An Integrated Introduction To Engineering, Mathematics, Physics (EMP)

The primary goal of this integrated course is to give first-year engineering students a sense of the excitement of modern engineering and of the foundational roles that mathematics and physics play in various engineering disciplines. Engineering, Math, and Physics (EMP) was the first course sequence developed by the Keller Center and is a key part of the center's efforts to shape engineering education for the 21st century. The 2015-16 academic year will mark the eleventh year of the course, which has now become an established part of the curriculum with an integrated two-course physics/math sequence in the fall semester and a separate introductory engineering course in the spring term.


Freshman year is a critical time for students who are contemplating the study of engineering. In their first year, undergraduates lay the fundamental mathematical and physical foundations for their later studies, while making crucial decisions about the field in which they would like to concentrate for the following three years. Yet the conventional freshman curriculum gives engineers only a glimpse of the exciting work that this foundation enables. The integrated approach reflects the nature of much engineering practice and research today, which involves solving problems that cut across conventional disciplines. The three courses that make up the EMP series are taught by 10 faculty members from eight departments, who work as a team to introduce calculus and physics in the form of motivational examples and laboratory experiences that are relevant to all branches of engineering.


The labs in the first semester of the sequence revolve around a single project to build, launch, and analyze the flight dynamics of water-propelled rockets. The project takes students from building their own circuit boards with micro-mechanical accelerometers to a detailed study of the interactions of gravity, thrust, momentum, and drag. These tasks integrate concepts from mathematics, physics, mechanical and aerospace engineering, electrical engineering, and computer science, engaging students in the lab experience in ways that conventional physics labs do not.

In the second semester, after a series of lectures on each engineering discipline, students work on three design projects, each based on a major theme: energy sources and the environment, robotic remote sensing, and wireless multimedia communication. Each project entails lectures on the technical background and hands-on work to apply the general principles of engineering to working devices. The sessions also include guest lectures that introduce societal, technical, and scientific issues related to the three major themes.


  • "The EMP labs are practical, fun, and fully maximize the allotted three hours. Last semester's highlight was launching the water rockets we built, but in the process we learned basics of soldering, circuitry, and analyzing data using Matlab." -- Nathan Keyes '11
  • "The biggest thing I've gained from the experience is a true understanding of how math and physics go hand-in-hand. Every week when we learn something new in physics that we had seen in our multivariable class, I get excited because I'm actually able to see the how the math plays out in the real world." -- Elizabeth Nadelman '11
  • "The highlight of EMP for me has certainly been its sense of community. During the first semester, we had two-hour evening problem sessions for both math and physics that almost the entire class attended... I experienced a taste of real academic collaboration." -- Megan Wong '11
  • "The camaraderie was very palpable. Because they went through the courses together, they all got to know each other. They worked together and helped each other, and the benefit that they got from that was significant." -- James Olsen, Assistant Professor, Physics



(also MAT 191/PHY 191) Fall (ST)

Taken concurrently with EGR/MAT/PHY 192. An integrated course that covers the material of PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with the emphasis on applications to engineering. Physics topics include: mechanics with applications to fluid mechanics; wave phenomena; and thermodynamics. 

One lecture, three preceptorials, one three-hour laboratory. Professor: Daniel Marlow


(also MAT 192/PHY 192) Fall (QR)

Taken concurrently with EGR/MAT/PHY 191. An integrated course that covers the material of PHY 103 (General Physics: Mechanics and Thermodynamics) and MAT 201 (Multivariable Calculus) with the emphasis on applications to engineering. Math topics include: vector calculus; partial derivatives and matrices; line integrals; simple differential equations; surface and volume integrals; and Green's, Stokes', and divergence theorems.

One lecture, two preceptorials. Professor: Guangbo Xu


(also MAT 194/PHY 194) Spring (ST)

This project-based course offers an introduction to the various disciplines of engineering.  Current projects include: energy conversion and the environment; robotic remote sensing; and wireless image and video transmission.  Projects focus on engineering disciplines and their relationship to the principles of physics and mathematics. 

Two lectures, one three-hour laboratory per week. Professors: J. Benziger, M. Littman, S. Lyon.