Student Solutions Manual to accompany Vector Calculus
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Student Solutions Manual to accompany Vector Calculus
Lovric, Miroslav
John Wiley & Sons Inc
09/2007
256
Mole
Inglês
9780471725718
15 a 20 dias
623
Descrição não disponível.
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
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
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theory of functions of several variables; modern vector calculus; two and three dimensions; carefully crafted examples; wide spectrum of applications; necessary technical and computational skills; chain rule; Implicit Function Theorem; parametrizations; Change of Variables Theorem
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
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
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
