MAT4305 – Partial Differential Equations and Sobolev Spaces I
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.
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 at UiO register for courses and exams in Studentweb.
Recommended previous knowledge
- emne: MAT2400
- emne: MAT3360
- 10 credits overlap with MAT9305 – Partial Differential Equations and Sobolev Spaces I.
- 10 credits overlap with MAT-INF3300 – Partial differential equations and Sobolev spaces I (discontinued).
- 10 credits overlap with MAT-INF4300 – Partial differential equations and Sobolev spaces I (continued).
4 hours of lectures/exercises per week.
Final written examination.
Examination support material
No examination support material is allowed.
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
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.