Norms In Mathematics

Author

Johnny E. Johnson Jr., Prairie View Agricultural and Mechanical College

Date of Award

8-1970

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

INTRODUCTION

Today, norms and their applications are recognized as an essential part of the background of the mathematical analysts. From the theoretical view point, this is because many proofs of the theorems have become clarified using norms. From the applied point of view, the norms are of tremendous value in the solution of problems of heat flow, potential theory, fluid mechanics, electromagnetic, and many other fields of science and engineering.

There are many kinds of notes in mathematics. However, only three will be discussed in this paper. They are (1) the absolute norm, (2) the Euclidean norm, and (3) the p-norm. In chapter II, several auxiliary theorems and lemmas will be stated without proof. Chapter III contains some basic inequalities dealing with real numbers, sequence of real numbers, and some important lorn as to be used in the application problem. In chapter IV, the important inequality.

will be established for each of the three norms. In chapter V, each of the three forms will be used to establish the existence and uniqueness theorem for a system of non linear differential equations. It will be proven, using the inequalities derived in chapter IV.

Committee Chair/Advisor

A.D. Stewart

Committee Member

E.E. Thornton

Committee Member

Clyde Christopher

Publisher

Prairie View Agricultural and Mechanical College

Rights

Date of Digitization

04/18/2022

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Johnson Jr., J. E. (1970). Norms In Mathematics. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1494