Scientific Computing with Case Studies
By: Dianne P. O'Leary.
Publisher: Society for Industrial and Applied Mathematics
Published: 2009
Place of publication: Philadelphia, PA, USA
Language: eng
Format: Paperback
ISBN-13: 9780898716665
Copyright date: 2009
Subjects: Mathematical models -- Data processing -- Case studies
Genres: Case studies.
Description: Learning through doing is the foundation of Scientific Computing with Case Studies, which allows readers to explore case studies as well as expository material. The book provides a practical guide to the numerical solution of linear an nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats, standard problems and introduces important variants such as space systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis is emphasized, and the MATLAB algorithms are grounded in sound principles of software design and in the understanding of machine arithmetic and memory management.

Nineteen case studies allow readers to become familiar with mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. A Web site provides solutions to the challenges that are offered throughout the book and also supplies relevant MATLAB codes derivations, and supplementary notes and slides.

The book is intended as a primary text for courses in numerical analysis, scientific computing, and computational science for advanced undergraduate and early graduate students. Physicist, chemists, biologists, earth scientists, astronomers, and engineers whose work involves numerical computing also will find the book useful as a reference and tool for self-study.
--back cover
Notes: Includes bibliographical references and index.
Table of contents: title: Preface; title: Part I. Preliminaries: Mathematical Modeling, Errors, Hardware, and Software; title: 1. Errors and arithmetic; title: 2. Sensitivity analysis: when a little means a lot; title: 3. Computer memory and arithmetic: a look under the hood; title: 4. Design of computer programs: writing your legacy; title: Part II. Dense Matrix Computations:; title: 5. Matrix factorizations; title: 6. Case study: image deblurring: I can see clearly now; title: 7. Case study: updating and downdating matrix factorizations: a change in plans; title: 8. Case study: the direction-of-arrival problem; title: Part III. Optimization and Data Fitting:; title: 9. Numerical methods for unconstrained optimization; title: 10. Numerical methods for constrained optimization; title: 11. Case study: classified information: the data clustering problem; title: 12. Case study: achieving a common viewpoint: yaw, pitch, and roll; title: 13. Case study: fitting exponentials: an interest in rates; title: 14. Case study: blind deconvolution: errors, errors, everywhere; title: 15. Case study: blind deconvolution: a matter of norm; title: Part IV. Monte Carlo Computations:; title: 16. Monte Carlo principles; title: 17. Case study: Monte-Carlo minimization and counting one, two, too many; title: 18. Case study: multidimensional integration: partition and conquer; title: 19. Case study: models of infections: person to person; title: Part V. Ordinary Differential Equations:; title: 20. Solution of ordinary differential equations; title: 21. Case study: more models of infection: it's epidemic; title: 22. Case study: robot control: swinging like a pendulum; title: 23. Case study: finite differences and finite elements: getting to know you; title: Part VI. Nonlinear Equations and Continuation Methods:; title: 24. Nonlinear systems; title: 25. Case study: variable-geometry trusses; title: 26. Case study: beetles, cannibalism, and chaos; title: Part VII. Sparse Matrix Computations with Application to Partial Differential Equations:; title: 27. Solving sparse linear systems: taking the direct approach; title: 28. Iterative methods for linear systems; title: 29. Case study: elastoplastic torsion: twist and stress; title: 30. Case study: fast solvers and Sylvester equations: both sides now; title: 31. Case study: eigenvalues: valuable principles; title: 32. Multigrid methods: managing massive meshes; title: Bibliography; title: Index.