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Course Contents

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.


Course Learning Outcomes

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.


Non-Homogeneous Integral Equations of second kind with Degenerate Kernel

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Sturm-Liouville System|Mathematical Method Of Physics

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Properties of the Regular Sturm-Liouville problem|Mathematical Method Of Physics

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Greens Function,Construction of Green’s Function using the Method of Variation of Parameters

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Properties of Green’s Function|Mathematical Method Of Physics

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Method of Separation of Variable|Mathematical Method Of Physics

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Solution of Wave Equatio|Mathematical Method Of Physics

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The method of successive approximation|Mathematical Method Of Physics

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The method of successive approximation|Mathematical Method Of Physics

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Formation of Volterra Integral Equation|Mathematical Method Of Physics

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Homogeneous Fredholm Integral equations with Degenerate Kernel

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Existence of solution of Fredholm integral equation when kernel is non-symmetric

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Existence of solution of Fredholm integral equation when kernel is non-symmetric

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Properties of Dirac Delta Function|Mathematical Method Of Physics

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One Dimensional Heat Equation

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Partial Differential Equation - Solution of one dimensional heat flow Equation

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Partial Differential Equation - Solution of One Dimensional Wave Equation

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one dimensional heat conduction equation derivation

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Partial Differential Equation - Solution by Separation of Variables

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Steady state solution for 1-dimensional heat equation.

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Heat Equation - Separation of Variables

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Properties of Green's function

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Properties of Green’s Function|Mathematical Method Of Physics

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solving boundary value problem using Green's function

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Calculus of variations: Basic concepts-I

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Euler's Lagrange equation: Some particular cases

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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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