Week 1: Introduction to linear differential equations ,Linear dependence, independence and Wronskian of functions,Solution of second-order homogeneous linear differential equations with constant coefficients-I,Solution of second-order homogeneous linear differential equations with constant coefficients-II,Method of undetermined coefficients
Week 2: Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-I,Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-II, Methods for finding Particular Integral for second-order linear differential equations with constant coefficients-III,Euler-Cauchy equations, Method of reduction for second-order, linear differential equations
Week 3: Method of variation of parameters , Solution of second order differential equations by changing dependent variable, Solution of second order differential equations by changing independent variable, Solution of higher-order homogenous linear differential equations with constant coefficients, Methods for finding Particular Integral for higher-order linear differential equations
Week 4: Formulation of Partial differential equations, Solution of Lagrange’s equation-I, Solution of Lagrange’s equation-II,Solution of first order nonlinear equations-I,Solution of first order nonlinear equations--II
Week 5: Solution of first order nonlinear equations-III, Solution of first order nonlinear equations-IV, Introduction to Laplace transforms,Laplace transforms of some standard functions, Existence theorem for Laplace transforms
Week 6: Properties of Laplace transforms--I, Properties of Laplace transforms--II, Properties of Laplace transforms--III, Properties of Laplace transforms--IV, Convolution theorem for Laplace transforms--I
Week 7: Convolution theorem for Laplace transforms--II, Initial and final value theorems for Laplace transforms, Laplace transforms of periodic functions, Laplace transforms of Heaviside unit step function, Laplace transforms of Dirac delta function
Week 8: Applications of Laplace transforms-I, Applications of Laplace transforms-II, Applications of Laplace transforms-III, Z – transform and inverse Z-transform of elementary functions, Properties of Z-transforms-I
Week 9: Properties of Z-transforms-II, Initial and final value theorem for Z-transforms, Convolution theorem for Z- transforms, Applications of Z- transforms--I, Applications of Z- transforms-II
Week 10: Applications of Z- transforms--III, Fourier series and its convergence--I, Fourier series and its convergence--II, Fourier series of even and odd functions, Fourier half-range series
Week 11: Parsevel’s Identity, Complex form of Fourier series, Fourier integrals, Fourier sine and cosine integrals, Fourier transforms
Week 12: Fourier sine and cosine transforms, Convolution theorem for Fourier transforms, Applications of Fourier transforms to BVP-I, Applications of Fourier transforms to BVP-II, Applications of Fourier transforms to BVP-III
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