Partial and integral equations

Dr. Slagana Brsakoska, Professor

Course content:

Partial DRs of the first order, linear PDRs, geometric interpretation and Cauchy's problem. Nonlinear DRs of the first order, systems of two harmonic PDRs. Pfaff's equations. Lagrange-Charpy method. Lagrangian theory for second-order PDR integrals, Cauchy integral. PDRs of the II order, linear PDRs and their classification. Reduction to canonical form. Methods for solving PDR. Integral equations. Fredholm equation with degenerate kernel. Analogy with linear algebraic equations. Integral equations with symmetric kernels. Banach's theorem in the theory of integral equations, Sturm-Liouville problem, Voltaire's integral equations, Singular integral equations, Application of Laplace transform. 

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