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COM S 322 Introduction to Scientific Computation (also ENGRD 322)

Spring, summer. 3 credits. Prerequisites: COM S 100 and MATH 221 or 294.

An introduction to elementary numerical analysis and scientific computation. Topics include interpolation, quadrature, linear and nonlinear equation solving, least-squares fitting, and ordinary differential equations. The MATLAB computing environment is used. Vectorization, efficiency, reliability, and stability are stressed. Special lectures on parallel computation.

From the Preface to the Text:

Matlab affects the way we do research in scientific computing because it encourages experimentation with interesting mathematical ideas. Visualization and vector-level thinking are supported in a way that permits focus on high-level issues. It is by clearing such a wide path from research to applications that Matlab has been such an uplifting force in computational science. For exactly the same reasons, Matlab can uplift the teaching of introductory scientific computing. Students need to play with the mathematics that stands behind each and every new method that they learn. They need graphics to appreciate convergence and error. They need a matrix-vector programming language to solidify their understanding of linear algebra and to prepare for a world of advanced array-level computing. 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. Indeed, the text revolves around examples that are packaged in 200+ M-files. 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. Numerical linear algebra is not confined to the matrix computation units. Because of the graphics thread throughout the text, it permeates the entire presentation beginning in Chapter 1. That first chapter is yet another get-started-with-Matlab tutorial, but it is driven by examples that set the stage for the numerical algorithms that follow.