An Introduction to Numerical Methods in C++

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. 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. Features of the language not used here are ignored. What remains, however, is a powerful framework for numerical computations and more than enough for an introductory text.

Contents

1. Preliminaries
   
2. Expressions, statements and functions
   
3. Errors, theorems and speed
   
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 systems of equations
    
13. Matrix eigenvalue problems
    
14. Interpolation and data fitting
    
15. Graphics
    
16. Differentiation and integration
    
17. Orthogonal polymonials
    
18. Differential equations
    
19. More about differential equations
    
20. Recursive data types-lists
    
21. Elements of Fourier analysis