TB Differential Equations & Integral Transforms

SYLLABUS- DIFFERENTIAL EQUATIONS & INTEGRAL TRANSFORMS,
Differential Equations
Unit-1: Formation of a differential equation (D.E.), Degree, order and solution of a D.E., Equations of first order and first degree : Separation of variables method, Solution of homogeneous equations, linear equations and exact equations, Linear differential equations with constant coefficients, Homogeneous linear differential equations,
Unit-2: Differential equations of the first order but not of the first degree, Clairaut's equations and singular solutions, Orthogonal trajectories, Simultaneous linear differential equations with constant coefficients, Linear differential equations of the second order (including the method of variation of parameters),
Unit-3: Series solutions of second order differential equations, Legendre and Bessel functions (Pn and Jn only) and their properties. Order, degree and formation of partial differential equations, Partial differential equations of the first order, Lagrange's equations, Charpit's general method, Linear partial differential equations with constant coefficients.
Unit-4(i): Partial differential equations of the second order, Monge's method.
Integral Transforms
Unit-4(ii): The concept of transform, Integral transforms and kernel, Linearity property of transforms, Laplace transform, Inverse Laplace transform, Convolution theorem, Applications of Laplace transform to solve ordinary differential equations.
Unit-5: Fourier transforms (finite and infinite), Fourier integral, Applications of Fourier transform to boundary value problems, Fourier series.