Youtor
Lect 13 Partial Differential Equations
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PAPER-XVII (2032): PARTIAL DIFFERENTIAL EQUATIONS • Unit-I : Curves and Surfaces, Genesis of first order P.D.E.,Classification of intergals, Linear Equations of the first order,Pfaffian differential Equations, Compatible systems, Charpit’s Method ,Jacobi’s Method, Integral Surfaces through a given curve. • Unit-II : Quasi-Linear equations, Non-linear first order P.D.E., genesis of second order • P.D.E.,Classification of second order P.D.E • . • Unit-III : One dimensional Wave equation, Vibrations of an infinite string , Vibrations of a Semi- • infinite string,Riemann,s Method, Vibrations of a string of finite Length. • Unit-IV : Laplace’s Equation, Boundary value problems, Maximum and Minimum Principles, The Cauchy problem, The Dirichlet Problem for the upper half plane, The Neumann problem for the upper half plane, The Dirichlet problem for a circle, The Dirichlet Exterior problem for a circle, The Neumann problem for a circle, The Dirichlet problem for a Rectangle , Harnack’s Theorem, Laplace’s equation- Green funcation, The Dirichlet problem for a half plane,The Dirichlet problem for a circle. • Unit-V: Heat conduction problem: Heat conduction- Infinite rod case, Heat conduction-finite rod case, Duhamel’s principle:Wave equation, Heat conduction equation. Classcification in the case of n –variables, Families of equipotential surfaces, Kelvin’s inversion theorem. • References : • ( 1 ) I.N. Sneddon : Elements of Partial Differential Equation, Mc Graw Hill, International Editon, • New York. • (2) Phoolan Prasad, Renuka Ravindram :Partial Differential equations, New Age and International • Publishers. • (3) Lawrence C. Evans: Partial Differential Equations, Vol. 19, AMS, 1998. • (4) T. Amaranath : An elementary course in Partial Differential Equations, 2nd Ed. Narosa Publishing • House, New Delhi. • (5) R.J. Leveque, Finite difference methods for ordinary and partial differential equations, July-2007 • #CurvesAndSurfaces, • #GenesisOfFirstOrderPDE. • ,#ClassificationOfIntergals, • #LinearEquationsOfTheFirstOrder, • #PfaffianDifferentialEquations, • #CompatibleSystems, • #CharpitsMethod , • #JacobisMethod, • #IntegralSurfacesThroughAgivenCurve, • #QuasiLinearEquations, • #Non-linear first order P.D.E., • #genesis of second order • #P.D.E.,Classification of second order P.D.E., • #One dimensional Wave equation, • #Vibrations of an infinite string , • #Vibrations of a Semi- • #infinite string,Riemann,s • #Method, Vibrations of a string of finite Length.Laplace’s Equation, • #Boundary value problems, • #Maximum and Minimum Principles, • #The Cauchy problem, • #The Dirichlet Problem for the upper half plane, • #The Neumann problem for the upper half plane, • #The Dirichlet problem for a circle, • #The Dirichlet Exterior problem for a circle, • #The Neumann problem for a circle, • #The Dirichlet problem for a Rectangle , • #Harnack’s Theorem, • #Laplace’s equation- Green funcation, • #The Dirichlet problem for a half plane, • #The Dirichlet problem for a circle. • .
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