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• 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