For
students with three semesters of calculus, this book is self-contained.
In particular, Section 1.1 contains a complete treatment of the
relevant types of ordinary differential equations. No previous course
in ordinary differential equations or linear algebra is necessary.
There are approximately 280 examples worked out in detail, and 600
exercises ranging from routine to challenging. Answers to selected
problems appear in the back of the book. Rigorous proofs of nearly all
results used are given after ample physical motivation. The book
documents extensive applications, including: heat conduction, wave
propagation, vibrations of strings, square drums, round drums, spheres
and manifolds, traffic flow shocks, evolution of population densities,
fluid flow, electrostatics, minimal surfaces, gravitation, quantum
mechanics (including the determination of the bound states of the
hydrogen atom). Convenient summaries appear at the end of each section.
Theorems and definitions are clearly off-set in boxes. The book
contains 97 figures, illustrations and tables (graphs of mathematical
functions of one or several variables were computer generated.).
