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A Pr oposal for Unifying some of the Fundamental Concepts of Engineer ing

Gr egor y S. Mowr y

Engineer ing Depar tment, Univer sity of St. Thomas

Abstract

Mathematics is the descriptive language of engineering while physics provides the foundation for engineering. At many engineering institutions, mathematics and physics are frequently taught by departments other than the engineering department. This tradition often has the result that undergraduate students experience considerable difficulty in applying their mathematics skills in physics and engineering. Additionally, students infrequently learn the relevance and significance of several of the common fundamental mathematical relationships that underscore all technical fields of study.

Two of the many important results from mathematics that are essential for all technically oriented students are Taylor’s theorem and Fourier analysis. A working knowledge of the implications and consequences of these theorems serves as a unifying theme that underscores many aspects of the foundation of engineering. Students skilled in the use of these theorems develop deeper insights into many different fields of study and are able to quickly comprehend fundamental concepts in many seemingly unrelated technologies.

The implications and application of Taylor’s theorem and Fourier analysis as foundational concepts has been successfully incorporated into several engineering and physics courses. In this paper the fundamental importance of these two theorems is discussed. A method that has been used to incorporate fundamental concepts into existing courses is reviewed. And finally, the foundation for a new course based on this approach, titled “Introduction to the Physics of Engineering,” is discussed.

Introduction

Students typically begin taking core undergraduate science and technology classes during their junior and senior years. By this time, the students have usually taken the prerequisite mathematics and physics. A typical mathematics curriculum for physics and engineering students usually includes calculus, differential equations, linear algebra, multivariable calculus, and occasionally complex variables. The introductory physics curriculum usually includes general calculus-based-physics with an introduction to classical and modern physics. Based on observations made at several institutions, the unfortunate reality is that even students who have excelled in these introductory classes often have difficulty in applying the basic principles to

Proceedings of the 2004 American Society of Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education

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Mowry, G. (2004, June), A Teaching Methodology For Unifying Some Of The Fundamental Concepts Of Engineering Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--13870