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Week 01: Introduction to Laplace and Fourier Methods
Week 02: The Laplace transform
Week 03: Inverse Laplace and applications of Laplace transforms
Week 04: The Fourier transforms. Properties and applications to differential equations
Week 05: Functions and Transform Methods
Week 06: Properties of Fourier transforms
Week 07: Green’s functions, Expansion and closed form Green’s functions
Week 08: Results in Laplace, Fourier transforms and Green functions
Week 09: Mid Term Exam
Week 10: Perturbation methods for algebraic equations, Perturbation methods for differential equations.
Week 11: Variational Methods: Euler-Lagrange equations.
Week 12: Integrand involving one, variable
Week 13: Integrand involving two, three variables
Week 14: Integrand involving n variable
Week 15: Special cases of Euler-Lagrange’s equations
Week 16: Necessary conditions for existence of an extremum of a functional
Week 17: Constrained maxima and minima
Week 18: Final term Exam

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