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
Myint UT, Partial Differential Equations for Scientists and Engineers, 3rd edition, North Holland, Amsterdam, 1987
Page # 1-11
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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
