Solutions of heat, wave and Laplace equations by Fourier transform.
Course Material
- Introduction: Definitions of ODE, PDE and basics
- The Cauchy’s problem for quasi-linear first-order PDEs, First order nonlinear equations
- Applications of PDE
- Formulation of partial differential equation
- Some classical Partial differentiation equations and classification of 2nd order PDE
- Solution of 1st and 2nd order PDE: Separation of variable
- Parabolic and hyperbolic PDEs in Cartesian and cylindrical coordinates
- Basic concepts and definitions, Mathematical problems, Linear operator
- Solutions of elliptic, parabolic and hyperbolic PDEs
- Mid Term Exam
- Canonical forms and Cauchy’s problem for second order PDEs in two independent variables
- Winter Break
- Laplace transform: Introduction and properties of Laplace transform and Dirac delta function
- Inverse Laplace transform, convolution theorem, solution of PDEs by Laplace transform, Fourier integral representation
- Fourier sine and cosine representation, finite Fourier transforms
- Solutions of heat, wave and Laplace equations by Fourier transform.
- Final Term Exam
- Chapters 17
- Department Mathematics
- Teacher
Ms. Maira Hafeez
