News
21.07.2022

Oral examBelow are listed dates and times for the oral exam. Please pick three timeslots for which you want to do the oral exam and email these to me. My email is nilsson@math.unisb.de
01.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15 02.08.2022: 10:15, 11:15, 14:15,... Read more Below are listed dates and times for the oral exam. Please pick three timeslots for which you want to do the oral exam and email these to me. My email is nilsson@math.unisb.de
01.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15 02.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15 03.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15 04.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15 05.08.2022: 10:15, 11:15, 14:15, 15:15, 16:15
You should register for the oral exam on the LSF. Please notify me if you are unable to register. 
18.07.2022

PresentationThe last student presentation will take place on the 20th of July 14:1515:00 Hörsaal 4. 
04.07.2022

PresentationsThe presentations are planned to be held on 1314 of July. On the 13th we will meet during the regular lecture hour in the usual lecture room and I will give an update later in the week regarding when and where to meet on the 14th. Please let me know as soon as... Read more The presentations are planned to be held on 1314 of July. On the 13th we will meet during the regular lecture hour in the usual lecture room and I will give an update later in the week regarding when and where to meet on the 14th. Please let me know as soon as possible if you plan to use a projector for your presentation. Also let me know in case you have a preference for presenting on the 13th or the 14th. Please send a draft of your manuscript to both me and Dan before the 9th of July, so that we can give you some feedback and suggestions for improvement. 
24.06.2022

Topics for presentationsBelow are listed topics for the student presentations.
Solutions of the wave equations in even and odd dimensions. Pages 7080 in [Evans, Partial differential equations].
Calculus of variations. Pages 453460 in [Evans, Partial differential... Read more Below are listed topics for the student presentations.
Solutions of the wave equations in even and odd dimensions. Pages 7080 in [Evans, Partial differential equations].
Calculus of variations. Pages 453460 in [Evans, Partial differential equations].
Good kernels and Cesaro and Abel summability. Pages 4856 in [Stein & Shakarchi, Fourier analysis: An introduction]
A continuous function with a diverging Fourier series. Pages 8387 in [Stein & Shakarchi, Fourier analysis: An introduction].
The hydrogen atom. Section 9.5 in [Strauss, Partial differential equations: an introduction].
Vibrations of a drumhead. Section 10.2 in [Strauss, Partial differential equations: an introduction].
Shock waves. Section 14.1 in [Strauss, Partial differential equations: an introduction].
You are to prepare a 3045 minute presentation on one of these topics. The presentations can be done in groups up to two persons.
Please notify me by 29 of June which topic you would like, either via email or during the lectures. The topics will be distributed on a first come first serve basis.
The presentations can be done either on the blackboard or by preparing lecture slides and using a projector. In either case, please send the lecture notes of your talk to me and Dan in advance of your presentation so that you can get feedback on them. The presentations are planned to be held in the period 1115 of July.
It is compulsory to give presentation and attend all the other presentations in order to qualify for the exam.
Please send an email to me or Dan should you have any questions.

22.06.2022

Exercise sheet 6Exercise sheet 6 can now be found under materials. The deadline to hand this in is 29.06.2022. 
08.06.2022

Exercise sheet 5Exercise sheet 5 can now be found under materials. The deadline to hand this in is 15.06.2022. 
25.05.2022

Exercise sheet 4Exercise sheet 4 can now be found under materials. The deadline to hand this in is 01.06.2022. 
13.05.2022

ODE Revision Tutorial (19.05.22)Next week's tutorial will be a recap of ODE theory, where we will review the basics for solving first and secondorder equations as well as some special examples that come from the study of PDEs. If there are any particular topics you would like me to cover... Read more Next week's tutorial will be a recap of ODE theory, where we will review the basics for solving first and secondorder equations as well as some special examples that come from the study of PDEs. If there are any particular topics you would like me to cover during this tutorial, please let me know.
Dan 
11.05.2022

Exercise sheet 3Exercise sheet 3 can now be found under materials. The deadline to hand this in is 18.05.2022. 
05.05.2022

No tutorial todayAs mentioned in the lecture yesterday, there will be no tutorial today. The next tutorial will be on Thursday 12th of May (12.05.22) once the submissions for Exercise Sheet 2 have been marked.

27.04.2022

exercise sheet 2 and todays lectureExercise sheet 2 can now be found under materials. The deadline to hand this in is 04.05.2022.
Due to a technical error, todays lecture was unfortunately not recorded. We covered pages 3441 during the lecture and next week we will continue on page... Read more Exercise sheet 2 can now be found under materials. The deadline to hand this in is 04.05.2022.
Due to a technical error, todays lecture was unfortunately not recorded. We covered pages 3441 during the lecture and next week we will continue on page 42. 
22.04.2022

Updated lecture notesThe lecture notes have now been updated. On Monday next week I plan to finish the section on meansquare convergence and continue with section on the Fourier transform. 
14.04.2022

ODE theorySome students have asked regarding a reference for the basic theory of ordinary differential equations. What is needed for this course is essentially covered in sections 2.12.4, of "Advanced Engineering Mathematics, sixth edition", by Kreyszig. You could also have... Read more Some students have asked regarding a reference for the basic theory of ordinary differential equations. What is needed for this course is essentially covered in sections 2.12.4, of "Advanced Engineering Mathematics, sixth edition", by Kreyszig. You could also have a look at section 2.7 of the same book where they consider the Euler equation, which appeared in Example 1.3 of my lecture notes. 
14.04.2022

Schedule for TutorialsThe tutorials are currently planned for each Thursday 14:0016:00, starting on the 28th April. The tutorials will take place in Seminarraum 4 E2.5. 
13.04.2022

Exercise sheet 1 and updated lecture notesExercise sheet 1 can now be found under materials.
During todays lecture we covered pages 1219, up until the proof of Corollary 2.7. We will continue next lecture with the proof of Corollary 2.7, and then continue with the section on Meansquare... Read more Exercise sheet 1 can now be found under materials.
During todays lecture we covered pages 1219, up until the proof of Corollary 2.7. We will continue next lecture with the proof of Corollary 2.7, and then continue with the section on Meansquare convergence.
Note that there is no lecture on Monday 18 of April due to the Easter holidays. 
11.04.2022

Lecture 1The lecture notes for the first lecture can now be found under materials.
In todays lecture we covered pages 15 and started on Example 1.3. Please read the rest of Example 1.3 and Example 1.4. 
Partial Differential Equations 1
This course serves as an introduction to linear partial differential equations. The main focus will be on the canonical examples of linear PDE's, namely Laplace's equation, the wave equation and the heat equation. Additionally the course contains introductions to Fourier analysis and distribution theory, tools which are important for studying PDE's.
The lectures will take place on Mondays 12:0014:00 and Wednesdays 14:0016:00 in Hörsaal 4. The first lecture will be on 11.04.2022.
The tutorials will take place on Thursdays 14:0016:00 in Seminarraum 4 E2.5. The first tutorial will be on 28.04.2022.
Under materials you can find a sheet with general information about the course.
The registration for the course will be open during the period 04.04.202222.04.2022.
Video recordings of the lectures can be found under materials.