Numerical Quadrature and Solution of Ordinary Differential Equations

1. Front Matter

   Pages i-xi

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2. Background Information

   • A. H. Stroud

   Pages 1-42

3. Interpolation

   • A. H. Stroud

   Pages 43-105

4. Quadrature

   • A. H. Stroud

   Pages 106-205

5. Initial Value Problems for Ordinary Differential Equations

   • A. H. Stroud

   Pages 207-303

6. Back Matter

   Pages 305-338

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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.

• Mean value theorem
• Numerical integration
• numerical analysis
• numerical quadrature
• ordinary differential equation
• partial differential equation
• ordinary differential equations

• Department of Mathematics, Texas A & M University, USA

  A. H. Stroud