CiNii Books - An introduction to numerical methods in C++

This text on numerical computing, presented through the medium of the C++ language, is designed for students of science and engineering who are seriously studying numerical methods for the first time. It should also be of interest to computing scientists who wish to see how C++ can be used in earnest for numerical computation. The mathematical prerequisites are those which an undergraduate student of science or engineering might be expected to possess after the earlier years of study: elementary calculus, linear algebra, and differential equations. The object is to understand how a program performs in practice. In computing, a good knowledge of at least one programming language, such as Basic, Fortran or Pascal, is assumed, while a working knowledge of C would be an advantage. However, no prior knowledge of C++ is assumed. The language is developed in step with its numerical applications, and to the extent required by them. Other features of the language are omitted. What results is a powerful framework for numerical computations. As befits an introductory text, programming effort relates mostly to the classical numerical algorithms. This book is intended for computing for scientists and engineers. Most likely 3rd or 4th year undergraduate.

Table of Contents

1.: Preliminaries. 2.: Expressions, statements and functions. 3.: Errors and theorems. 4.: Roots of non-linear equations. 5.: Classes. 6.: Derived classes and streams. 7.: Integer arithmetic. 8.: Tests of randomness. 9.: Vectors and matrices. 10.: Direct solution of linear equations. 11.: Errors in matrix manipulation. 12.: Iterative solutions of linear equations. 13.: Matrix Eigenvalue problems. 14.: Interpolation and data fitting. 15.: Graphics. 16.: Differences and integration. 17.: Orthogonal polynomials. 18.: Differential equations. 19.: More about differential equations. 20.: Recursive data types - lists. 21.: Elements of Fourier analysis. Appendix A, standard.h. Appendix B, mystring.h. Appendix C, rational.h. Appendix D, random.h. Appendix E, vecmat.h. Appendix F, stdgraph.h. Appendix G, list.h. Bibliography. Index

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An introduction to numerical methods in C++

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