They need a total problem solving environment tapping into the very latest algorithmic research that has a bearing on science and engineering. In short, they need Matlab. In this textbook I present all the topics that are usually covered in a one-semester introduction to scientific computing. But graphics and matrix-vector manipulation have been folded into the presentation in a way that gets students to appreciate the connection between continuous mathematics and computing. Each of the nine chapters comes equipped with a theorem.
Analysis is complemented with computational experiments that are designed to bolster intuition.
These codes are critical to the overall presentation. Collectively they communicate all the key mathematical ideas and an appreciation for the subtleties of numerical computing. They also illustrate many features of Matlab that are likely to be useful later on in the student's computational career. Snapshots of advanced computing are given in sections that deal with parallel adaptive quadrature and parallel matrix computations. Our treatment of recursion includes divided differences, adaptive approximation, quadrature, the fast Fourier transform, Strassen matrix multiplication, and the Cholesky factorization.