《多元微積分（第3版）》是2012年6月1日世界圖書出版社出版的圖書，作者是浪（Lang H.）。
基本介紹
- 中文名：多元微積分（第3版）
- 作者：浪（Lang H.）
- ISBN：9787510044076
- 頁數：503頁
- 定價：71.10元
- 出版社：世界圖書出版社
- 出版時間：2012年6月1日
內容簡介,圖書目錄,
內容簡介
《數學經典教材（影印版）：多元微積分（第3版）》是全面，知識體系新穎的多變數微積分教程。旨在解決廣大多變數微積分學者遇到的新老問題，包內包括：（第一部分）基礎資料：向量；向量微分；多變數函式；鏈式法則和梯度；（第二部分）大值，小值和泰勒公式：大值和小值；高階導數；（第三部分）曲線積分和雙積分：勢函式；曲線積分；雙積分；格林定理；（第四部分）三重積分和曲面積分：三重積分；曲面積分；（第五部分）映射、反映射和變數變換公式：矩陣；線性映射；行列式；多變數函式的套用；變數變換公式；附錄：傅立葉級數。
《數學經典教材（影印版）：多元微積分（第3版）》讀者對象：數學專業的本科生、研究生和相關專業的數學工作者。
圖書目錄
PART ONE Basic Material
CHAPTER Ⅰ Vectors
1.definition of points in space
2.located vectors
3.scalar product
4.the norm of a vector
5.parametric lines
6.planes
7.the cross product
CHAPTER Ⅱ Differentiation Of Vectors
1.derivative
2.length of curves
CHAPTER Ⅲ Functions Of Several Variables
1.graphs and level curves
2.partial derivatives
3.differentiability and gradient
4.repeated partial derivatives
CHAPTER Ⅳ The Chain Rule and the Gradient
1.the chain rule
2.tangent plane
3.directional derivative
4.functions depending only on the distance from the origin
5.the law of conservation of energy
6.further technique in partial differentiation
PART TWO maxima, minima, and taylor's formula
chapter Ⅴ Maximum and Minimum
1.critical points
2.boundary points
3.lagrange multipliers
CHAPTER Ⅵ higher derivatives
1.the first two terms in tayior's formula
2.the quadratic term at critical points
3.algebraic study of a quadratic form
4.partial differential operators
5.the general expression for tayior's formula
appendix.taylor's formula in one variable
NOTE.Chapter Ix on Double Integrals is self contained, and could be covered here.
PART THREE Curve Integrals and Double Integrals
CHAPTER Ⅶ Potential Functions
1.existence and uniqueness of potential functions
2.local existence of potential functions
3.an important special vector field
4.differentiating under the integral
5.proof of the local existence theorem
CHAPTER Ⅷ curve integrals
1.definition and evaluation of curve integrals
2.the reverse path
3.curve integrals when the vector field has a potential function
4.dependence of the integral on the path
