### Classical methods for Partial Differential Equations (Winter Semester 2017/18)

- Lecturer: Dr. Ioannis Anapolitanos
- Classes: Lecture (0105300), Problem class (0105310)
- Weekly hours: 4+2

**The second exam will take place on the 31st of August in 1.067 between 11:00 and 13:00. The registration of the exam is open in the campus system and it is closing at the 25fth of August**

A request: After the registration please logout from the system and log in and check that the registration has indeed worked. In the past people have written to us that they thought that the registration worked but it did not.

Schedule | ||
---|---|---|

Lecture: | Monday 9:45-11:15 | SR 3.61 |

Tuesday 8:00-9:30 | SR 3.61 | |

Problem class: | Wednesday 14:00-15:30 | SR 2.66 |

Lecturers | ||
---|---|---|

Lecturer | Dr. Ioannis Anapolitanos | |

Office hours: With appointment | ||

Room 2.025 Kollegiengebäude Mathematik (20.30) | ||

Email: ioannis.anapolitanos@kit.edu | ||

Problem classes | Dr. Markus Lange | |

Office hours: | ||

Room 2.030 Kollegiengebäude Mathematik (20.30) | ||

Email: markus.lange@kit.edu |

# A few words about the course

A differential equation is a relation between an unknown function (to be determined) and its derivatives. While for ordinary differential equations the unknown function depends on a single independent variable, it depends on several variables for partial differential equations and the equation contains partial derivatives. Differential equations model numerous phenomena and have applications in physics, chemistry, biology, economics and enginiering. Examples of partial equations that we will study is the Laplace und Poisson equation, the diffusion or heat equation, the wave equation. We will mostly learn classical methods for partial differential equations. Time permitting we will talk towards the end of the course about weak solutions of partial differential equations and Sobolev spaces.

The Analysis I-III and Linear Algebra I-II, respectively the higher mathematics courses, are important prerequisites for our course. If you do not have some of the prerequisites but still want to visit the course, please write to me an email so that we can talk personally.

The course will be accompanied by an exercise session. The participation in it is highly recommended.

# Summaries of the lectures

Posting of brief summaries of the lectures is planned to be done till Saturday night of the weak before them. These files give a very dry text having only the notation, definitions and theorems, without any proofs, examples, remarks or motivation. The purpose of this is that you get the possibility to see a little bit what will come in the next week each time. It is highly recommended that you read it and think about it even for a short of time before coming to the lecture. Such a small effort from your side might make you understand much more during the lecture than you would understand without any preparation. The file will be updated every week. If you find any typos please send an email to ioannis.anapolitanos@kit.edu, so that they get corrected.

The following file, which is still under changes and NOT yet finilized, will be formulas that will be given in the exam. Each formulas will be given independently on whether you need it or not. The paper will be given to you from us and you do not have to bring it.

# Lecture notes

In the following link you find informal lecture notes for the course. Some additional small explanations given in the lecture might not always be here but the most important parts are written here.

The other way around too, some staff that we did not have enough time to go thoughroully during the lecture might be explained in a more detail in the notes. If you find any typos please send an email to ioannis.anapolitanos@kit.edu

http://www.math.kit.edu/iana1/edu/classicalmethpde2017w/page/lecturenotes/

# Exercise sheets

In the following link you can find the exercise sheets

http://www.math.kit.edu/iana1/lehre/classicalmethpde2017w/seite/exercises/

# Feedback for the course

Your feedback for the course (suggestions, difficulties, critisism) is highly appreciated. You can either talk to us, or if you are too shy to do this, you can anonymously write in the following link.

# Interaction during the lectures

If the link http://nukit.aifb.kit.edu/nukit/ you can choose during the course HM_ETIT and login with a name of your choice. It gives you the option to vote anonymously for the tempo of the course

and to ask questions anonymously even though you are encouranged to do it orally. You can also vote for multiple choice questions that the audience is asked.

# Examination

Exercises of the exam Solutions of the exam

# References

1. Strauss, Partial Differential Equations, Vieweg

2. John, Partial Differential Equations, Springer

3. Folland, Introduction to Partial Differential Equations, Princeton University Press

4. Evans, Partial Differential Equations, AMS