NMAK10019U Differential Operators and Function Spaces (DifFun)
MSc Programme in Mathematics
Differential operators. Distribution theory, Fourier transform of distributions. Function spaces. Applications to concrete differential operator problems.
Knowledge:
- Linear differential equations and their relevant side conditions (e.g. boundary, initial)
- Concept of ellipticity
- Distributions and their convergence properties
- Multiplication by smooth functions and derivatives of distributions
- Fourier transform of distributions
- Function classes such as Sobolev spaces or Lp spaces and the action on differential operators and the Fourier transform on these
- Unbounded operators on Hilbert spaces
- Solution methods for differential equations such as methods based on the Fourier transform or a variational approach
Competences:
- Understand the different realizations of differential operators on relevant function spaces
- Understand concepts such as existence uniqueness and regularity of solutions to differential equations within the relevant function spaces
- Determine when a certain solution method applies
- Calculate with distributions (derivatives, multiplication, ...)
- Calculate Fourier transform of distributions, and functions in different function classes
- Know the relations (inclusions) of relevant function spaces
Skills:
- Solve classical differential equations
- Establish existence, uniqueness and regularity of solutions to certain differential equations
- Describe the different realizations of concrete differential operators on Hilbert spaces
- Calculate properties (e.g., domain, spectra) of realizations of differential operators
Knowledge of the Fourier transform corresponding to FunkAn is desirable.
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Lectures
- 40
- Preparation
- 117
- Theory exercises
- 16
- Guidance
- 13
- Exam
- 20
- Total
- 206
- Credit
- 7,5 ECTS
- Type of assessment
- Written assignment, Two 7 days take home assignmentsWritten examination, 3 hours under invigilationThe two written 7 days take home assignments count each 20% toward the final grade. The final exam counts 60%
In 2022 the exam will be held as an ITX-analogue exam. This means that the exam assignment will be handed out electronically via the ITX-computer, while the students hand-in must be written with pen and paper. - Aid
- All aids allowed
The University will make computers available to students taking on-site exams at ITX. Students are therefore not permitted to bring their own computers, tablets or mobile phones. If textbooks and/or notes are permitted, according to the course description, these must be in paper format or uploaded through Digital Exam.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
Written exam, 3 hours under invigilation. All aids allowed.
The final grade is the largest of the two numbers: 1) Written exam counts 100% and 2) Written exam counts 60% and the results of the two take home assignments count 20% each.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.
Course information
- Language
- English
- Course code
- NMAK10019U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- C
- Course capacity
- No limit
The number of seats may be reduced in the late registration period - Course is also available as continuing and professional education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Jan Philip Solovej (7-787471747b6a6f457266796d33707a336970)