Synopses & Reviews
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!
Synopsis
Calculate this: calculus just got a whole lot easier
In this easy-to-follow guide, calculus instructor David Bachman explains this complex mathematics topic in an effective and enlightening way. You will learn about vectors, multiple variables, multiple integrals, partial derivatives, integral theorems of vector analysis, and much more. The book features hundreds of practice problems and solutions, sample quizzes, and a final exam.
About the Author
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.
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