Applications of Sequences and Limits in Calculus (UMAP)

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

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