Equations of Mathematical Physics

Derivation of partial differential equations from laws of physics. Elliptic, parabolic and hyperbolic equation. Concepts of the solution. Classification and canonization of equations of 2nd order. Problems of mathematical physics. Initial and boundary conditions. Cauchy problem, boundary value problems. Well- and ill-posed problems. Analytical methods of solution. Method of coordinates and characteristics. Fundamental solution. Operator method. Fourier method. Method of integral transforms.

NB! This course will take place in autumn semester 2024/2025 which starts on 2nd of September and ends 26th of January (you can find that information under Start date section). The real course start and end dates will be announced at the beginning of September at the latest.

When finished the course the student: • is able to formulate main notions of theory of partial differential equations knows foundations of the theory of partial differential equations, • knows classification of partial differential equations and main problems, • solves main types of the partial differential equations.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

The main part of the course takes place in hybrid mode, but 4 assessments must be taken on campus at TalTech.

The possibilities are following:

1. 2 assessments in the middle of the semester;
2. 2 assessments at the end of the semester;
3. all 4 assessments at the end of the semester.

Specific dates are to be determined.

• P. Drábek, G. Holubová, Elements of Partial Differential Equations. de Gruyter, 2014.

lectures, exercises