An Introduction to Scientific Computing

Numerical Approximation of Model Partial Differential Equations.- Nonlinear Differential Equations: Application to Chemical Kinetics.- Polynomial Approximation.- Solving an Advection-Diffusion Equation by a Finite Element Method.- Solving a Differential Equation by a Spectral Method.- Signal Processing: Multiresolution Analysis.- Elasticity: Elastic Deformation of a Thin Plate.- Domain Decomposition Using a Schwarz Method.- Geometrical Design: Bézier Curves and Surfaces.- Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem.- Thermal Engineering: Optimization of an Industrial Furnace.- Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations.

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)