Date of Award
7-11-2011
Document Type
Thesis
Degree Name
Mathematics, MSE
First Advisor
Jie Miao
Committee Members
Debra Ingram; Susanne Melescue
Call Number
LD251 .A566t 2011 K3
Abstract
The Weierstrass approximation theorem is well known in analysis. This theorem states that on a closed interval we can find a sequence of polynomials that comes closer and closer to any continuous real function. The importance of this theorem is that it is valid for both differentiable and non-differentible functions. In this paper we review and prove this theorem in one and higher dimensions by a constructive method and then give examples. An idea - different from the one used in Walter Rudin's book "Principles of Mathematical Analysis" - enables us to prove this theorem in one and higher dimensions in the same fashion. The first chapter focuses on the one variable case which we illustrate by an example.The second chapter focuses on both the two and multiple variables cases which we also illustrate by an example. We use Mathematica 8 in constructing the examples.
Rights Management
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Kaplan, Orhan, "Stone-Weierstrass Approximation Theorem, a Constructive Approach" (2011). Student Theses and Dissertations. 927.
https://arch.astate.edu/all-etd/927
