MAT4301 – Partial Differential Equations
Schedule, syllabus and examination date
Course content
We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates. Furthermore, the course gives an introduction to nonlinear equations: Hamilton-Jacobi equations and conservation laws.
The course can be seen as a continuation of MAT3360 – Introduction to Partial Differential Equations, where increased insight into the theory of partial differential equations is obtained without relying on more advanced tools from mathematical analysis, such as measure theory and functional analysis.
Learning outcome
After completing the course you
- will have learned how integration by parts techniques in Rn yield estimates for solutions of PDEs
- will have good knowledge of maximum principles for elliptic equations
- will have good knowledge of the importance of Green functions
- will have knowledge of energy estimates for solutions of several PDEs
- will have knowledge of variational techniques for PDEs and the relation to the finite element method
- will have basic knowledge of solutions to Hamilton-Jacobi equations
- will have knowledge of entropy solutions of conservation laws.
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.
Recommended previous knowledge
- MAT1100 – Calculus
- MAT1110 – Calculus and Linear Algebra
- MAT1120 – Linear Algebra
- MAT3360 – Introduction to Partial Differential Equations
Teaching
4 hours of lectures/exercises per week throughout the semester.
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 participate in the final exam.
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 submit your response 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:
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.