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This book provides fifteen computational projects aimed at numerically solving problems from a broad range of applications including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing. For each project the reader is guided through the typical steps of scientific computing from physical and mathematical description of the problem to numerical formulation and programming and finally to critical discussion of numerical results. Considerable emphasis is placed on practical issues of computational methods. The last section of each project contains the solutions to all proposed exercises and guides the reader in using the MATLAB scripts. The mathematical framework provides a basic foundation in numerical analysis of partial differential equations and main discretization techniques, such as finite differences, finite elements, spectral methods and wavelets.
The book is primarily intended as a graduate-level textin applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
The second edition builds upon its earlier material (revised and updated) with three all-new chapters intended to reinforce the presentation of mathematical aspects on numerical methods: Fourier approximation, high-order finite difference methods, and basic tools for numerical optimization. Corresponding new applications and programs concern spectral Fourier methods to solve ordinary differential equations, finite difference methods up to sixth-order to solve boundary value problems and, finally, optimization strategies to fit parameters of an epidemiological model.
The book is primarily intended as a graduate-level textin applied mathematics, but it may also be used by students in engineering or physical sciences. It will also be a useful reference for researchers and practicing engineers.
The second edition builds upon its earlier material (revised and updated) with three all-new chapters intended to reinforce the presentation of mathematical aspects on numerical methods: Fourier approximation, high-order finite difference methods, and basic tools for numerical optimization. Corresponding new applications and programs concern spectral Fourier methods to solve ordinary differential equations, finite difference methods up to sixth-order to solve boundary value problems and, finally, optimization strategies to fit parameters of an epidemiological model.
From the reviews: "In An Introduction to Scientific Computing, the authors present approaches to the numerical solution of problems drawn from a variety of applications. ... This is a graduate-level introduction and the pace is brisk. ... This is a strong text on scientific computing for advanced students in applied mathematics. ... the book is most appropriate for students with some prior experience in scientific computing ... ." (William J. Satzer, MathDL, February, 2007) "The book is based on material offered by the authors at Universite Pierre et Marie Curie (Paris, France) and different engineering schools. It is intended as a graduate-level text in applied mathematics, but it may also be used by students in engineering or physical sciences. It may also be used as a reference for researchers and practicing engineers. Since different possible levels of each project are suggested, the text can be used to propose assignments at different graduate levels." (I. N. Katz, Zentralblatt MATH, Vol. 1119 (21), 2007) "An Introduction to Scientific Computing plunges into solving PDEs by numerical approximation. ... the book is an attempt to completely discuss numerical issues for reasonably complex problems at the level of a graduate textbook. A project-based approach is used. ... Overall, this is a pleasing and useful companion to more complete expositions of the topic. ... If you're preparing advanced students for a workshop, or organizing a numerical analysis club for the semester, then the book is perfect." (Sorin Mitran, SIAM Review, Vol. 50 (1), 2008)