Formation and classification of partial differential equations. Methods of separation of variables for solving elliptic, parabolic and hyperbolic equations. Eigen functions expansions. Some properties of Surm-Liouville equations. Regular, periodic and singular Strum-Liouville systems. Properties of Strum-Liouville Systems. Green’s functions method. Modified Green’s functions. Green’s function in one and two dimensions. Euler-Lagrange equations when integrand involves one, two, three and n variables; Special cases of Euler-Lagranges equations. Necessary conditions for existence of an extremum of a functional, constrained maxima and minima. Formation and classification of integral equations. Degenerate Kernels. Method of successive approximation. Hilbert Smidth method.

Upon completion of this course students will become familiar with the different techniques to solve the PDEs. They can apply course meterial along with procedures and techniques covered in this course to solve problems.

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Book Title : Mathematical Physics

Author : E.L. Butkov

Edition : 3RD EDITION

Publisher : Addison-Wesley, 1973

Book Title : Mathematical Methods for Physics

Author : G. Arfken

Edition :

Publisher : Academic Press, 1985

Book Title : MATHEMATICAL METHODS FOR PHYSICISTS

Author : George B. Arfken Miami University Oxford, OH Hans J. Weber University of Virginia Charlottesville, V

Edition : SIXTH EDITION

Publisher : Elsevier Inc.

Book Title : 5. K.L. Mir, Problems and Methods in Mathematical Physics and Applied Mathematics, Ilmi Kitab Khana, Lahore, 1997.

Author : K.L. Mir

Edition : 2005

Publisher : Ilmi Kitab Khana, Lahore

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