Numerical Quadrature and Solution of Ordinary Differential Equations

This is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject. The prerequisites are calculus, some knowledge of ordinary differential equations, and knowledge of computer programming using Fortran. Normally this should be half of a two semester course, the other semester covering numerical solution of linear systems, inversion of matrices and roots of polynomials. Neither semester should be a prerequisite for the other.
This would prepare the student for advanced topics on numerical analysis such as partial differential equations. We are philosophically opposed to a one semester surveyor "numerical methods" course which covers all of the above mentioned topics, plus perhaps others, in one semester. We believe the student in such a course does not learn enough about anyone topic to develop an appreciation for it. For reference Chapter I contains statements of results from other branches of mathematics needed for the numerical analysis. The instructor may have to review some of these results. Chapter 2 contains basic results about interpolation. We spend only about one week of a semester on interpolation and divide the remainder of the semester between quadrature and differential equations. Most of the sections not marked with an * can be covered in one semester. The sections marked with an * are included as a guide for further study.