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Unit - 1 Multivariable Calculus

Module 3 First order ordinary Differential Equation

3.1 Exact Differential Equation

3.2 Linear differential equation

3.3 Bernoulli equation

3.4 Eulers equation

3.5 Equation not of first degree

3.6 Clairauts equation

Unit - 2 First Order Ordinary Differential Equations

Module 3 Ordinary Differential Equation of higher orders

3.1 Second order Linear Differential equation with variable coefficient

3.2 Method of variation of Parameters

3.3 Cauchy Euler Equation

3.4 Power Series solution

3.5 Legendre’s Equation

3.6 Bessel function

Unit - 3 Ordinary Differential Equations of Higher Orders

Module 3CPartial Differential equation First order

3.1 First Order Partial differential equation

3.2 Solution of first order linear and nonlinear partial differential equation

Unit - 4 Complex Variable – Differentiation

Module 3DPartial Differential Equation Higher Order

3.1 Solution to homogenous and non homogenous linear partial differential equation second and higher order by CF and PI

3.2 Flows Vibrations Diffusion

3.3 Second order linear equation and their classification

3.4 Initial and Boundary condition

3.6 Duhamel’s Principle for One Dimensional Wace Equation

3.7 Method of separation of variables

3.8 Laplacian in plane Cylindrical and Spherical polar coordinates

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