Elementary Theory and Application of Numerical Analysis Revised Edition

This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It considers a relatively small number of basic concepts and techniques, focusing on how and why each method works. The authors offer careful consideration of error-analysis aspects related to the problems and algorithms.
The treatment also reviews and solidifies basic concepts from elementary calculus, emphasizing theory and proofs. It makes repeated use of the mean-value theorem, intermediate-value theorem, and Taylor's series. Many exercises appear throughout the text, most with solutions, and an extensive tutorial explains how to solve problems with C++.

An emeritus Professor of Mathematics at Transylvania University, James E. Miller has published several computer-related titles and specializes in teaching the use of software in solving mathematics problems.

Table of ContentsPreface to the Revised 2011 Dover Edition1. Solution of Equations by Fixed Point Iteration2. Matrix Computations and Solution of Linear Equations3. Iterative Solution of Systems of Equations4. Polynomials, Taylor's Series and Interpolation Theory5. Errors and Floating-Point Arithmetic6. Numerical Differentiation and Integration7. Introduction to the Numerical Solution of Ordinary Differential Equations8. Numerical Solution of Ordinary Differential EquationsAppendix A: C++ ProgrammingAppendix B: Answers to Selected ExercisesBibliographyIndex