Partial Differential Equations

(3 Credit Hours) · Undergraduate

Partial differential equations (PDE) have long been attracting the interest of a large portion of the scientific community, since they can be employed for modelling a plethora of fascinating phenomena arising in various areas of the sciences such as fluid dynamics, quantum mechanics, mathematical biology and mathematical finance and economics. It is important that such equations are studied rigorously as mathematical objects. On the one hand, this may lead to new mathematical theories while on the other, it helps other scientists to better understand the validity of the models and ultimately the underlying physical phenomena. This course provides an introduction of the basic ideas and techniques that have been proved useful for studying the basic properties of PDE and whenever possible for solving them analytically or numerically. Also, it prepares students for taking interdisciplinary courses using PDE, like Mathematical Methods in Financial Economics (Math 40570), and graduate PDE courses.