A Survey of Numerical Mathematics

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Designed for a three-semester course in numerical analysis, this highly regarded work provides a comprehensive overview of computer-oriented numerical algorithms for solving various mathematical problems. It aims to impart practical techniques for real-world problem-solving while preparing students for advanced graduate studies. Key topics include the evaluation of elementary functions, solutions of nonlinear equations (with a focus on polynomial equations), interpolation and approximation, numerical differentiation, quadrature, ordinary differential equations, and computational issues in linear algebra. It also covers the numerical solution of elliptic and parabolic partial differential equations using finite difference methods, as well as iterative methods for large linear systems. In addition to fundamental concepts, the text features an introduction to computer arithmetic and error analysis of linear algebraic equations with rational coefficients, emphasizing both computational and mathematical aspects. Targeted at senior undergraduates and first-year graduate students, it assumes prior knowledge of advanced calculus, elementary complex analysis, matrix theory, and differential equations, yet remains largely self-contained with basic material summarized in an appendix, making it suitable for self-study. This resource serves as an ideal course text in numerical analysis or as a supplementary guide in numerical methods, eff