《多元微积分(第3版)》是全面，知识体系新颖的多变量微积分教程。旨在解决广大多变量微积分学者遇到的新老问题，包内包括：(第一部分)基础资料：向量；向量微分；多变量函数；链式法则和梯度；(第二部分)最大值，最小值和泰勒公式：最大值和最小值；高阶导数；(第三部分)曲线积分和双积分：势函数；曲线积分；双积分；格林定理；(第四部分)三重积分和曲面积分：三重积分；曲面积分；(第五部分)映射、反映射和变量变换公式：矩阵；线性映射；行列式；多变量函数的应用；变量变换公式；附录：傅里叶级数。本书由浪(Lang，S.)著。

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

……

PART FOUR triple and surface integrals

PART FIVE mappings, inverse mappings, and change of variables formula

APPENDIX Fourier Series

answers

index