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""The objective of this book is for readers to learn where approximation methods come from, why they work, why they sometimes don?t work, and when to use which of the many techniques that are available, and to do all this in an environment that emphasizes readability and usefulness to the numerical methods novice. Each chapter and each section begins with the basic, elementary material and gradually builds up to more advanced topics. The text begins with a review of the important calculus results, and why and where these ideas play an important role throughout the book. Some of the concepts required for the study of computational mathematics are introduced, and simple approximations using Taylor?s Theorem are treated in some depth. The exposition is intended to be lively and "student friendly". Exercises run the gamut from simple hand computations that might be characterized are "starter exercises", to challenging derivations and minor proofs, to programming exercises. Eleven new exercises have been added throughout including: Basins of Attraction; Roots of Polynomials I; Radial Basis Function Interpolation; Tension Splines; An Introduction to Galerkin/Finite Element Ideas for BVPs; Broyden?s Method; Roots of Polynomials, II; Spectral/collocation methods for PDEs; Algebraic Multigrid Method; Trigonometric interpolation/Fourier analysis; and Monte Carlo methods. Various sections have been revised to reflect recent trends and updates in the field"-- Provided by publisher."

"Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs or write their own based on the models included in the book."

"This student-friendly introduction to the fundamental concepts and techniques of numerical analysis and numerical methods aims to develop concepts and techniques in a clear, concise, easy-to-read manner, and features fully-worked examples"