MAT4301 – Partial Differential Equations

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.

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.

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.

• MAT1100 – Calculus
• MAT1110 – Calculus and Linear Algebra
• MAT1120 – Linear Algebra / MAT1125 – Advanced linear algebra
• MAT3360 – Introduction to Partial Differential Equations

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.

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.