书名：CALCULUS CALCU LUS Ⅲ

 

作者：Paul Dawkins

 

文件格式：PDF

 

文件大小：1.94M

 

页数：286

 

资料类别：微积分

 

影印版

 

是否缺页：不缺

 

目录：

Preface .......................................................................................................................................... iii

Outline .......................................................................................................................................... iv

Three Dimensional Space.............................................................................................................. 1

Introduction ............................................................................................................................................... 1

The 3-D Coordinate System ....................................................................................................................... 3

Equations of Lines .................................................................................................................................... 9

Equations of Planes ................................................................................................................................. 15

Quadric Surfaces ..................................................................................................................................... 18

Functions of Several Variables ................................................................................................................ 24

Vector Functions ..................................................................................................................................... 31

Calculus with Vector Functions ............................................................................................................... 40

Tangent, Normal and Binormal Vectors .................................................................................................. 43

Arc Length with Vector Functions ........................................................................................................... 46

Curvature ................................................................................................................................................. 49

Velocity and Acceleration ........................................................................................................................ 51

Cylindrical Coordinates ........................................................................................................................... 54

Spherical Coordinates .............................................................................................................................. 56

Partial Derivatives ....................................................................................................................... 62

Introduction ............................................................................................................................................. 62

Limits ...................................................................................................................................................... 63

Partial Derivatives ................................................................................................................................... 68

Interpretations of Partial Derivatives ....................................................................................................... 77

Higher Order Partial Derivatives .............................................................................................................. 81

Differentials ............................................................................................................................................ 85

Chain Rule .............................................................................................................................................. 86

Directional Derivatives ............................................................................................................................ 96

Applications of Partial Derivatives .......................................................................................... 105

Introduction ............................................................................................................................................105

Tangent Planes and Linear Approximations ...........................................................................................106

Gradient Vector, Tangent Planes and Normal Lines ...............................................................................110

Relative Minimums and Maximums .......................................................................................................112

Absolute Minimums and Maximums ......................................................................................................121

Lagrange Multipliers ...............................................................................................................................129

Multiple Integrals ...................................................................................................................... 139

Introduction ............................................................................................................................................139

Double Integrals .....................................................................................................................................140

Iterated Integrals ....................................................................................................................................144

Double Integrals Over General Regions .................................................................................................151

Double Integrals in Polar Coordinates ....................................................................................................162

Triple Integrals .......................................................................................................................................173

Triple Integrals in Cylindrical Coordinates .............................................................................................181

Triple Integrals in Spherical Coordinates ................................................................................................184

Change of Variables ...............................................................................................................................188

Surface Area ...........................................................................................................................................197

Area and Volume Revisited ....................................................................................................................200

Line Integrals ............................................................................................................................. 201

Introduction ............................................................................................................................................201

Vector Fields ..........................................................................................................................................202

Line Integrals – Part I ..............................................................................................................................207

Line Integrals – Part II ............................................................................................................................218

Line Integrals of Vector Fields................................................................................................................221

Fundamental Theorem for Line Integrals ................................................................................................224

Conservative Vector Fields .....................................................................................................................228

Calculus III

© 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx

Green’s Theorem ....................................................................................................................................235

Curl and Divergence ...............................................................................................................................243

Surface Integrals ........................................................................................................................ 247

Introduction ............................................................................................................................................247

Parametric Surfaces ................................................................................................................................248

Surface Integrals ....................................................................................................................................254

Surface Integrals of Vector Fields ...........................................................................................................263

Stokes’ Theorem ....................................................................................................................................273

Divergence Theorem ...............................................................................................................................278