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Analytical methods in differential equations – Syllabus

Strum Theory. Proof of existence of eigenvalues of the Strum-Liouville problem, and properties of these eigenvalues. Properties of the Eigen functions of the Strum-Liouville Problem. The adjoint operator, and the self-adjoint operator. The Fredholm Alternative theorem. Solvability conditions. Bessd Functions. The Legendre Polynomials. Other special functions such as the gamma Function, the Beta Functions. The Hilbert-Schmidt theorem. Convergence theorems for series of Eigen functions. The Rayleigh-Ritz theorem. The Fourier Transform. The Laplace Transform. Application of all the above to PDEs (with 2 or 3 special variables, as well as time).

Analytical methods in differential equations – Technical details

  1. A four-hour lecture course which provides four academic points.
  2. A weekly homework assignment will be provided.
  3. There will be a final exam.
  4. One of the questions at the final exam will be similar to one of the questions in the homework.
  5. The lecturer will prepare formula sheets for use at the final exam. These formula sheets will be available on the course website throughout the semester.
  6. A large collection of old exam will be available for students on the course website.