FRS 001F — Sec. 001 — (1 unit) — CRN 75078 — T 2:10 – 3:00 pm — 1070 Bainer
Learning Calculus Using Physical Experiments and Their Computer Modeling & Simulation

Instructors: Mohamed Hafez, Department of Mechanical & Aeronautical Engineering, College of Engineering and Bruce Gates, Department of Chemical Engineering & Materials Science, College of Engineering

Description: Mathematical concepts of calculus are developed and explained via results of simple and easily visualized experiments in the laboratory (draining of water from a tank, the experiment of Torricelli, a colleague of Gallileo) and their numerical modeling and simulation on the computer. Functions, limits, differences and derivatives, summations and integrals are demonstrated using physical systems in operation, and measurements are documented and compared with the results of the analysis. Examples of derivatives and integrals (as anti-derivatives) are explained with simple models. Applications using first and second derivatives (linearization and optimization) as well as differential and integral equations (e.g., kinetic reaction equations and Newton's second law of motion) are also discussed. In particular, the data from the draining tank are used to determine a model of the draining process, and these are used to make predictions of draining times, which are checked in the laboratory. These seminars will be prepared for freshmen who are interested to learn calculus via a tangible approach based on physical experiments and computer simulation. The relevant concepts will be explained in a simple manner using intuition built on observation rather than abstract arguments.

Format: Nine lectures including lab and computer demonstrations are planned to cover the main aspects of the subject. A textbook will be used to back up the lectures and for further readings. Homework will be assigned every lecture. Instructors will be available during regular office hours for helping the students. Grading: The grades will be based on homework assignments, participation in the experiments as well as a final exam (written-open book) equally weighted.

About the Instructors: