Advanced Mathematical Physics: Course Outline

• Nonlinear ordinary differential equations.
• Bernoulli’s equation.
• Riccati equation.
• Lane-Emden equation.
• Nonlinear Pendulum.
• Duffing’s equation.
• Pinney’s equation.
• Perturbation theory.
• Bogoliubov- Krilovmethod.
• Linear partial differential equations.
• Classification.
• Initial and boundary values problems.
• Fourier analysis.
• Heat equation.
• Wave equation.
• Laplace equation etc.
• Integral equations.
• Classification.
• Integral transform separable kernels.
• Singular integral equations.
• Wiener-Hopf equations.
• Fredholm theory.
• Series solutions.
• Variational methods.
• The Euler-Lagrange equations.
• Solutions to some famous problems.
• Sturm-Liouville Problem and variational principles.
• Rayleigh-Ritz Methods for partial differential equations.
• Matrix algebra.
• Method of Faddeev.
• Caley-Hamilton’ theorem.
• Functions of matrices.
• Functions of matrices.
• Kronecker and Tensor products.
• Special matrices.

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