MAT9305 – Partial Differential Equations and Sobolev Spaces
Course description
Schedule, syllabus and examination date
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
PhD candidates from the Faculty of Mathematics and Natural Sciences at 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
Overlapping courses
- 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).
Teaching
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.
Examination
Final written exam or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 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.
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 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: MAT4305 – Partial Differential Equations and Sobolev Spaces I
Examination support material
No examination support material is allowed.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.