The first half of this book is designed as a course for first year graduate students in the sciences. Problems are chosen to illustrate mathematical and physical subjects. In this first half only a moderate background in physics and mathematics is assumed. Integration, Monte Carlo techniques, the solution of linear systems and finite element methods are treated with enough depth to allow the student to understand them. An introduction to modeling with differential methods, digital signal processing and chaos is given. One chapter provides an introduction to common computer architectures.In...