{"product_id":"vector-calculus-wse-9780471725695","title":"Vector Calculus WSE","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWith this book, readers will develop a strong foundation in the theory of functions of several variables and of modern vector calculus in two and three dimensions. It utilizes a clear and easy-to-follow writing style along with carefully crafted examples and numerous illustrations to explain complex concepts.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eCHAPTER 1 Vectors, Matrices, and Applications 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Vectors 1\u003c\/p\u003e \u003cp\u003e1.2 Applications in Geometry and Physics 10\u003c\/p\u003e \u003cp\u003e1.3 The Dot Product 20\u003c\/p\u003e \u003cp\u003e1.4 Matrices and Determinants 30\u003c\/p\u003e \u003cp\u003e1.5 The Cross Product 39\u003c\/p\u003e \u003cp\u003eChapter Review 48\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2 Calculus of Functions of Several Variables 52\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Real-Valued and Vector-Valued Functions of Several Variables 52\u003c\/p\u003e \u003cp\u003e2.2 Graph of a Function of Several Variables 62\u003c\/p\u003e \u003cp\u003e2.3 Limits and Continuity 76\u003c\/p\u003e \u003cp\u003e2.4 Derivatives 93\u003c\/p\u003e \u003cp\u003e2.5 Paths and Curves in R2 and R3 112\u003c\/p\u003e \u003cp\u003e2.6 Properties of Derivatives 123\u003c\/p\u003e \u003cp\u003e2.7 Gradient and Directional Derivative 135\u003c\/p\u003e \u003cp\u003e2.8 Cylindrical and Spherical Coordinate Systems 151\u003c\/p\u003e \u003cp\u003eChapter Review 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3 Vector-Valued Functions of One Variable 164\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 World of Curves 164\u003c\/p\u003e \u003cp\u003e3.2 Tangents, Velocity, and Acceleration 181\u003c\/p\u003e \u003cp\u003e3.3 Length of a Curve 191\u003c\/p\u003e \u003cp\u003e3.4 Acceleration and Curvature 200\u003c\/p\u003e \u003cp\u003e3.5 Introduction to Differential Geometry of Curves 209\u003c\/p\u003e \u003cp\u003eChapter Review 215\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4 Scalar and Vector Fields 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Higher-Order Partial Derivatives 219\u003c\/p\u003e \u003cp\u003e4.2 Taylor’s Formula 230\u003c\/p\u003e \u003cp\u003e4.3 Extreme Values of Real-Valued Functions 242\u003c\/p\u003e \u003cp\u003e4.4 Optimization with Constraints and Lagrange Multipliers 261\u003c\/p\u003e \u003cp\u003e4.5 Flow Lines 272\u003c\/p\u003e \u003cp\u003e4.6 Divergence and Curl of a Vector Field 278\u003c\/p\u003e \u003cp\u003e4.7 Implicit Function Theorem 292\u003c\/p\u003e \u003cp\u003e4.8 Appendix: Some Identities of Vector Calculus 298\u003c\/p\u003e \u003cp\u003eChapter Review 302\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5 Integration Along Paths 306\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Paths and Parametrizations 306\u003c\/p\u003e \u003cp\u003e5.2 Path Integrals of Real-Valued Functions 316\u003c\/p\u003e \u003cp\u003e5.3 Path Integrals of Vector Fields 325\u003c\/p\u003e \u003cp\u003e5.4 Path Integrals Independent of Path 341\u003c\/p\u003e \u003cp\u003eChapter Review 360\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6 Double and Triple Integrals 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Double Integrals: Definition and Properties 363\u003c\/p\u003e \u003cp\u003e6.2 Double Integrals Over General Regions 375\u003c\/p\u003e \u003cp\u003e6.3 Examples and Techniques of Evaluation of Double Integrals 394\u003c\/p\u003e \u003cp\u003e6.4 Change of Variables in a Double Integral 401\u003c\/p\u003e \u003cp\u003e6.5 Triple Integrals 417\u003c\/p\u003e \u003cp\u003eChapter Review 427\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7 Integration Over Surfaces, Properties, and Applications of Integrals 431\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Parametrized Surfaces 431\u003c\/p\u003e \u003cp\u003e7.2 World of Surfaces 448\u003c\/p\u003e \u003cp\u003e7.3 Surface Integrals of Real-Valued Functions 462\u003c\/p\u003e \u003cp\u003e7.4 Surface Integrals of Vector Fields 474\u003c\/p\u003e \u003cp\u003e7.5 Integrals: Properties and Applications 484\u003c\/p\u003e \u003cp\u003eChapter Review 495\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 8 Classical Integration Theorems of Vector Calculus 499\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Green’s Theorem 499\u003c\/p\u003e \u003cp\u003e8.2 The Divergence Theorem 511\u003c\/p\u003e \u003cp\u003e8.3 Stokes’ Theorem 524\u003c\/p\u003e \u003cp\u003e8.4 Differential Forms and Classical Integration Theorems 536\u003c\/p\u003e \u003cp\u003e8.5 Vector Calculus in Electromagnetism 553\u003c\/p\u003e \u003cp\u003e8.6 Vector Calculus in Fluid Flow 566\u003c\/p\u003e \u003cp\u003eChapter Review 576\u003c\/p\u003e \u003cp\u003eAPPENDIX A Various Results Used in This Book and Proofs of Differentiation Theorems 581\u003c\/p\u003e \u003cp\u003eAPPENDIX B Answers to Odd-Numbered Exercises 590\u003c\/p\u003e \u003cp\u003eIndex 615\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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