# Course

## M454 - Partial Differential Equations

Course No:
M454
Credit:
4
Prerequisites:
M301
Approval:
2014
UG-Elective
Syllabus:
Classification of Partial Differential Equations, Cauchy Problem, Cauchy Kowalevski Theorem, Lagrange-Green identity, The uniquness theorem of Holmgren,
Transport equation: Initial value problem, nonhomogeneous problem
Laplace equation: Fundamental solution, Mean Value formula, properties of Harmonic functions, Green’s function, Energy methods, Harnack’s inequality.
Heat Equation: Fundamental solution, Mean value formula, properties of solutions.
Wave equation: Solution by spherical means, Nonhomogeneous problem, properties of solutions.
Reference Books:
1. L. C. Evans, “Partial Differential Equations”, Graduate Studies in Mathematics 19, American Mathematical Society, 2010.
2. F. John, “Partial Differential Equations”, Springer International Edition, 2009.
3. G. B. Folland, “Introduction to Partial Differential Equations”, Princeton University Press, 1995.
4. S. Kesavan, “Topics in Functional Analysis and Applications”, John Wiley & Sons, 1989.