Week 08: Methods of separation of variables: Solutions of elliptic, parabolic and hyperbolic PDEs in Cartesian and cylindrical coordinates.
Myint UT, Partial Differential Equations for Scientists and Engineers(4th edition, North-Holland, Amsterdam, 2007)
Page No: 232-243
Course Material
- Week 01: First order PDEs: Introduction, formation of PDEs, solutions of PDEs of first order,
- Week 02: The Cauchy’s problem for quasi-linear first order PDEs, First order nonlinear equations
- Week 03: Special types of first order equations Second order PDEs: Basic concepts and definitions, Mathematical problems.
- Week 04: Linear operators, Superposition, Mathematical models: The classical equations, the vibrating string.
- Week 05: The vibrating membrane, conduction of heat solids, canonical forms and variable.
- Week 06: PDEs of second order in two independent variables with constant and variable coefficients.
- Week 07: Cauchy’s problem for second order PDEs in two independent variables.
- Week 08: Methods of separation of variables: Solutions of elliptic, parabolic and hyperbolic PDEs in Cartesian and cylindrical coordinates.
- Week 09: Mid Term Exam
- Week 10: Laplace transform: Introduction and properties of Laplace transform, transforms of elementary functions, periodic functions, error function and Dirac delta function.
- Week 11: inverse Laplace transform, convolution theorem, and Examples.
- Week 12: Solution of PDEs by Laplace transform, Diffusion and wave equations.
- Week 13: Fourier transforms: Fourier integral representation.
- Week 14: Fourier sine and cosine representation.
- Week 15: Fourier transform pair, transform of elementary functions and Dirac delta function.
- Week 16: Finite Fourier transforms, solutions of heat.
- Week 17: Wave and Laplace equations by Fourier transform.
- Week 18: Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Dr. Muhammad Abbas
