News
Oral examWritten on 21.07.22 by Dag Nilsson 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,… 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. 
PresentationWritten on 18.07.22 by Dag Nilsson The last student presentation will take place on the 20th of July 14:1515:00 Hörsaal 4. 
PresentationsWritten on 04.07.22 by Dag Nilsson 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… 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. 
Topics for presentationsWritten on 24.06.22 by Dag Nilsson 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… 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.

Exercise sheet 6Written on 22.06.22 by Dag Nilsson Exercise sheet 6 can now be found under materials. The deadline to hand this in is 29.06.2022. 
Exercise sheet 5Written on 08.06.22 by Dag Nilsson Exercise sheet 5 can now be found under materials. The deadline to hand this in is 15.06.2022. 
Exercise sheet 4Written on 25.05.22 by Dag Nilsson Exercise sheet 4 can now be found under materials. The deadline to hand this in is 01.06.2022. 
ODE Revision Tutorial (19.05.22)Written on 13.05.22 by Dan Hill 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… 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 
Exercise sheet 3Written on 11.05.22 by Dag Nilsson Exercise sheet 3 can now be found under materials. The deadline to hand this in is 18.05.2022. 
No tutorial todayWritten on 05.05.22 by Dan Hill As 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.

exercise sheet 2 and todays lectureWritten on 27.04.22 by Dag Nilsson 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. 
Updated lecture notesWritten on 22.04.22 by Dag Nilsson The 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. 
ODE theoryWritten on 14.04.22 (last change on 14.04.22) by Dag Nilsson 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… 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. 
Schedule for TutorialsWritten on 14.04.22 (last change on 14.04.22) by Dan Hill The 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. 
Exercise sheet 1 and updated lecture notesWritten on 13.04.22 (last change on 19.04.22) by Dag Nilsson 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… 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. 
Lecture 1Written on 11.04.22 (last change on 11.04.22) by Dag Nilsson The 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.