UNIT 1:
Introduction, Applications and Formation of partial differential equation
Formation of partial differential equation
Solutions of standard types of first order PDE
Tutorial 1: Problems based on Formation of partial differential equations
Solutions of standard types of first order PDE
Standard types and Equations reducible to standard types
Lagrange’s Linear equation
Lagrange’s Linear equation
Tutorial 2: Problems based on Lagrange’s Linear equation
Solution of linear equations of second and higher order with constant coefficients
Solution of linear equations of higher order with constant coefficients
Tutorial 3: Problems based on Solution of linear equations of higher order with constant coefficients
UNIT 2:
Introduction and Application of General Fourier series- Dirichlet’s conditions
Problems based on full range series
Problems based on full range series.
Tutorial 1: Problems under full range series
Tutorial 2: problems under half range sine series & Cosine series.
Complex form of Fourier series
Tutorial 3: Problems under Parseval’s identity , complex form and harmonic analysis
UNIT 3:
Introduction and Application of one and two dimensional heat equations - Classification
Method of separation of variables
Solutions of one dimensional wave equation
Tutorial 1: problems in Solutions of one dimensional wave equation
Solutions of one dimensional wave equation
Solutions of one dimensional heat equation
Solutions of one dimensional heat equation.
Tutorial 2: Problems under Solutions of one dimensional heat equation
Steady state solution of two-dimensional heat equation
Steady state solution of two-dimensional heat equation
Fourier series solutions in Cartesian coordinates
Tutorial 3: Problems in Steady state solution of two-dimensional heat equation
UNIT 4:
Introduction and Application of Fourier transforms – Fourier Integral theorem
Inverse Fourier transform
Tutorial 1: Problems under Fourier integral theorem, Fourier Transform and Parseval’s identity.
Properties of Fourier Transforms
Fourier cosine Transforms
Tutorial 2: Problems under Fourier sine and cosine Transforms
Transform of elementary functions
Tutorial 3: Problems under Convolution theorem
UNIT 5:
Introduction and Application of Z-Transform
Problems based on Z-transform
Tutorial 1: Problems based on Z-transform
Tutorial 2: Problems under Inverse Z-transform and Convolution theorem
Initial and Final value theorems
Formation of difference equation
Solution of difference equation using Z-transform.
Tutorial 3: Problems under Solution of difference equation using Z-transform.
