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This book provides professionals and students with a thorough understanding of the interface between mathematics and scientific computation. Ranging from classical questions to modern techniques, it explains why numerical computations succeed or fail. The book is divided into four sections, with an emphasis on the use of mathematics as a tool in determining the success rate of numerical methods. The text requires only a modest level of mathematical training, and is ideally suited for scientists and students in mathematics, physics and engineering.
List of contents
- Part I: The entrance fee
- 1: Floating numbers
- 2: A flavour of numerical analysis
- 3: Algebraic preliminaries
- Part II: Polynomial and trigonometric approximation of functions
- 4: Interpolation and divided differences
- 5: Least squares for polynomials
- 6: Splines
- 7: Fourier's world
- 8: Quadrature
- Part III: Numerical linear algebra
- 9: Gauss' world
- 10: Theoretical interlude
- 11: Iterations and recurrences
- 12: Pythagoras' world
- Part IV: Non-linear problems
- 13: Spectra
- 14: Non-linear equations and systems
- 15: Solving differential systems
- 16: Single step schemes
- 17: Linear multi-step schemes
- 18: Toward partial differential equations
- Bibliography
- Index
About the author
Professor Michelle Schatzman, MAPLY, 21 Avenue Claude Bernard, UCBL, F-69622 Villeurbanne Cedex, Tel: +33 4 72 44 85 26, Fax: +33 4 74 22 80 53, Email: schatz@maply.univ-lyon1.fr
Summary
Numerical analysis explains why numerical computations work - or fail. These are mathematical questions, and the book answers in kind, providing students with a complete presentation of the interface between mathematics and scientific computation. It includes a range of exercises, and is suitable as a textbook at the advanced undergraduate level.
Additional text
... the physical detail in which many problems are introduced is one of the strong points of the book. Another strong point is the mathematical rigour which is definitely above the average for a numerical analysis textbook.
