A Course of Mathematics for Engineers and Scientists
- 1st Edition - January 1, 1964
- Latest edition
- Authors: Brian H. Chirgwin, Charles Plumpton
- Language: English
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… Read more
Description
Description
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.
Table of contents
Table of contents
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
Product details
Product details
- Edition: 1
- Latest edition
- Published: November 13, 2013
- Language: English