A Course of Mathematics for Engineers and Scientists

Preface Chapter I. Vector Analysis Transformation of coordinates Scalar fields: gradient Vector fields Line and surface integrals Applications to vector analysis Green's theorem Discontinuities; surface derivatives Uniqueness theorems and Green's function Variation with time Orthogonal curvilinear coordinates Suffix notation and the summation convention Cartesian tensorsChapter II. The Solution of Some Differential Equations Laplace's equation in two and three dimensions Solution in series of ordinary differential equations The behavior of the solution of a differential equation Eigenvalues: Sturm-Liouville systemsChapter III. Some Special Functions Bessel functions Legendre polynomials Other special functionsChapter IV. The Differential Equations of Field Lines and Level Surfaces Introduction Field lines Lagrange's partial differential equation Level surfaces and orthogonal trajectoriesChapter V. Matrices Introduction and notation Matrix algebra The rank of a matrix: singular matrices The reciprocal of a square matrix Partitioned matrices The solution of linear equations Vector spaces Eigenvalues and eigenvectors Quadratic forms Simultaneous reduction of quadratic forms Multiple eigenvalues Hermitian matricesBibliography Answers to the Exercises Index