MAT4305 – Partial Differential Equations and Sobolev Spaces I

Schedule, syllabus and examination date

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Exams after the reopening

As a general rule, exams will be conducted without physical attendance in the autumn of 2021, even after the reopening. See the semester page for information about the form of examination in your course. See also more information about examination at the MN Faculty in 2021.

Course content

The course provides an introduction to the theoretical basis for linear partial differential equations, focusing on elliptic equations and eigenvalue problems. The techniques and methods developed are general and based on functional analysis and Sobolev spaces. They provide qualitative information about solutions even when explicit solution formulas do not exist. Sobolev spaces, and the theory of Sobolev/Poincaré inequalities and Rellich-Kondrachov compactness, form an essential part of modern research on partial differential equations. The course also provides an introduction to the theory of numerical methods, including the Galerkin method.

Learning outcome

After completing the course you:

  • are familiar with Sobolev spaces and their role in analysing partial differential equations;
  • know what is meant by weak differentiability and can define weak solutions of elliptic equations;
  • can use the Lax-Milgram theorem and give proofs for the existence and uniqueness of weak solutions;
  • are familiar with eigenvalues and eigenfunctions of elliptic equations;
  • know basic theory for regularity of weak solutions;
  • have some knowledge of numerical methods for partial differential equations.

Admission to the course

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.

  • emne: MAT2400 
  • emne: MAT3360 

Overlapping courses


4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.


Final written exam 4 hours or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 15 October/15 March for the autumn semester and the spring semester respectively.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT9305 – Partial Differential Equations and Sobolev Spaces I

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. 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.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Oct. 20, 2021 2:32:43 PM

Facts about this course

Teaching language