Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

This document looks at specific applications of calculus to engineering. It is noted that for an automobile traveling at constant speed, the mathematical relationship between the directional heading and the angular deflection of the steering wheel can be calculated with respect to time. An analysis is presented which derives the relationship from…

To expertly solve engineering and science problems one needs to know science and engineering as well as have a tool kit of problem-solving methods. This book is about problem-solving methods: it presents the methods professional problem solvers use, explains why these methods have evolved, and shows how a student can make these methods his/her…

This instructional module examines a key function of science and technology: problem solving. It studies the meaning of problem solving, looks at techniques for problem solving, examines case studies that exemplify the problem-solving approach, presents problems for the reader to solve, and provides a student self-quiz. (Author/CT)

Slope Stability is one in a series of single-topic problem modules intended for use in undergraduate and earth science courses. The module, also appropriate for use in undergraduate civil engineering and engineering geology courses, is a self-standing introduction to studies of slope stability. It has been designed to supplement standard…

Models of the motion of an object through space are discussed. The material begins with the simplest view possible in which gravity is the only force examined. Discussion progresses to an examination of the drag force, which is the resistive air force of the wind. Suggestions for further improvements are made at the conclusion of the presentation.…

This document consists of three modules. The first looks at applications of analysis to medical radiology. The goals are to provide: 1) acquaintance with a significant applied mathematics problem utilizing Fourier Transforms; 2) generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) introduction to…

This publication was developed as a portion of a two-semester sequence commencing at either the sixth or seventh term of the undergraduate program in electrical engineering at the University of Pittsburgh. The materials of the two courses, produced by a National Science Foundation grant, are concerned with power conversion systems comprising power…

One module is presented in units 203, 204, and 205, as a guide for students, and presents a general strategy for solving integrals effectively. With this material is a solutions manual to exercises. This document set also includes a unit featuring applications of calculus to geography: 206-Mercator's World Map and the Calculus. Unit 207-Management…

We have designed model-development sequences using a common context to provide authentic problem-solving experiences for first-year students. The model-development sequence takes a model-eliciting activity a step further by engaging students in the exploration and adaptation of a mathematical model (e.g., procedure, algorithm, method) for solving…

The purpose of this module is to introduce students (grades 10-11) to critical bioethical issues by considering moral dilemmas and knowledge of biomedical advances. The module is organized into 12 topic areas, each containing a dilemma story, introductory reading material, sample student responses, and questions. Dilemmas are essentially brief…

This module is designed to provide students (grades 10-11) with experiences in examining how technology has changed our lives and in anticipating future changes. The module is divided into three sections. Role-playing simulations and readings are used in section 1 to examine the dynamic relationship between science/technology/society. Five…

Model-eliciting activities (MEA), specially designed client-drive, open-ended problems, have been implemented in a first-year engineering course and in secondary schools. The educational goals and settings are different, but the design of an MEA enables it to be versatile. This paper will introduce the reader to the principles that guide MEA…

This package consists of course syllabi, an instructor's handbook, and a student laboratory manual for a 1-year vocational training program to prepare students for entry-level employment as automated equipment repair technicians. The program was developed through a modification of the DACUM (Developing a Curriculum) technique. The course syllabi…