Dirichiet conditions. Expansion of periodic functions into Fourier series. Change of interval. Fourier series for even and odd functions. Half-range expansions. RMS value of a function. Parseval's relation. Fourier series in complex form. Harmonic analysis.
Definition of Fourier Transform (finite and infinite). Inverse Fourier Transform. Properties. Fourier Sine and Cosine transforms. Inverse Fourier Sine and Cosine transforms. Properties. Convolution theorem for Fourier Transform.
Formation of PDE. Solution of standard types of first order equations. Lagrange's linear equation. Second and higher order homogeneous and non-homogeneous linear equations with constant coefficients.
One-dimensional wave equation and one-dimensional heat flow equation. Method of separation of variables. Fourier series solution.
Two-dimensional heat flow equation in steady state. Laplace equation in Cartesian and polar co ordinates. Method of separation of variables. Fourier series solution.
1. GREWAL, B.S., Higher Engineering Mathematics, Khanna Publishers.
2. KANDASAMY, P. THILAGAVATHY, K. AND GUNAVATHY, K., Engineering Mathematics, Vol. III, Chand and Company.
3. VENKATARAMAN, M.K., Engineering Mathematics Vol.III, National Publishing Company.
