Partial Differential Equation Msc3

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[@vedprakashnishad-z6u]

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[@Mr.singhalji]

Partial Differential equation Ki only 2 units ki fees bata dijiye

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250 ji

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Syllabus send kijiyega

[@Mr.singhalji]

I Examples of PDE, Classification, Transport equation: Initial value problem,non-homogeneous equation, Laplace's equation: Fundamental solution, Mean value formulas, Properties of harmonic functions, Energy methods. II Heat equation: Fundamental solution; Mean value formula, Properties of solutions, Energy methods, Wave equation: Solution by spherical means, non-homogeneous equations, Energy methods. III Nonlinear first order PDE complete integrals, Envelopes, Characteristics; Hamilton Jacobi equations (Calculus of variations, Hamilton's ODE, Legendre transform,Hopf-Laxformula,Weaksolutions,Uniqueness),Conservationlaws(Rankine-Hugoniotcondition,Lax-Oleinik formula, Weak solutions, Uniqueness). IV Representation of Solutions-Separation of Variables, Similarity Solutions (Plane and Traveling Waves, Similarity Linder Scaling), Fourier and Laplace Transform, Hopf-Cole Transform, Hodograph and Legendre Transforms, Potential Functions. V Applications of PDE: Vibration governed by one- and two-dimensional wave equations, vibrations of string and membranes, three dimensional problems, Diffusion equation, resolution of boundary value problems for diffusion equations and elementary solutions of diffusion equation.