Applied Vector Analysis

Cover
Preface
Contents
CHAPTER 1 Algebra of Vectors
	1-1: Scalars and Vectors
	1-2: Equality of Vectors
	1-3: Multiplication of Vectors by Scalars
	1-4: Addition and Subtraction of Vectors
	1-5: Scalar or Dot Product
	1-6: Vector or Cross Product
	1-7: Scalar Triple Product
	1-8: Vector Triple Product
	1-9: Basis
	Solved Problems
CHAPTER 2 Vectors in the Rectangular Coordinate System
	2-1: Analytic Representation of Vectors
	2-2: Vector Algebra Using Analytic Representation
	2-3: Base Vectors and Position Vectors
	2-4: Scalar Product
	2-5: Vector Product
	2-6: Analytic Characterization of Vectors
	2-7: Triple Products
	2-8: Basis
	Solved Problems
CHAPTER 3 Applications to Geometry
	3-1: Application of Vector Methods to Elementary Geometry
	3-2: Vector Equation of a Straight Line
	3-3: Vector Equation of a Plane
	3-4: Distance Formulas
	Solved Problems
CHAPTER 4 Differentiation of Vectors
	4-1: Vector Functions
	4-2: Ordinary Differentiation of Vectors
	4-3: Partial Derivatives of Vector Functions of More Than One Variable
	4-4: Space Curves
	4-5: Surfaces
	4-6: Tangent, Curvature, and Torsion
	Solved Problems
CHAPTER 5 Gradient, Divergence, and Curl
	5-1: Directional Derivative and the Gradient of a Scalar Function
	5-2: The Operator Del
	5-3: Divergence of a Vector Function
	5-4: Curl of a Vector Function
	5-5: Operations with Del and Some Vector Identities
	Solved Problems
CHAPTER 6 Vector Integration
	6-1: Line Integrals
	6-2: Surface Integrals
	6-3: Volume Integrals
	6-4: Divergence and Curl of a Vector
	6-5: Alternate Definitions of Gradient, Divergence, and Curl
	Solved Problems
CHAPTER 7 Integral Theorems
	7-1: Divergence Theorem (or Gauss\' Theorem)
	7-2: Green\'s Theorems
	7-3: Volume-to-Surface Integral Transformations
	7-4: Stokes\' Theorem
	7-5: Surface-to-Line Integral Transformations
	7-6: Irrotational and Solenoidal Fields
	Solved Problems
CHAPTER 8 Curvilinear Orthogonal Coordinates
	8-1: Curvilinear Coordinates
	8-2: Orthogonal Curvilinear Coordinates
	8-3: Gradient, Divergence, and Curl in Orthogonal Curvilinear Coordinates
	8-4: Special Coordinate Systems
	Solved Problems
CHAPTER 9 Applications to Mechanics
	9-1: Displacement, Velocity, and Acceleration Vectors
	9-2: Angular Velocity and Angular Acceleration
	9-3: Force and Moment
	9-4: Work and Energy
	Solved Problems
CHAPTER 10 Applications to Fluid Mechanics
	10-1: Equation of Continuity
	10-2: Equation of Motion
	10-3: Fluid Statics
	10-4: Steady Flow and Streamlines
	10-5: Irrotational Flow and Velocity Potential
	10-6: Vortex Flow and Circulation
	10-7: Equation of Energy
	Solved Problems
CHAPTER 11 Applications to Electromagnetic Theory
	11-1: Equation of Continuity
	11-2: Electromagnetic Field
	11-3: Equations of Electromagnetic Theory
	11-4: Potential Functions of the Electromagnetic Field
	11-5: Energy in the Electromagnetic Field and the Poynting Vector
	11-6: Static Fields
	Solved Problems
FINAL EXAMINATION
APPENDIX A Summary of Vector Relations
APPENDIX B Vector Differential Operations in Orthogonal Coordinates
INDEX