MAT4305 – Partial differential equations and Sobolev spaces I

Schedule, syllabus and examination date

Choose semester

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

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.

Prerequisites

Recommended previous knowledge

MAT2400 - Real Analysis and MAT3360 - Introduction to Partial Differential Equations.

Teaching

4 hours of lectures/exercises per week.

Examination

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 examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

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.

Evaluation

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

Credits

10

Teaching

Every spring

Examination

Every spring

Teaching language

English

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