The Drexel Engineering Curriculum

Physical Foundations of Engineering (TDEC 111, 113 & 115).***************************************************************************************************************************

Course objectives:All fields of engineering, chemical, civil, electrical, materials, mechanical, etc., share a common body of fundamental concepts from mathematics and science. The broad objective of the courses Mathematical Foundations of Engineering (MFE) and the Physical Foundations of Engineering (PFE) I, II and III are to develop the mathematical and scientific foundations common to all the various engineering disciplines. In particular, PFE I, II and III focus on the role of mechanics and electricity and magnetism in engineering today. We study the interrelationships - how each reinforces and depends upon the other. As new mathematics and physics concepts are introduced, we emphasize the use of these concepts and principles by studying real-life engineering applications and problems.The three-term sequence of PFE courses is taught by a team of physics and engineering faculty. A faculty team, interdisciplinary and diverse, designed the syllabus which is fully coordinated with the MFE course in order to integrate topics in physics with related calculus concepts. In addition, both the physics and calculus topics are illustrated with engineering applications as and when appropriate. Great care is exercised to incorporate lecture demonstrations to enhance the understanding of both physics and calculus. Due to non-availability of a mathematics or a physics book written especially for engineers, the courses are supplemented with applications and resource books prepared by the faculty. These include a number of engineering design and applications problems. In addition, special assignments employing numerical and algebraic computations, and using Microsoft Excel® and Maple® are included every term. These assignments stress the need to understand and appreciate the powerful mathematical techniques available to study many engineering problems and at the same time incorporate the use of computers in freshman courses.

The first term of the mechanics portion of PFE includes units and measurements, vectors and applications, free-body force diagrams, force systems and analyses, static equilibrium, examples on simple structures, rectilinear and planar motions, Newton's laws, and applications including static and kinetic friction. Typical examples include many engineering problems involving the design of structures, the loading and unloading of crates using cranes, workers aligning and mounting beams, the study of traffic patterns and the timing of the signals, the design of highway ramps, the packaging of tennis balls in containers, the loading and unloading of freight cars, the design and operation of elevators, the loading and unloading of packages on inclines and conveyors in warehouses and airports and many other examples of engineering applications.

In addition to incorporating engineering and design, PFE also stresses the use of calculus. The understanding of limits and derivatives is made easy in physics lecture demonstrations wherein average velocity measurements of gliders on smooth air-tracks are made and the results are extrapolated graphically to visualize the true meaning of instantaneous velocity and acceleration. This demonstration is shown at the same time calculus introduces limits and derivatives. Also, when the students encounter the chain rule in MFE, the concept is simultaneously discussed in many physics and engineering problems. Similarly, MFE adds numerous applications of the derivative to physics and engineering problems; for example, the differential applied to tolerance analysis and optimization problems.

In later terms, when PFE analyzes various forces, it includes gravitational and electrostatic forces as examples of inverse square law forces. The concept of central force is also introduced and many problems including planetary motion are studied. Also, coulomb-force problems in electrostatics are discussed as examples of this same basic concept.

As MFE course develops the theory and techniques of integration, including problems involving the work done by a force, the PFE course draws immediate attention to the related MFE discussion by introducing work-energy as an example of line integrals. In addition, the scalar product of vectors is revisited and its physical significance is emphasized while studying work-energy in PFE. When gravitational and electrostatic potential energy introduced, equivalence between the potential energy stored in a spring and a capacitor is emphasized. Discussion of energy conservation problems clearly leads to a discussion of engineering applications. For example, the impulse and momentum topic is followed by a discussion of momentum conservation in direct and oblique impacts of spheres. While studying these engineering problems, analyses employing kinetics and the energy approach are included wherever possible. The study of linear momentum concludes with an introduction to variable mass problems similar to rocket motion. Plane polar coordinates are also introduced in the discussion of the normal and tangential components of momenta and space dynamics problems.

MFE, in the meanwhile, emphasizes the numerical techniques, including Newton's method and quadrature to enable students to understand MAPLE® during the second term. MFE III discusses the moment of inertia of rigid bodies extensively after PFE introduces rigid body kinematics. Plane rotation, including torque, angular momentum and rotational kinetic energy, is dealt with very rigorously. The study of rolling, with or without slipping, relative velocity and acceleration in linkages, cranks and sliders, including problems on "Slider-Crank" and "Scotch-Yoke" mechanisms, etc constitutes some of the applications of rigid body motion. All of the applications-oriented concepts mentioned above are not typically broached in a traditional freshman physics course. The third term concludes with a detailed study of electromagnetic forces, electromagnetic induction, a-c and d-c circuits and many problems based on engineering applications. The study of current electricity, including Kirchoff's junction and loop rules, gives them a different perspective when introduced by a team of physics and engineering faculty.

Physical Foundations of Engineering: Applications and Resource BookThis applications and resource book to Physical Foundations of Engineering was originally developed during the experimental phase of the E4 program (Enhanced Educational Experience for Engineers)- a program designed to develop and implement new strategies to enhance undergraduate engineering curriculum at Drexel University. This project was supported jointly by the university and the National Science Foundation (Grant USE-8854555). Additional support came from a number of organizations including General Electric Foundation and the Ben Franklin Partnership. This book has many standard physics problems and, in addition, it supplements the traditional freshman physics textbook by providing an opportunity to learn the importance of applying physics and calculus to engineering problems. Also, it helps students see different perspectives given by mathematics, physics and engineering faculty teams and develop a process by which they can synthesize the problem in small pieces before they put the solution together. More detailed information about Physical foundations of Engineering courses is available in Gateway Coalition report submitted for 1998-99 year. We have also included a few examples of engineering applications of Physics and Calculus from Physical Foundations of Engineering Applications and Resource Book at this site. This book is currently custom published by Wiley Custom Services, John Wiley & Sons, Inc.

This Physical Foundations of Engineering (PFE) course page:Physical Foundations of Engineering I, II & III (TDEC111,113,115)course homepage has been developed for the specific purpose of communicating to the freshman engineering students. Students receive all the assignments, material summaries and help with the PFE course material and, also be able to communicate with faculty. This homepage is updated every week. Prof. T. S. Venkataraman (e-mail: venkat@drexel.edu ) is the course director for the PFE sequence.One of the aims of this course is togive our students an enjoyable, rewarding and challenging freshman year engineering experience.

Main Features of this site include but not limited toPFE course syllabus,Course Description, Computational Assignments,Weekly Quiz Schedule, Weekly Recitation Schedule, Contents of Review lecturesand Weekly Announcements.In addition,Course help pageincludes answers, hints and suggestions for all assigned and recommended homework problems andAssignments pagelists weekly PFE Homework/Recitation Assignments. Quiz/Exam Solutions are posted regularly on theQuiz/Exam page.Finally this site also includes links to all the other freshman engineering sites.

A few Engineering Examples introduced in the PFE Courses are given below:

Equilibrium-Worker-beamFree Fall-Packaging Tennis BallsCollision- Conveyor BeltMotion-Optimization Problem

Energy-Rotation Luggage HandlingWork-Energy: MaterialsElectromagnetic Induction-GeneratorDielectric-Capacitor

Also, some Maple assignments given to the freshman class in recent years are shown below:

SampleFall99Fall99SolutionSample Winter00Winter00Solution

SampleFall98Fall98 SolutionSampleWinter99Winter99Solution