UNIT 1:
Problems based on full range series (0, 2l)
Half range sine& Cosine series
Problems on odd and even functions (-l, l)
Problems on odd and even functions (-π, π)
Problems based on full range series (0, 2Ï€)
Introduction and Application of General Fourier series- Dirichlet’s conditions
Problems on Harmonic Analysis
UNIT 2:
Inverse Fourier Transform
Fourier cosine Transforms
Transform of Simple functions
Properties of Fourier Transforms
Introduction and Application of Fourier transforms
UNIT 3:
Problems on Lagranges Linear equation
Introduction, Applications and Formation of partial differential equation
Formation of partial differential equation
Solutions of standard types of first order PDE (Type I, II)
Problems on Lagranges Linear equation
Solutions of standard types of first order PDE (Type I, II)
Solutions of standard types of first order PDE (Type III, Type IV)
Standard types and Equations reducible to standard types
Lagranges Linear equation
Solution of linear equations of second and higher order with constant coefficients-Homogeneous
Problems on Solution of linear equations of higher order with constant coefficients – Homogeneous.
UNIT 4:
Steady state solution of two-dimensional heat equation
Problems on Solutions of one dimensional heat equation.
Solutions of one dimensional heat equation
Solutions of one dimensional wave equation –Non zero velocity
Solutions of one dimensional wave equation –Zero velocity
Solutions of one dimensional wave equation
Problems on Steady state solution of two-dimensional heat equation
UNIT 5:
Introduction and Application of Z-Transform
Problems based on Z-transform
Initial and Final value theorems
Formation of partial differential equation
Solution of difference equation using Z-transform.
