Applied vector analysis / Matiur Rahman, Isaac Mulolani.

Format:

Book

Author/Creator:

Rahman, M. (Matiur), 1940-

Contributor:

Mulolani, Isaac.

Series:

Electrical engineering textbook series

Language:

English

Subjects (All):

Vector analysis.

Physical Description:

xi, 272 pages : illustrations ; 25 cm.

Place of Publication:

Boca Raton : CRC Press, [2001]

Summary:

Vector analysis is an important branch of mathematics and is essential to solving real problems in science and engineering. Unlike many of the more theoretical books, this text clearly illustrates the application of vector calculus to physical problems. The authors clearly explain the theory and provide an abundance of examples and exercises. An outgrowth of class notes used over many years of teaching vector analysis, this book is an ideal text for a one-semester course for senior undergraduate or graduate engineering students.

Contents:

1 Historical Background 1

1.2 Hamilton's Quaternions 2

1.3 Grassmann's Calculus of Extension 3

1.4 The Work of Maxwell 4

1.5 Modern Vector Analysis 5

1.6 Other Contributions 6

2 The Algebra of Vectors 9

2.1 Addition and Subtraction of Vectors 11

2.2 Scalar and Vector Products 12

2.3 Scalar and Vector Projections 15

2.4 Cartesian Frame of Reference 17

2.4.1 Definition of a Position Vector R 17

2.5 Vector Algebra Using Coordinates 18

2.6 Mixed Product in Coordinate Form 22

2.7 Vector Representation Using Coordinates 31

2.8 Lines and Planes Using Vector Algebra 34

2.8.1 Lines 34

2.8.2 The Equation of a Plane 37

2.9 Partial Derivatives 37

2.10 Iterated Partial Derivatives 40

3 Vector Functions of One Variable 49

3.1 Vector Differentiation 50

3.2 Geometric Interpretation of R' 51

3.3 Higher-Order Derivatives 53

3.4 Curves, Length and Arc Length 54

3.5 Motion on a Curve, Velocity and Acceleration 56

3.6 Curvature, Components of Acceleration 57

3.7 Curvature, Tangential and Normal Components of Acceleration 61

4 The Del Operator 75

4.1 Gradient Characterizes Maximum Increase 80

4.2 Tangent Planes and Normal Lines 83

4.3 Tangent Plane 87

4.4 Normal Lines 88

4.5 Divergence and Curl of a Vector Field 90

4.6 Physical Interpretation of Divergence 91

4.7 Physical Interpretation of the Curl 93

4.8 The Laplacian Operator 96

4.9 Vector Identities 98

5 Line, Surface and Volume Integrals 107

5.2 Line Integrals and Vector Functions 118

5.3 Work 120

5.4 Line Integrals Independent of Path 123

5.5 Conservative Vector Fields 130

5.6 Surface Integrals 131

5.7 Orientation of a Surface 136

5.8 Volume Integration 138

5.9 Triple Integrals in Cylindrical Coordinates 144

5.10 Triple Integrals in Spherical Coordinates 149

6 Integral Theorems 163

6.1 Green's Theorem 163

6.2 Region with Holes 170

6.3 Integrals over Vector Fields 176

6.4 Stokes' Theorem 181

6.5 Green's Theorem in 3-D 182

6.6 The Divergence Theorem 193

7 Applications 207

7.2 Acceleration Vector 207

7.3 Continuity Equation of Fluid Flow 212

7.3.1 Euler's Equation of motion 217

7.4 Continuity Equation and Heat Conduction 220

7.5 Poisson's Equation 221

7.6 Vectors in Electromagnetic Theory 224

7.7 The Continuity Equation Revisited 224

7.8 Maxwell's Equations for Electromagnetic Fields 226

7.9 Waves Solutions of Maxwell's Equations 234

7.10 Ocean Wave Interactions 243

7.11 Solution Techniques for S[subscript nl] 245

7.12 Graphical Simulation of a Vector Field 248

B Vector Formulae at a glance 265.

Notes:

Includes bibliographical references and index.

ISBN:

0849310881

OCLC:

46660819