The well-organized textbook covers ordinary and partial differential equations, nonlinear differential equations and stability, calculus of variations, and applications. The breadth of the book is such that the discussion of finite differences will elucidate for the undergraduate the connection to derivatives while the in-depth look at the stability of subsystems via linearization and Liapounov provides suitable grist for the graduate.
The soul of this book is to underscore the importance and relevance of the underlying mathematics for avoiding errors in computer solutions while applying numerical methods and the calculus of variations to physical problems. Toward this end, spotlights of enlightenment occur throughout via more than 100 solved problems with detailed explanations. An additional 120 exercises feature solution hints and answers throughout the six sections of the book. What would really help in this bookâ€™s endeavor would be clear algorithms in pseudo-code for ready implementation or, better yet, mating the text with a popular mathematics package, such as Matlab or Maple and syntax-specific examples and exercises.
Accompanying the book is a CD-ROM, but it is limited to the Linux operating system. Among the appendices are tables of Laplace transforms and specialized Laplace inverses.