Introduction to Partial Differential Equations (MAA 510)

News

16. Nov Hier ist der Link der Vorlesungsevaluierung: https://evasys.uni-mannheim.de/evasys/online.php?pswd=UQGCN

15 Nov – Please take the feedback survey https://evasys.uni-mannheim.de/evasys/online.php?pswd=LAJ6V

3 Nov – Wie wir diskurtiert haben, finden die Prüfung an drei Daten statt:

1. Prüfungszeit:
Mo 19. Dez

2. Prüfungszeit:
Mo 16. Jan
Mo 6. Feb

Sie können frei wählen, welches Datum Ihnen am besten passt. Schreiben Sie Ross bitte ein Email mit Ihrer Entscheidung. Dann kann ich genauere Zeitraüme verteilen (aber wahrscheinlich am Morgen). Vergessen Sie nicht, sich zur Prüfung in Portal2 auch anzumelden. Die Prüfungen läuft in Präsenz, mündlich, ~30 mins. Sie dürfen Deutsch oder English sprechen. Wenn Sie noch Fragen haben, fragen Sie per Email oder im Tutorium.

13 Sept – We had some trouble changing the room booking for the tutorial. We will try to have the tutorial in 101 as much as possible. As back-up option we still have 301 and we will sneak into 303 if it unused.

08 Sept – The time of the Thursday lecture has been changed to the morning. Both the lectures and the exercises have also changed rooms.

Lectures: Martin Schmidt

tuesday 5:15 pm – 6:45 pm in B6 Teil A 101
thursday 8:30 am – 10:00 am in B6 Teil A 101

Script

Exercises: Ross Ogilvie – r.ogilvie uni-mannheim.de

tuesday 3:30 pm – 5:00 pm in B6 Teil A 101 / 301.

The first tutorial will mostly consider background material and you do not have to submit the first exercise sheet. Thereafter, please email your exercises by 12:00 the day before the tutorial, so I (Ross) can mark them and give feedback. A minimum of 50% of the exercise points is necessary to be admitted to the exam.

Exercise Sheets:

Sheet 1Solutions

Sheet 2Solutions – B6 Teil A 101 – Transport Eqn, Burger's Eqn

Sheet 3Solutions – B6 Teil A 101- There is a justification of the entropy condition on physical grounds in Evans' book Partial Differential Equations pg 142–3.

Sheet 4Solutions – B6 Teil A 301 – All the points from the last exercise are to be considered as bonus points, so the sheet was out of 19. Here is a scan of the additional exercises we did in class. The quasi-linear PDE whose characteristics we looked at in (x1,x2,z) space is here. I made it so you can put in any function as the initial condition. Observe the crossing of the characteristics is when the surface is not a graph over (x1,x2).

Sheet 5Solutions – B6 Teil A 101 – Compact Support, Convolution

Sheet 6Solutions – B6 Teil A 301

Sheet 7Solutions – B6 Teil A 101

Sheet 8Solutions – B6 Teil A 301 – Spherical Means for Distributions

Sheet 9Solutions – All Saints Day – The tutorial will take place on Friday at 15:30 in B6 Teil A 101.

Sheet 10Solutions – B6 Teil A 301 – Heat Equation Examples, Heat Ball

Sheet 11Solutions – B6 Teil A 101

Sheet 12Solutions – B6 Teil A 301

Sheet 13Solutions – B6 Teil A 101 – Standing Waves, Reflected Waves, Video of Reflected Waves

Sheet 14 – Solutions – B6 Teil A 301

For your interest, here are two papers about PDE theory broadly: a historical perspective and on the unity of the subject.