Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 218A: Partial Differential Equations
Approved: 2001-10-12, S. Shkoller

Suggested Textbook: (actual textbook varies by instructor; check your instructor)

Course Description:

  • Laplace's and linear heat equation.
  • Fundamental solution.
  • Mean-value formula.
  • Green's function.
  • Energy methods.
  • Linear wave equation.
  • Representation of solutions and energy methods.
  • Transform methods.
  • Fourier, Laplace and Similarity transforms.
  • Linear Elliptic and Evolution equations.
  • Distribution theory and weak solutions.
  • Sobolev spaces.
  • Weak derivatives and approximation of smooth function spaces.
  • Extension and trace theorems.
  • Basic inequalities.
  • Gagliardo-Nirenberg.
  • Sobolev Embedding Theorem.
  • Second Order Elliptic Boundary Value Problems.
  • Weak Solutions, Elliptic Regularity, and Maximum Principles.
  • Eigenvalue Problems.