Syllabus

Differential Equations (18.03 or 18.034). Complex Variables with Applications (18.04) or Functions of a Complex Variable (18.112) are useful, as well as previous acquaintance with the equations as they arise in scientific applications.

Textbook

Haberman, R. Applied Partial Differential Equations. 4th ed. Upper Saddle River, New Jersey: Prentice Hall, March 24, 2003. ISBN: 0130652431.

Assignments and Exams

There will be 6 problem sets given throughout the term. There will be two in-class tests and a final exam.

Outline

1. The Heat Equation in one space variable
   • Separation of variables, Fourier Series, Sturm-Liouville Eigenvalue problems
     
     
2. The Wave Equation in one space variable
   • Method of characteristics
     
     
3. Method of characteristics solution to quasilinear PDEs
   
   
   
4. The heat and wave equations with two or three space variables
   • Bessel functions, Laplace's equation
     
     
5. The Heat Equation and Laplace's equation on unbounded spacial domains
   • Fourier Transform
     
     
6. Green's Function method for solving ODEs, PDEs