Survey of Numerical Mathematics, Volume I

Designed as a text for a three-semester course in numerical analysis, this highly regarded work presents a broad overview of computer-oriented numerical algorithms for solving various types of mathematical problems. The book is intended not only to impart a working knowledge of practical techniques for solving real problems but to prepare the student for advanced studies at the graduate level.
Topics include:
Evaluation of elementary functions
Solution of a single nonlinear equation with specific reference to polynomial equations
Interpolation and approximation
Numerical differentiation and quadrature
Ordinary differential equations
Computational problems in linear algebra
Numerical solution of elliptic and parabolic partial differential equations by finite difference methods
Solution of large linear systems by iterative methods
In addition to thorough coverage of the fundamentals, these wide-ranging volumes contain such special features as an introduction to computer arithmetic, including an error analysis of a system of linear algebraic equations with rational coefficients, and an emphasis on computations as well as mathematical aspects of various problems.
Geared toward senior-level undergraduates and first-year graduate students, the book assumes some knowledge of advanced calculus, elementary complex analysis, matrix theory, and ordinary and partial differential equations. However, the work is largely self-contained, with basic material summarized in an appendix, making it a perfect resource for self-study.
Ideal as a course text in numerical analysis or as a supplementary text in numerical methods, A Survey of Numerical Mathematics judiciously blends mathematics, numerical analysis, and computation. The result is an unusually valuable reference and learning tool for modern mathematicians, computer scientists, programmers, engineers, and physical scientists.