Search Site



Advanced Search


 
Product No. 99780 Supplementary Print Price: FREE with membership
 

Applications of Sequences and Limits in Calculus (UMAP)

Yves Nievergelt


Mathematics Topic:
Analysis, Calculus, Precalculus
Application Areas:
Chemistry, finance
Prerequisites:
A working knowledge of rational arithmetic, the concepts of mathematical functions, and mathematical induction.

| ©2000 by COMAP, Inc. | Tools for Teaching 1999 | 26 pages |


This module introduces applications of the mathematical concepts of "sequence" and "limit" by way of the method of bisection. In precalculus, bisection provides an example of an algorithm, together with approximations of solutions, estimates of accuracy, sequence, and mathematical induction. In beginning calculus and real anaylsis, bisection provides a motivation for precise definitions of the real numbers, for instance, as Dedekind cuts, or as equivalence classes of Cauchy sequences of rational numbers.

Table of Contents:

INTRODUCTION

REASONS FOR SOLVING EQUATIONS

SOLVING EQUATIONS THROUGH BISECTION

FURTHER ISSUES

SOLVING EQUATIONS THROUGH REGULA FALSI

CONCLUSIONS

SOLUTIONS TO THE ODD-NUMBERED EXERCISES

REFERENCES

ABOUT THE AUTHOR