3rd sem syllabus of mathematics III

MA1201                                      MATHEMATICS III



 1. PARTIAL DIFFERENTIAL EQUATIONS 9 
Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions – Solution of standard types of first order partial differential equations – Lagrange’s linear equation – Linear partial differential equations of second and higher order with constant coefficients.

2. FOURIER SERIES 9
Dirichlet’s conditions – General Fourier series – Odd and even functions – Half range sine series – Half range cosine series – Complex form of Fourier Series – Parseval’s identify – Harmonic Analysis.
 
3. BOUNDARY VALUE PROBLEMS 9
Classification of second order quasi linear partial differential equations – Solutions of one dimensional wave equation – One dimensional heat equation – Steady state solution of two-dimensional heat equation (Insulated edges excluded) – Fourier series solutions in Cartesian coordinates.
 
4. FOURIER TRANSFORM 9
Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.
 
5. Z -TRANSFORM AND DIFFERENCE EQUATIONS 9
Z-transform - Elementary properties – Inverse Z – transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z - transform.