Mathematics 522. Partial Differential Equations and Applied Mathematics

Instructor: Lawrence E. Thomas
Office: 219 Kerchof Hall
e-mail Address let@virginia.edu
Office hours: 1:30-3:00, Monday, 2:-3:30 Tuesday

Text: Advanced Engineering Mathematics, 6th edition
P. V. O'Neil
Thompson, Toronto, Ontario,2007

Prerequisites Math 521.

For whom the course is intended: This course is a continuation of Math 521 (Advanced Calculus with Applied Mathematics). It is intended to meet the mathematical needs of physics, mathematics, and other science and engineering majors. The material presented in the course is selected with a view toward its applications in electrodynamics, hydrodynamics and quantum mechanics. A familiarity with these subjects is not assumed. Coming out of these courses, you should have the required mathematics background for upper level and graduate courses in these fields.

Homework and examinations: There will be assigned homework to be turned in, two take-home midterm examinations, and a take-home final examination. The final grade will be weighted on the basis of: 30% for homework, 20% for each midterm examination, and 30% for the final. Late homework will not be accepted. Class attendance and participation is encouraged and expected.

Course content: Topics to be covered in the course will include:

• Complex Analysis (continued)
  • Cauchy Theorem
  • Cauchy integral formula
  • Residue Calculus
  • Harmonic functions
• Fourier Series and Transforms
  • Convergence of Fourier series and transforms
  • Applications to differential equations
  • Fast Fourier transform, Wavelets
  • Special functions
• Partial Differential Equations
  • Wave, Heat, and Laplace Equations
  • Introduction to non-linear wave equations

Please see the assignment/calendar page, Click here.