Course: MAT 356 2.0 Applicable Mathematics (Optional)
Course Content:
Hilbert, Banach and Sobolev spaces and particularly useful spaces in PDE theory; Introduction to distribution theory and weak derivatives; Weak form of a PDE and weak solution of a PDE; Galerkin approximation of solution of a PDE; Solve 2D-wave equation in spherical coordinate system; Fundamental solution of Heat equation; Solving Laplace’s equation by means of fundamental solutions; Solution of Transport equation; Introduction to calculus of variation; First variation of Euler-Lagrange equation; Second variation of Euler-Lagrange equation; Systems.
Recommend Readings:
- Evans,L.R. (2010). Partial Differential Equations (2nd ed). Graduate studies in Mathematics, American Mathematical Society.
- Kreyszig,E. (2006). Advanced Engineering Mathematics (9th ed). John Willey and Sons, Inc.
- Forray,M.W. (1968). Variational Calculus in Science and Engineering. McGraw Hill Book Company.