Begin2.DVI

Table of Contents

Chapter 8 Vector Calculus II................................................ 173

Vector Fields, Divergence of Vector Field, The Gauss Divergence Theorem,

Physical Interpretation of Divergence, Green’s Theorem inthe Plane, Area

Inside Simple Closed Curve, Change of Variable in Green’s Theorem, The Curl of

a Vector Field, Physical Interpretation of Curl, Stokes Theorem, Related Integral

Theorems, Region of Integration, Green’s First and Second Identities, Additional

Operators, Relations Involving the Del Operator, Vector Operators and

Curvilinear Coordinates, Orthogonal Curvilinear Coordinates, Transformation of

Vectors, General Coordinate Transformation, Gradient in aGeneral Orthogonal

System of Coordinates, Divergence in a General Orthogonal System of Coordinates,

Curl in a General Orthogonal System of Coordinates, The Laplacian in Generalized

Orthogonal Coordinates

Chapter 9 Applications of Vectors........................................ 241

Approximation of Vector Field, Spherical Trigonometry, Velocity and Acceleration

in Polar Coordinates, Velocity and Acceleration in Cylindrical Coordinates,

Velocity and Acceleration in Spherical Coordinates, Introduction to Potential

Theory, Solenoidal Fields, Two-Dimensional ConservativeVector Fields, Field Lines

and Orthogonal Trajectories, Vector Fields Irrotational and Solenoidal, Laplace’s

Equation, Three-dimensional Representations, Two-dimensional Representations,

One-dimensional Representations, Three-dimensional Conservative Vector Fields,

Theory of Proportions, Method of Tangents, Solid Angles, Potential Theory,

Velocity Fields and Fluids, Heat Conduction, Two-body Problem, Kepler’s Laws,

Vector Differential Equations, Maxwell’s Equations, Electrostatics, Magnetostatics

Chapter 10 Matrix and Difference Calculus............................ 307

The Matrix Calculus, Properties of Matrices, Dot or Inner Product, Matrix Multiplica-

tion, Special Square Matrices, The Inverse Matrix, Matrices with Special Properties, The

Determinant of a Square Matrix, Minors and Cofactors, Properties of Determinants, Rank

of a Matrix, Calculation of Inverse Matrix, Elementary Row Operations, Eigenvalues and

Eigenvectors, Properties of Eigenvalues and Eigenvectors, Additional Properties Involv-

ing Eigenvalues and Eigenvectors, Infinite Series of SquareMatrices, The Hamilton-Cayley

Theorem, Evaluation of Functions, Four-terminal Networks, Calculus of Finite Differences,

Differences and Difference Equations, Special Differences, Finite Integrals, Summation of

Series, Difference Equations with Constant Coefficients, Nonhomogeneous Difference Equa-

tions

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