多元微积分 原书第3版 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

多元微积分 原书第3版 英文PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

PART ONE Basic Material1

CHAPTER Ⅰ Vectors3

1．Definition of Points in Space3

2．Located Vectors11

3．Scalar Product14

4．The Norm of a Vector17

5．Parametric Lines32

6．Planes36

7．The Cross Product44

CHAPTER Ⅱ Differentiation of Vectors49

1．Derivative49

2．Length of Curves62

CHAPTER Ⅲ Functions of Several Variables66

1．Graphs and Level Curves66

2．Partial Derivatives70

3．Differentiability and Gradient77

4．Repeated Partial Derivatives82

CHAPTER Ⅳ The Chain Rule and the Gradient87

1．The Chain Rule87

2．Tangent Plane92

3．Directional Derivative99

4．Functions Depending only on the Distance from the Origin103

5．The Law of Conservation of Energy111

6．Further Technique in Partial Differentiation114

PART TWO Maxima,Minima,and Taylor's Formula121

CHAPTER Ⅴ Maximum and Minimum123

1．Critical Points123

2．Boundary Points126

3．Lagrange Multipliers135

CHAPTER Ⅵ Higher Derivatives143

1．The First Two Terms in Taylor's Formula143

2．The Quadratic Term at Critical Points149

3．Algebraic Study of a Quadratic Form155

4．Partial Differential Operators162

5．The General Expression for Taylor's Formula170

Appendix.Taylor's Formula in One Variable176

PART THREE Curve Integrals and Double Integrals181

CHAPTER Ⅶ Potential Functions183

1．Existence and Uniqueness of Potential Functions184

2．Local Existence of Potential Functions188

3．An Important Special Vector Field194

4．Differentiating Under the Integral198

5．Proof of the Local Existence Theorem201

CHAPTER Ⅷ Curve Integrals206

1．Definition and Evaluation of Curve Integrals207

2．The Reverse Path217

3．Curve Integrals When the Vector Field Has a Potential Function220

4．Dependence of the Integral on the Path228

CHAPTER Ⅸ Double Integrals233

1．Double Integrals233

2．Repeated Integrals242

3．Polar Coordinates252

CHAPTER Ⅹ Green's Theorem269

1．The Standard Version269

2．The Divergence and the Rotation of a Vector Field280

PART FOUR Triple and Surface Integrals291

CHAPTER Ⅺ Triple Integrals293

1．Triple Integrals293

2．Cylindrical and Spherical Coordinates298

3．Center of Mass313

CHAPTER Ⅻ Surface Integrals318

1．Parametrization,Tangent Plane,and Normal Vector318

2．Surface Area325

3．Surface Integrals333

4．Curl and Divergence of a Vector Field342

5．Divergence Theorem in 3-Space345

6．Stokes' Theorem355

PART FIVE Mappings,Inverse Mappings,and Change of Variables Formula.365

CHAPTER ⅩⅢ Matrices367

1．Matrices367

2．Multiplication of Matrices372

CHAPTER ⅩⅣ Linear Mappings385

1．Mappings385

2．Linear Mappings392

3．Geometric Applications398

4．Composition and Inverse of Mappings404

CHAPTER ⅩⅤ Determinants412

1．Determinants of Order 2412

2．Determinants of Order 3416

3．Additional Properties of Determinants420

4．Independence of Vectors428

5．Determinant of a Product430

6．Inverse of a Matrix431

CHAPTER ⅩⅥ Applications to Functions of Several Variables434

1．The Jacobian Matrix434

2．Differentiability438

3．The Chain Rule440

4．Inverse Mappings443

5．Implicit Functions446

6．The Hessian450

CHAPTER ⅩⅦ The Change of Variables Formula453

1．Determinants as Area and Volume453

2．Dilations463

3．Change of Variables Formula in Two Dimensions469

4．Application of Green's Formula to the Change of Variables Formula474

5．Change of Variables Formula in Three Dimensions478

6．Vector Fields on the Sphere483

APPENDIX Fourier Series487

1．General Scalar Products487

2．Computation of Fourier Series494