Hilbert space, Hilbert space and Fourier series. Orthogonal polynomial systems. Operators on Hilbert space.

Complex analysis, Cauchy’s theorem, Cauchy’s integral formula, Residue theorem and its applications

Introduction to partial differential equations. Heat equation, wave equation, Laplace’s and Poisson’s equation.

Introduction to the theory of distributions.

The fourth semester of the four-semester course on Applied Mathematics. Hilbert spaces. Complex analysis.

Introduction to partial differential equations and theory of distribution.