Advanced Calculus Demystified (高級微積分解密)

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!

Table of Contents

(1) Functions of Multiple Variables
(a) Three-dimensional coordinates
(b) Graphing Functions of multiple variables
(2) Parameterizations
(a) Polar Coordinates
(b) Spherical and Cylindrical Coordinates
(c) Parameterized Curves
(d) Parameterized Surfaces
(3) Partial Derivatives
(a) Vectors and dot products
(b) Partial Derivatives
(c) Second Partials
(d) Gradients
(e) Max/Min problems
(f) Lagrange multipliers
(4) Multiple Integrals
(a) Volumes
(b) Repeated Integrals
(c) Integrals over non-rectangular domains
(5) Vector Operators
(a) Cross products
(b) Vector Fields
(c) Gradients, revisited
(d) Divergence
(e) Curl
(6) Integral Theorems
(a) Independence of path and line integrals
(b) Green's theorem
(c) Stokes' theorem
(d) Gauss' Theorem
(7) Other Integrals
(a) Arc Length
(b) Surface Area