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An Instructional Framework for Introducing Wavelet-Based Problem Solving Techniques to Advanced Civil Engineering Students Joshua M. Peschel and Anthony T. Cahill Department of Civil Engineering, Texas A&M University

Introduction

Wavelet-based problem solving techniques are a relatively new addition to a growing number of advanced undergraduate and graduate engineering curriculums. Traditionally, wavelet theory and methods have been taught as either a separate semester-long mathematics course or within an electrical engineering context3. While these curriculum options do provide viable pathways for learning wavelet concepts, prerequisite courses and a general lack of related application focus often make them inaccessible for civil engineering students who often do not possess a mathematical background beyond differential equations or linear algebra.

Within the civil engineering profession and its related research communities, wavelet-based techniques and applications continue to be developed. Examining the various sub-discipline areas, such as water resources5,2, structures6,4, transportation11,13, and materials7,9, results have indicated that wavelet-based techniques can often provide a unique insight into the analysis and characterization of time series data, versus classical methods.

The inherent non-stationary nature of signals that civil engineers may encounter makes a satisfactory analysis by classical spectral methods, such as Fourier analysis, very difficult or often impossible to perform; wavelets provide a solution to this problem. While wavelets are an extension along the general ideas of Fourier analysis, they do represent a new area of research in the field of engineering education. As such, teaching methods have not been developed, nor do many of the mainstream textbooks present wavelet theory and applications in a tractable manner for students without an advanced mathematical background.

Objectives

This paper presents the development of an instructional framework to introduce and assess student (learner) understanding of wavelet-based problem solving techniques within an advanced undergraduate- and graduate-level civil engineering course at Texas A&M University. The instructional framework is outlined within the following six core domains:

1. Learning Challenges and Learning Objectives 2. Authentic Scientific Inquiry 3. Embedded Information Technology 4. Assessment and Learning Products 5. Learning Experiences with Instructional Technologies 6. Strategic Planning for Implementation

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Cahill, A., & Peschel, J. (2005, June), An Instructional Framework For Introducing Wavelet Based Problem Solving Techniques To Advanced Civil Engineering Students Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14611