Syllabus
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Course Code: MT-501 Course Name: (B) Partial Differential Equations and Integral Transforms |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Classification of linear partial differential equations of second order, Hyperbolic, parabolic and elliptic types, Reduction of second order linear partial differential equations to Canonical (Normal) forms and their solutions. Cauchy’s problem for second order partial differential equations, Characteristic equations and characteristic curves of second order partial differential equation. | |
| 2 | Solution of linear hyperbolic equations. Monge’s method for solving non-linear second order partial differential equations. Laplace equation: elementary solutions of Laplace’s equation, families of equipotential surfaces. Method of separation of variables: Solution of Laplace’s equation, Wave equation and Diffusion (Heat) equation in one and two dimensions Cartesian Co-ordinate system. |
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| 3 | Laplace Transforms – Existence theorem for Laplace transforms, Linearity of the Laplace transforms, Shifting proprties, Laplace transforms of derivatives and integrals, Differentiation and integration of Laplace transforms, Convolution theorem, Inverse Laplace transforms, convolution theorem, Inverse Laplace transforms of derivatives and integrals, solution of differential equations using Laplace transform. | |
| 4 | Fourier transforms: Linearity property, Shifting, Modulation, Convolution Theorem, Fourier Transform of Derivatives, Parseval’s identity for Fourier transforms, relation between Laplace and Fourier transform. Solution of differential Equations using Fourier Transforms. | |
