# 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. INTRODUCTION2. THE TWO DIMENSIONAL CASE3. THE THREE DIMENSIONAL CASE4. FINDING A BETTER APPROXIMATING PLANE5. THE FORMULA AT LAST!6. EXAMPLE7. THE QUESTION OF CONVERGENCE8. A COMPUTER PROGRAM9. AN EXAMPLE USING SURFACE AREA10. AN EXAMPLE FROM PROBABILITY11. SAMPLE TEST12. REFERENCES13. ACKNOWLEDGMENT14. ANSWERS TO EXERCISES15. ANSWERS TO SAMPLE TEST**

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

You must have a **Full Membership** to download this resource.

If you're already a member, **login here**.