geometric Interpretation of Curl
  • 11.6 Gauss’ Theorem
  • 11.7 Geometric Interpretation of Divergence
  • Quiz
  • Final Exam
  • Answers to Problems
  • Index