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Advanced Mathematical Physics: Course Outline

Mathematical physics refers to development of mathematical methods for application to problems in 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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