TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
Laplace Transform of Standard functions, derivatives and integrals – Inverse Laplace transform –Convolution theorem-Periodic functions – Application to ordinary differential equations and simultaneous equations with constant coefficients and integral equations.
Fourier series – Dirichlet’s conditions - Half range Fourier cosine and sine series - Parseval's relation - Fourier series in complex form - Harmonic analysis.
Fourier transforms - Fourier cosine and sine transforms - inverse transforms - convolution theorem and Parseval's identity for Fourier transforms - Finite cosine and sine transforms.
Formation of partial differential equations eliminating arbitrary constants and functions - solution of first order equations - four standard types - Lagrange’s equation - homogeneous and non-homogeneous type of second order linear differential equation with constant coefficients.
One-dimensional wave equation and one-dimensional heat flow equation - method of separation of variables - Fourier series solution.
Venkataraman, M.K., 'Engineering Mathematics Vol.4', National publishing company,2004.
Grewal.B.S.,Higher Engineering Mathematics,Khanna Publishers,2000.
