Advanced Calculus Demystified

David Bachman

  • 出版商: McGraw-Hill Education
  • 出版日期: 2007-06-01
  • 售價: $990
  • 貴賓價: 9.5$941
  • 語言: 英文
  • 頁數: 274
  • 裝訂: Paperback
  • ISBN: 0071481214
  • ISBN-13: 9780071481212
  • 相關分類: 微積分 Calculus
  • 海外代購書籍(需單獨結帳)




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




- 大量詳細的示例以說明基本概念
- 對向量運算(如散度、梯度和旋度)的幾何解釋
- 重要積分定理的涵蓋,包括格林、斯托克斯和高斯定理
- 每章結束時的測驗以加強學習
- 提供在考試或工作中表現更好的省時方法



1. 多變數函數
a. 三維坐標
b. 多變數函數的圖形

2. 參數化
a. 極坐標
b. 球面和柱面坐標
c. 參數化曲線
d. 參數化曲面

3. 偏導數
a. 向量和點積
b. 偏導數
c. 二階偏導數
d. 梯度
e. 最大/最小問題
f. 拉格朗日乘數

4. 多重積分
a. 體積
b. 重複積分
c. 非矩形域上的積分

5. 向量運算
a. 叉積
b. 向量場
c. 重新討論梯度
d. 散度
e. 旋度

6. 積分定理
a. 路徑獨立和線積分的獨立性
b. 格林定理
c. 斯托克斯定理
d. 高斯定理

7. 其他積分
a. 弧長
b. 曲面積