Student Solutions Manual to Accompany Vector Calculus (Paperback)

· 제목 : Student Solutions Manual to Accompany Vector Calculus (Paperback) 
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 미적분학
· ISBN : 9780471725718
· 쪽수 : 256쪽
· 출판일 : 2007-02-28

Vectors, Matrices, and Applications 1

Vectors 1

Applications in Geometry and Physics 10

The Dot Product 20

Matrices and Determinants 30

The Cross Product 39

Chapter Review 48

Calculus of Functions of Several Variables 52

Real-Valued and Vector-Valued Functions of Several Variables 52

Graph of a Function of Several Variables 62

Limits and Continuity 76

Derivatives 93

Paths and Curves in R[superscript 2]-and R[superscript 3] 112

Properties of Derivatives 123

Gradient and Directional Derivative 135

Cylindrical and Spherical Coordinate Systems 151

Chapter Review 159

Vector-Valued Functions of One Variable 164

World of Curves 164

Tangents, Velocity, and Acceleration 181

Length of a Curve 191

Acceleration and Curvature 200

Introduction to Differential Geometry of Curves 209

Chapter Review 215

Scalar and Vector Fields 219

Higher-Order Partial Derivatives 219

Taylor's Formula 230

Extreme Values of Real-Valued Functions 242

Optimization with Constraints and Lagrange Multipliers 261

Flow Lines 272

Divergence and Curl of a Vector Field 278

Implicit Function Theorem 292

Appendix: Some Identities of Vector Calculus 298

Chapter Review 302

Integration Along Paths 306

Paths and Parametrizations 306

Path Integrals of Real-Valued Functions 316

Path Integrals of Vector Fields 325

Path Integrals Independent of Path 341

Chapter Review 360

Double and Triple Integrals 363

Double Integrals: Definition and Properties 363

Double Integrals Over General Regions 375

Examples and Techniques of Evaluation of Double Integrals 394

Change of Variables in a Double Integral 401

Triple Integrals 417

Chapter Review 427

Integration Over Surfaces, Properties, and Applications of Integrals 431

Parametrized Surfaces 431

World of Surfaces 448

Surface Integrals of Real-Valued Functions 462

Surface Integrals of Vector Fields 474

Integrals: Properties and Applications 484

Chapter Review 495

Classical Integration Theorems of Vector Calculus 499

Green's Theorem 499

The Divergence Theorem 511

Stokes' Theorem 524

Differential Forms and Classical Integration Theorems 536

Vector Calculus in Electromagnetism 553

Vector Calculus in Fluid How 566

Chapter Review 576

Various Results Used in This Book and Proofs of Differentiation Theorems 581

Answers to Odd-Numbered Exercises 590

Index 615