MAT4301 – Partial differential Equations

Schedule, syllabus and examination date

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Course content

We study the classic linear PDEs in Rn: Poisson’s equation, the heat equation and the wave equation. The representation of solutions, maximum principles and energy estimates. separation of variables and Fourier representations. Introduction to variational methods and Hamilton-Jacobi equations. This course is meant to be at a level between MAT3360 - Introduction to partial differential equations and MAT4305 - Partial differential equations and Sobolev spaces I.

The course can be seen as a continuation of MAT3360, where increased insight into the theory of partial differential equations is obtained without relying on more advanced tools from mathematical analysis, such as measure theory and functional analysis.

Learning outcome

Upon completion of the course, you will have:

  • learned how integration by parts techniques in Rn yield estimates for solutions of PDEs;
  • good knowledge of maximum principles for elliptic equations;
  • good knowledge of the importance of Green functions;
  • knowledge of representation formulas for solutions of elliptic and parabolic equations;
  • knowledge of energy estimates for solutions of several PDEs;
  • knowledge of variational techniques for PDEs and the relation to the finite element method;
  • basic knowledge of solutions to Hamilton-Jacobi equations.


Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.


2 hours of lectures and 2 hours of exercises per week.


1 mandatory assignment.

Final written examination.

Examination support material

No examination support material is allowed.

Language of examination

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed exam at the beginning of the next semester.

New examinations are offered at the beginning of the next semester for students who do not successfully complete the exam during the previous semester.

We do not offer a re-scheduled exam for students who withdraw during the exam.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Every autumn


Every autumn

Teaching language

Norwegian (English on request)