# Introduction to Partial Differential Equations (MAA 510)

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

Exam Schedule:

Monday 6 February

11:50 – Mihail Birsan (IntroPDE)
12:25 – Kenny Tran (IntroPDE)
13:00 – Marc-André Bach (IntroPDE)
14:10 – Max Eppler (Ana3)
14:45 – Valeriia Zhidkova (Ana3)
15:20 – Sven Thomes (Ana3)
16:30 – Niklas Seyrich (Ana3)

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 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 14Solutions – 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.