The Three Dimensional Trapezoid Rule (UMAP)
Author: Sheldon P. Gordon and Raymond N. Greenwell
The Three Dimensional Trapezoid Rule is a very simple ad reasonably accurate method which can be used to approximate the value of a double integral. The formula for it is a natural extension of the usual trapezoid rule in one variable. A variety of examples are provided in the module to compare the numerical results of the method with those obtained with the Riemann Sum approach and the iterated integral approach. A computer program written in BASIC is provided.
Table of Contents:
1. INTRODUCTION
2. THE TWO DIMENSIONAL CASE
3. THE THREE DIMENSIONAL CASE
4. FINDING A BETTER APPROXIMATING PLANE
5. THE FORMULA AT LAST!
6. EXAMPLE
7. THE QUESTION OF CONVERGENCE
8. A COMPUTER PROGRAM
9. AN EXAMPLE USING SURFACE AREA
10. AN EXAMPLE FROM PROBABILITY
11. SAMPLE TEST
12. REFERENCES
13. ACKNOWLEDGMENT
14. ANSWERS TO EXERCISES
15. ANSWERS TO SAMPLE TEST
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