MATS340 Partial Differential Equations 2 (5 cr)

Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

Description

Sobolev spaces and inequalities (review), elliptic partial differential equations in divergence form and their weak solutions, existence of solutions, maximum and comparison principles, uniqueness of solutions, regularity of solutions, parabolic partial differential equations and their weak solutions

Learning outcomes

After taking the course a student:


  • is able to use basic tools of Sobolev spaces in dealing with partial differential equations 
  • knows the weak definition of a solution to a partial differential equation and can verify in simple cases that a given example is a weak solution
  • recognizes elliptic and parabolic partial differential equations and knows applicable existence, uniqueness and regularity results and techiques
  • can apply the results for partial differential equations

Description of prerequisites

MATS230 Partial differential equations, MATS110 Measure and integration theory

Study materials

Lecture note

Literature

  • Wu, Yin, Wang: Elliptic and parabolic equations
  • Evans: Partial differential equations

Completion methods

Method 1

Evaluation criteria:
Grade is based on the points earned from returned exercises.
Select all marked parts

Method 2

Evaluation criteria:
Points of the final exam.
Select all marked parts
Parts of the completion methods
x

Participation in teaching (5 cr)

Type:
Participation in teaching
Grading scale:
0-5
Evaluation criteria:
Grade is based on the points earned from homework.
Language:
English, Finnish
Study methods:

Lectures and homework

Study materials:

Lecture note

Literature:
  • Evans: Partial differential equations

Teaching

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Points of the final exam.
Language:
English, Finnish
Study methods:

Independent study. Final exam.

Study materials:

Lecture notes

No published teaching