Week 13: Solution of PDEs by Laplace transform, Diffusion and wave equations
Myint UT, Partial Differential Equations for Scientists and Engineers, 3rd edition, North Holland, Amsterdam, 1987
Page # 343-356
Course Material
- Week 1: First order PDEs: Introduction, formation of PDEs
- Week 2: Solutions of PDEs of first order
- Week 3: The Cauchy’s problem for quasilinear first order PDEs, First order nonlinear equations, Special types of first order equations, Mathematical problems, Linear operators, Superposition
- Week 4: Mathematical models: The classical equations, the vibrating string, the vibrating membrane, conduction of heat solids
- Week 5: Second order PDEs: Basic concepts and definitions
- Week 6: Canonical forms and variable, PDEs of second order in two independent variables with constant and variable coefficients, Cauchy’s problem
- Week 7: Methods of separation of variables: Solutions of elliptic PDEs
- Week 8: Solution of parabolic and hyperbolic PDEs by separation of variables method
- Week 9: Mid Term
- Week 10: Laplace transform: Introduction and properties of Laplace transform
- Week 11: Transforms of elementary functions, periodic functions, error function and Dirac delta function
- Week 12: Inverse Laplace transform, convolution theorem
- Week 13: Solution of PDEs by Laplace transform, Diffusion and wave equations
- Week 14: Fourier transforms: Fourier integral representation
- Week 15: Fourier sine and cosine representation
- Week 16: Fourier transform pair, transform of elementary functions and Dirac delta function, Finite Fourier transforms
- Week 17: Solutions of heat and wave and Laplace equations by Fourier transforms
- Week 18: Final Term
- Chapters 18
- Department Mathematics
- Teacher
Dr. Javaria Farooq
