• Notation
• Scientific computing
• Systems of linear equations
• Linear least squares
• Eigenvalue problems
• Nonlinear equations
• Optimization
• Interpolation
• Numerical integration and differentiation
• Initial value problems for ODEs
• Boundary value problems for ODEs
• Partial differential equations
• Fast fourier transform
• Random numbers and simulations

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results. In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
(source: Nielsen Book Data)

• Numerical algorithms
• Roundoff errors
• Nonlinear equations in one variable
• Linear algebra background
• Linear systems: direct methods
• Linear least squares problems
• Linear systems : iterative methods
• Eigenvalues and singular values
• Nonlinear systems and optimization
• Polynomial interpolation
• Piecewise polynomial interpolation
• Best approximation
• Fourier Transform
• Numerical differentiation
• Numerical integration
• Differential equations.

This book is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues, and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB℗®, with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. A variety of exercises are provided within each chapter along with review questions aimed at self-testing. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science, and industrial mathematics.

• Numerical algorithms
• Roundoff errors
• Nonlinear equations in one variable
• Linear algebra background
• Linear systems : direct methods
• Linear least squares problems
• Linear systems : iterative methods
• Eigenvalues and singular values
• Nonlinear systems and optimization
• Polynomial interpolation
• Piecewise polynomial interpolation
• Best approximation
• Fourier transform
• Numerical differentiation
• Numerical integration
• Differential equations.

• Mathematical preliminiaries-- Solutions of equations in one variable-- Interpolation and polynomial approximation-- Numerical differentiation and integration-- Initial-value problems for ordinary differential equations-- Direct methods for solving linear systems-- Iterative techniques in matrix algebra-- Approximation theory-- Approximating Eigenvalues-- Numerical solutions of nonlinear systems of equations-- Boundary-value problems for ordinary differential equations-- Numerical solutions to partial differential equations-- Index of algorithms.
• (source: Nielsen Book Data)

This text aims to balance theory and applications to give an introduction to the techniques and ideas of numerical analysis. Each chapter offers a basic introduction to the topics under study including methods, theoretical discussion and examples. Survey of methods and software sections have been added to provide a reference to the latest technology in the field.
(source: Nielsen Book Data)