Laplace transforms of standard functions, Transform of Periodic functions, Step function, Inverse transforms of derivatives and integrals, Convolution theorem , applications to solutions of ordinary differential equations .
Laplace transforms of standard functions, Transform of Periodic functions, Step function, Inverse transforms of derivatives and integrals, Convolution theorem , applications to solutions of ordinary differential equations .
Rank, solution of system of linear equations, Eigen values, Eigen vectors,Cayley Hamilton theorem, Quadratic forms and Diagonalization. Sequences and Series : Convergence and Divergence, Ratio Test, Comparison test, Absolute and Conditional Convergence.
Formation of PDEs by elimination of arbitrary constants and arbitrary functions, Method of separation of variables, one dimensional wave equation, heat equation,
Laplace equation.
The Bisection Method, The Method of False Position, Newton-Raphson Method,
Solution of linear simultaneous equation by Gauss elimination method, Gauss matrix and Gauss- Seidal iteration method.
Interpolation : Newton's forward and backward interpolation formulae,
Lagrange's formulae.
Trapezoidal rule, Simpson's 1/3 ,3/8 Rule. Numerical solution of Ordinary Differential equations : Solution by Taylor's series, Picard's Method of successive Approximations, Euler's Method, Runge-Kutta Methods, Predictor-Corrector Method, Milne's Method.