Overview
One primary goal of science is to observe nature and figure out its basic governing laws. This pursuit of accurate predictions of nature frequently requires us to frame nature laws in mathematical equations. Partial Differential Equations (PDEs) is a special form of equation which has played a prominent role in our current engineering and technological advancement. The focus of this course is to understand how PDEs come out as a natural mathematical tool to study problems like climate change, pollution control, aerodynamics, civil engineering, etc.
Pedagogy
The course will be divided into 10 projects. Each project will have following components:
- A real life or at least non-mathematical situation from, e.g, image processing, turbine design, climate study, bridge design, etc.
- Review of necessary physics or any other background information necessary to study this area.
- Derivation of project specific PDEs.
- Use of a software to plot and analyze the solutions of the PDE. (No prior computational experience necessary)
- Report submission on consistency between: underlying problem, PDE, and plotted solutions.
- So what? Imagine another situation where similar PDE fits.
References
- An Introduction to Partial Differential Equations with MATLAB, Mathew P. Coleman (Second Edition)
- A collection of Problems in Mathematical Physics, B. M. Budak and A. A. Samarskii
Assessment
Based on project reports