MAT9305 – Partial Differential Equations and Sobolev Spaces I
Schedule, syllabus and examination date
Changes in the course due to coronavirus Spring 2020
Teaching and examinations will take place digitally. This may result in changes to your schedule, mandatory activities, exam form and grading scale. See updated information on the semester page and in Canvas.
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
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
emne: MAT2400 and emne: MAT3360
- 10 credits overlap with MAT4305 – 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.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Examination support material
No examination support material is allowed.
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
Studenter som dokumenterer gyldig fravær fra ordinær eksamen, kan ta utsatt eksamen i starten av neste semester.
Det tilbys ikke ny eksamen til studenter som har trukket seg under ordinær eksamen, eller som ikke har bestått.