# MA208

## Unit I

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.

## Unit II

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.

## Unit III

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.

## Unit IV

One-dimensional wave equation and one-dimensional heat flow equation. Method of separation of variables. Fourier series solution.

## Unit V

Two-dimensional heat flow equation in steady state. Laplace equation in Cartesian and polar co ordinates. Method of separation of variables. Fourier series solution.

## References

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.