Scientific Computing With Case Studies

This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.

Dianne P. O'Leary is Professor of Computer Science at the University of Maryland, College Park, and also holds an appointment in the university's Institute for Advanced Computer Studies (UMIACS) and in the Applied Mathematics and Scientific Computing program. Her research is in computational linear algebra and optimization, with applications to solution of ill-posed problems, image deblurring, information retrieval, and quantum computing.