FRS 001O — Sec. 001 — (1 unit) — CRN 55881 — R 12:10-1:00pm— 2130 Bainer
Understanding Calculus Using Physical Experiments

Instructor: Mohamed Hafez, Department of Mechanical & Aeronautical Engineering, 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-derivates) 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 taken 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.

Prerequisites: High School Math (geometry, algebra & trig., calculus) and High School Science (chemistry, physics).

Format: Ten 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 and participation in the experiments equally weighted.

About the Instructor: Prof. M. Hafez is a faculty member of Mechanical and Aeronautical Engineering since 1985. He teaches three undergraduate courses E-180 (Engineering Analysis) in the Fall, EAe-126 (Theoretical and Computational Aerodynamics ) in the Spring and EAE 189 Rocket Propulsion) in the summer session II. In the winter he teaches a graduate course EMA-262 (Theoretical Aerodynamics) or EMA-264 (Computational Aerodynamics). His research projects deal with Computational Fluid Dynamics(CFD) and Low & High Speed Aerodynamics.