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 thei 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 differnetial 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
- Category
- Hours
- Exam
- 20
- Guidance
- 13
- Lectures
- 40
- Preparation
- 117
- Theory exercises
- 16
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Written assignment, Two 1 week take home assignmentsWritten examination, 3 hours under invigilationThe two written 1 week take home assignments count each 20% toward the final grade. The final exam counts 60%
- Aid
- All aids allowed
NB: If the exam is held at the ITX, the ITX will provide computers. Private computers, tablets or mobile phones CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
Same as ordinary exam. If one of the assignments or both received a failing mark (i.e., less than half the maximal number of points for the assignment) before the ordinary exam it (or they) can be resubmitted no later than two weeks before the beginning of the re-exam week. If an assignment is resubmitted it will be the resubmitted assignment that will count towards the grade.
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
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Jan Philip Solovej (7-787471747b6a6f457266796d33707a336970)