MA 5920 Partial Differential
Equations
Course
contents: First order partial differential equations: Linear, quasi-linear and fully nonlinear equations-Lagrange and
Charpit methods. Second order partial differential equations:
Classification and Canonical forms of equations
in two independent variables, One dimensional wave equation- D'Alembert's
solution, Reflection method for half-line, Inhomogeneous wave equation, Fourier Method.
One
dimensional diffusion equation:
Maximum Minimum principle for the diffusion equation, Diffusion equation on the whole line, Diffusion on the half-line, inhomogeneous equation on the whole line, Fourier method.
Laplace equation:
Maximum -Minimum principle, Uniqueness of solutions;
Solutions of Laplace equation in Cartesian and polar coordinates-Rectangular regions, circular regions, annular regions; Poison integral formula
Diffusion and wave equations
in higher dimensions. Text Books: 1.
Ioannis P Stavroulakis and Stepan A Tersian, Partial
differential equations- an introduction with mathematica and maple, world -
Scientific, Singapore, 1999 References: 1.
Jeffery Cooper, Introduction to partial
differential equations with matlab, Birkhauser, 1998 2.
Clive R Chester, Techniques in partial
differential equations, McGraw-Hill, 1971 3.
K Sankara Rao, Introduction to partial
differential equations, Prentice Hall India,1997 4.
I. N. Sneddon, Elements of partial differential
equations, McGraw-Hill, New York,1986 5.
W. E.
Williams, Partial differential equations, Clarendon Press, Oxford, 1980. |