Advanced partial differential equations with applications

Lectures: 2 sessions / week, 1.5 hours / session

The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.

Differential Equations (18.03 or 18.034); Complex Variables with Applications (18.04), Advanced Calculus for Engineers (18.075), or Functions of a Complex Variable (18.112)

Basic theory of one complex variable and ordinary differential equations (ODE). No prior knowledge of partial differential equations theory is assumed.

This is just to give you an idea of the flavor. Some things may be covered in more detail than this implies, or the reverse.

There is no required textbook for this course. A list of a few recommended textbooks can be found in the Readings section.

There will be two exams, one at midterm and one during the last week of class. There is no final exam. There will be 5 problem sets (one every 1-2 weeks).

I strongly urge you to become proficient in MATLAB® It is a very useful tool, and I may use it from time to time to illustrate points in the course. In addition, the problem sets may require some computations, easily done if you know MATLAB. See the Related Resources section for more information about MATLAB.

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