A Course of Mathematics for Engineers and Scientists, Volume 4 focuses on mathematical methods required in the more advanced parts of physics and engineering. Organized into five chapters, this book begins by elucidating vector analysis and the differential and integral operations and theorems concerning vectors. Chapter II shows solution of ordinary and some partial differential equations. Chapter III addresses the properties of Bessel, Legendre, Laguerre, and Hermite functions that commonly occur in the solution of boundary and initial value problems. The last two chapters detail the differential equations of field lines and level surfaces, as well as the matrices. This book will be useful to undergraduate students so that they can appreciate and use the mathematical methods required in the more advanced parts of physics and engineering.
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 tensors Chapter 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 systems Chapter III. Some Special Functions Bessel functions Legendre polynomials Other special functions Chapter IV. The Differential Equations of Field Lines and Level Surfaces Introduction Field lines Lagrange's partial differential equation Level surfaces and orthogonal trajectories Chapter 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 matrices Bibliography Answers to the Exercises Index
- No. of pages:
- © Pergamon 1964
- 1st January 1964
- eBook ISBN: