Elementary Techniques of Numerical Integration (UMAP)

A unit that uses calculus and elementary techniques of numerical integration. By the end of this module students will be able to: 1) write programs in BASIC to calculate Riemann Sums for various functions; 2) approximate integrals using the Trapezoidal Rule and Simpson's Rule and write programs in BASIC to do this; 3) explain why the Trapezoidal Rule and Simpson's Rule give better approximations of most integrals than rectangle approximations; and 4) know the method of doubling the number of subintervals to improve approximations to definite integrals.

Table of Contents:

1. INTRODUCTION AND OVERVIEW

2. APPROXIMATING INTEGRALS USING RIEMANN SUMS
2.1 The Left-Rectangle Method
2.2 The Right-Rectangle Method

3. THE TRAPEZOID RULE

4. SIMPSON'S RULE

5. DOUBLING THE NUMBER OF SUBINTERVALS IN PARTITIONS OF UNIFORM WIDTH

BIBLIOGRAPHY

APPENDIX A

APPENDIX B

APPENDIX C