Advanced Calculus Demystified by Bachman, David -- Read -- Imperial Library of Trantor

Index

Cover Demystified Series Copyright Dedication About the Author 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 75 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