Mathematics for the Physical Sciences

This book is intended to furnish a bridge from courses in general physics to the intermediate-level courses in classical mechanics, electrodynamics, and quantum mechanics. It emphasizes the use of physical concepts to illustrate and clarify the mathematical methods.The book begins with a short review of some topics from general physics that then provide the physical contexts for the later discussions. Thus, for example, the concept of magnetic flux serves to give physical meaning to the integral theorems of vector calculus; the a conducting sphere in an electric field, a vibrating drum head, the harmonic oscillator, and a particle in a box illustrate the discussion of differential equations; and coupled oscillators and the principal axes of a rotating rigid body supply the physical context for the discussion of matrices.Problems at the end of each chapter furnish the student with experience in applying the mathematics and illustrative exercises throughout give guidance. Many of the exercises call for graphical representations, and some are particularly amenable to the use of numerical methods, but the treatment avoids the implication that computers are necessary to solve the problems.