Unit - I : Differential Equations
Linear differential equations of nth order with constant coefficients, Complementary functions and particular integrals, Simultaneous linear differential equations, Solution of second order differential equation by changing dependent and independent variables, Method of variation of parameters, Applications to engineering problems (without derivation).
Unit - II : Series Solution and Special Functions
Series solution of ordinary differential equation of 2 nd order with variable coefficients (Frobenius Method), Bessel and Legendre equations and their series solutions, Properties of Bessel functions and Legendre polynomials.
Unit - III : Laplace Transform
Laplace transform, Existence theorem, Laplace transform of derivatives and integrals, Inverse Laplace transform, Unit step function, Dirac delta function, Laplace transform of periodic functions, Convolution theorem, Application to solve simple linear and simultaneous differential equations.
Unit - IV : Fourier Series and Partial Differential Equations
Periodic functions, Trigonometric series, Fourier series of period 2, Eulers formulae, Functions having arbitrary period, Change of interval, Even and odd functions, Half range sine and cosine series, Harmonic analysis. Solution of first order Lagrange’s linear partial differential equations, Linear partial differential equations with constant coefficients of 2nd o.
Unit - V : Applications of Partial Differential Equations
Method of separation of variables for solving partial differential equations, Wave equation up to two-dimensions, Laplace equation in two-dimensions, Heat conduction equations up to two-dimensions, Equations of transmission lines.