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
Exercises: Ross Ogilvie – r.ogilvieuni-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 2 – Solutions – B6 Teil A 101 – Transport Eqn, Burger's Eqn
Sheet 3 – Solutions – 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 4 – Solutions – 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 5 – Solutions – B6 Teil A 101 – Compact Support, Convolution
Sheet 6 – Solutions – B6 Teil A 301
Sheet 7 – Solutions – B6 Teil A 101
Sheet 8 – Solutions – B6 Teil A 301 – Spherical Means for Distributions
Sheet 9 – Solutions – All Saints Day – The tutorial will take place on Friday at 15:30 in B6 Teil A 101.
Sheet 10 – Solutions – B6 Teil A 301 – Heat Equation Examples, Heat Ball
Sheet 11 – Solutions – B6 Teil A 101
Sheet 12 – Solutions – B6 Teil A 301
Sheet 13 – Solutions – 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.