PREV

• 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