Osmania University - M.Sc Astronomy - Semester 1 - Differential Equations and Special Functions

Theory Paper 2: Differential Equations and Special Functions

Unit 1
Ordinary differential equations

Definition, order and degree of a differential equation. Solution by power series methods, Solutions of Legender's, Bessel's, Laguerre's and Hermit's differential equations.

Unit 2
Partial differential equations

Solutions by the method of separation of variables. Wave, diffusion and Laplace's equations and their solutions.
Unit 3
Special functions

Gamma, Beta, Legendre and Bessel functions of the first kind and their properties.

Unit 4
Fourier Series and Transforms

Definition and expansion of a function of x. Extension of interval. Advantages of Fourier series. Complex form of Fourier series. Fourier's integrals. Fourier transform and their inverse. Use of Fourier transform in solving some simple definite integrals.

REFERENCES

1. Shepley and Ross: Differential Equations.
2. Piper and Harvill: Applied Mathematics for Engineers and Physicists .
3. J.Irving and Mullineus: Mathematics in Physics and Engineering.
4. V.I.Awmianoc translated by D.E.Brown: A course of Higher Mathematics Vol-IV.
5. I.N. Sneddon: Fourier Series.

Reference: http://www.osmania.ac.in/