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 2025/2026 which starts on 1st of September and ends on 25th of January (you can find that information under Start date section). TalTech's timetables for Autumn semester 2025 will be published at the end of June via tunniplaan.taltech.ee. Switch the page to English and use "Search" and "Open detailed search" to find your course. NB! Some courses are taught by several lecturers during the same semester. Make sure that the course name and lecturer/teacher infromation of your course match with the information given in the Course Catalogue.

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 course takes place in blended mode.

During the course, 4 assessments must be taken. The possibilities are following:

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

The assessment dates will be agreed upon with the instructor.

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

lectures, exercises