#### Date of Award

8-1963

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Degree Discipline

Mathematics

#### Abstract

INTRODUCTION

The reader should have, at one time or another, encountered power series in his mathematical study. A power series is a series whose terms are monomial ascending power of x and in the form of

a0 4- a.jX + a2x 2 + • • • • [1, 350]

Such series are important in the study of calculus.

The particular series to be enlarged upon in this paper is the Taylor's Theorem. The purpose is to show how Taylor's Theorem is derived* To accomplish this purpose we will prove and discuss a sequence of theorems. The first theorem we will prove is Rolle's Theorem. Since the remainder of the theorems must satisfy the conditions of Rolle's Theorem, we may say that it is the core of our discussion*

There are many uses of the word "continuous" in mathematics. In some areas of mathematics, continuous is more important than in other. For example, in calculus several of our important theorems are based on the idea that the function f(x) is continuous# To achieve our purpose, the proof of each theorem is based on this continuous idea# Continuous means without interruption. In mathematics, it must be assured that there are no interruptions. If there are none, we can say a continuous function is a function which acts in a well defined manner throughout a closed interval# Before we can say a function f(x) is continuous, it must satisfy certain conditions# If these conditions are not met then the function is not continuous# Since these factors are so important the question should arise, what then must be true for f(x) to be continuous? This question will be answered later#

#### Committee Chair/Advisor

Samuel H. Douglas

#### Committee Member

Samuel H. Douglas

#### Publisher

Prairie View Agricultural and Mechanical College

#### Rights

© 2021 Prairie View A & M UniversityThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

#### Date of Digitization

11/15/2021

#### Contributing Institution

John B Coleman Library

#### City of Publication

Prairie View

#### MIME Type

Application/PDF

#### Recommended Citation

Doggett, D. V. (1963). The Development Of Taylors Theorem. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/729