Scientific Computing with Case Studies
Scientific Computing with Case Studies
AUD$200.00
exc GSTThis 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.
- A practical guide that offers exercises throughout the book
- Includes nineteen case studies to allow readers to become familiar with mathematical modelling and algorithm design
- A supporting website supplies relevant MATLAB codes, derivations, and supplementary notes and slides
Product details
April 2009Paperback
9780898716665
395 pages
254 × 174 × 17 mm
0.81kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- Preface
- Part I. Preliminaries: Mathematical Modeling, Errors, Hardware, and Software
- 1. Errors and arithmetic
- 2. Sensitivity analysis: when a little means a lot
- 3. Computer memory and arithmetic: a look under the hood
- 4. Design of computer programs: writing your legacy
- Part II. Dense Matrix Computations:
- 5. Matrix factorizations
- 6. Case study: image deblurring: I can see clearly now
- 7. Case study: updating and downdating matrix factorizations: a change in plans
- 8. Case study: the direction-of-arrival problem
- Part III. Optimization and Data Fitting:
- 9. Numerical methods for unconstrained optimization
- 10. Numerical methods for constrained optimization
- 11. Case study: classified information: the data clustering problem
- 12. Case study: achieving a common viewpoint: yaw, pitch, and roll
- 13. Case study: fitting exponentials: an interest in rates
- 14. Case study: blind deconvolution: errors, errors, everywhere
- 15. Case study: blind deconvolution: a matter of norm
- Part IV. Monte Carlo Computations:
- 16. Monte Carlo principles
- 17. Case study: Monte-Carlo minimization and counting one, two, too many
- 18. Case study: multidimensional integration: partition and conquer
- 19. Case study: models of infections: person to person
- Part V. Ordinary Differential Equations:
- 20. Solution of ordinary differential equations
- 21. Case study: more models of infection: it's epidemic
- 22. Case study: robot control: swinging like a pendulum
- 23. Case study: finite differences and finite elements: getting to know you
- Part VI. Nonlinear Equations and Continuation Methods:
- 24. Nonlinear systems
- 25. Case study: variable-geometry trusses
- 26. Case study: beetles, cannibalism, and chaos
- Part VII. Sparse Matrix Computations with Application to Partial Differential Equations:
- 27. Solving sparse linear systems: taking the direct approach
- 28. Iterative methods for linear systems
- 29. Case study: elastoplastic torsion: twist and stress
- 30. Case study: fast solvers and Sylvester equations: both sides now
- 31. Case study: eigenvalues: valuable principles
- 32. Multigrid methods: managing massive meshes
- Bibliography
- Index.
