# Course

## M478 - Advanced Partial Differential Equations

Course No:
M478
Credit:
4
Prerequisites:
M401
Approval:
2014
UG-Elective
Syllabus:
Distribution Theory, Sobolev Spaces, Embedding theorems, Trace theorem. Dirichlet, Neumann and Oblique derivative problem, Weak formulation, Lax–Milgram, Maximum Principles– Weak and Strong Maximum Principles, Hopf Maximum Principle, Alexandroff-Bakelmann-Pucci Estimate.
Reference Books:
1. L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics 19, American Mathematical Society, 2010.
2. H. Brezis, “Functional Analysis, Sobolev Spaces and Partial Differential Equations”, Universitext, Springer, 2011.
3. R. A. Adams, J. J. F. Fournier, “Sobolev Spces”, Pure and Applied Mathematics 140, Elsevier/Academic Press, 2003.
4. S. Kesavan, “Topics in Functional Analysis and Applications”, John Wiley & Sons, 1989.
5. M. Renardy, R. C. Rogers, “An Introduction to Partial Differential Equations”, Springer, 2008.