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