A Student's Guide to Numerical Methods

The plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.

Ian H. Hutchinson (Author)

9781107095670, Cambridge University Press

Hardback, published 30 April 2015

221 pages, 73 b/w illus.
23.1 x 15.5 x 1.5 cm, 0.48 kg

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introductory class, this compact textbook provides a thorough grounding in computational physics and engineering.

Preface
1. Fitting functions to data
2. Ordinary differential equations
3. Two-point boundary conditions
4. Partial differential equations
5. Diffusion: parabolic PDEs
6. Elliptic problems and iterative matrix solution
7. Fluid dynamics and hyperbolic equations
8. Boltzmann's equation and its solution
9. Energy-resolved diffusive transport
10. Atomistic and particle-in-cell simulation
11. Monte Carlo techniques
12. Monte Carlo radiation transport
13. Next steps
Appendix A. Summary of matrix algebra
Index.

Subject Areas: Computer science [UY], Computing & information technology [U], Mathematics & science [P]