Pipes L.A. Applied Mathematics for Engineers and Physicists

New York and London: McGraw-Hill Book Company. - 1946. - 618 p.
There has been a great impetus given during the last years to the application of mathematical analysis for the solution of technical problems. This interest in the use of mathematics by the technologist is a result of the remarkable developments that have appeared in the various branches of engineering and physics as a result of close collaboration of theory and experiment in the research laboratories of industrial plants and elsewhere.
A century ago, engineers regarded the differential and integral calculus as a mystery beyond the reach of the majority. However, at present, the engineering student takes the calculus in his stride. The use of complex quantities in the solution of electrical and mechanical problems has brought the engineer to at least a superficial study of the rudiments of the complex variable. Other studies of the behavior of systems of technical importance have ushered in matrix algebra, operational methods, the study of orthogonal functions, partial differential equations, and other mathematical techniques into the required mathematical equipment of a person who uses mathematics to solve technical problems of various kinds, such as acoustical, electrical, aeronautical, mechanical, thermal, etc. During the same years, the author has given a course in applied mathematics at the Graduate School of Engineering of Harvard University. This course is designed to acquaint graduate students in engineering and physics with the mathematical methods used in solving technical problems. By its nature, this course appeals to a group of students of very diversified interests, and it was found that although many excellent texts exist, nevertheless most of them are not directly concerned with actual applications of mathematics to technical problems, or if they are, they are somewhat too specialized in different fields. Accordingly, the author found it necessary to prepare some mimeographed lecture notes from which this book has been developed.Infinite series
Mathematical representation of periodic phenomena, Fourier series and the Fourier
Complex numbers
Integral
Linear algebraic equations, determinants and matrices
The solution of transcendental and polynomial equations
Linear differential equations with constant coefficients
Laplacian transforms of use in the solution of differential equations
Oscillations of linear, lumped electrical circuits
Elastic vibrations of systems with a finite number of degrees of freedom
The differential equations of the theory of structures
The calculus of finite differences and linear difference equations with constant coefficients
Partial differentiation
The gamma, beta, and error functions
Bessel functions
Legendre’s differential equation and Legendre polynomials.
Vector analysis
The wave equation
Simple solutions of Laplace’s differential equation
The equation of heat conduction or diffusion
The elements of the theory of the complex variable
The solution of two-dimensional potential problems by the method of conjugate functions.
The operational calculus
The analysis of nonlinear oscillatory systems