Basic Numerical Mathematics

There is no doubt nowadays that numerical mathematics is an essential component of any educational program. It is probably more efficient to present such material after a reasonable competence in (at least) linear algebra and calculus has already been attained - but at this stage those not specializ ing in numerical mathematics are often interested in getting more deeply into their chosen field than in developing skills for later use. An alternative approach is to incorporate the numerical aspects of linear algebra and cal culus as these subjects are being developed. Long experience has persuaded us that a third attack on this problem is the best and this is developed in the present two volumes, which are, however, easily adaptable to other circum stances. The approach we prefer is to treat the numerical aspects separately, but after some theoretical background. This is often desirable because of the shortage of persons qualified to present the combined approach and also because the numerical approach provides an often welcome change which, however, in addition, can lead to better appreciation of the fundamental con cepts. For instance, in a 6-quarter course in Calculus and Linear Algebra, the material in Volume 1 can be handled in the third quarter and that in Volume 2 in the fifth or sixth quarter.

1. Manipulation of Vectors and Matrices. - 2. Norms of Vectors and Matrices. - 3. Induced Norms. - 4. The Inversion Problem I: Theoretical Arithmetic. - 5. The Inversion Problem II: Practical Computation. - 6. The Characteristic Value Problem Generalities. - 7. The Power Method, Deflation, Inverse Iteration. - 8. Characteristic Values. - 9. Iterative Methods for the Solution of Systems Ax=b. - 10. Application: Solution of a Boundary Value Problem. - 11. Application: Least Squares Curve Fitting. - 12. Singular Value Decomposition and Pseudo-Inverses. - Solutions to Selected Problems. - Bibliographical Remarks.