多元微积分 : 第3版

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

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