Partial Differential Equations (FSI-SPD)

The course aims are to introduce students to partial differential equations, their fundamental properties, and their applications in mathematical modeling. Students will learn to formulate initial and boundary value problems that model selected specific physical situations. Another objective is to familiarize students with classical solution methods and teach them how to solve simple problems related to equations of mathematical physics.

Solution of algebraic equations and system of linear equations, differential and integral calculus of functions of one and more variables, Fourier series, ordinary differential equations.

Partial differential equations - basic concepts and mathematical models.
Linear first-order equations - methods of characteristics and characteristic coordinates. Linear second-order equations - classification and transformation to canonical form. Derivation of selected equations in mathematical physics (heat conduction, string vibration), formulation of initial and boundary value problems. Laplace and Poisson equations - solving boundary value problems. Methods of integral transformations, Green's function method, and maximum principles.

To obtain course credit, one must pass one written test successfully. The exam grade consists of a written and an oral part.

There will be no distinction between exercises and lectures. According to the topic being covered, examples will be solved in real time.