# ADVANCED MATHEMATICS FOR PH.D
CANDIDATES IN THE ENGINEERING
SCIENCES: ANALYSIS AND TOPOLOGY 2005

### Time and place:

Dates: Oct. 24, 25, Nov. 7, 8, 28, 29, 30

Time: 9:00-15:00.

Place: Kroghstræde 7, room 63 all days except November 28, when it is at Kroghstræde 3 room 1115
## Course description.

As you can see from the course description on the PhD-school pages, the aim of this course is to give the participants an idea of how the mathematical vocabulary is used and the strength of using it properly. This is needed by engineering PhD's when reading papers, which will often use the common language of mathematics and in particular when writing papers. Moreover, it is crucial, that engineers understand when a given mathematical toolbox is applicable and when it is not. As an example: In favorable cases, differential equations have unique solutions, but this is not always true, and trying to approximate a solution in such cases may lead to results which are simply wrong.

Hence we need to take a different approach to mathematics than when it is taught as a tool for a specific set of problems. We focus on a few areas of mathematics which are easy to define properly, and in which one can hence see whether a given property holds or not without resorting to "handwaving". The idea is that the participants will get a better understanding of the need for precision and also the ability to see the difference between a precise argumentation and handwaving.

Following the response we got from the participants in this course in 2004, the course in 2005 will be slightly different. As a consequence, linear algebra and vectorspaces will be one of the areas covered in the manner mentioned above.
### Lecture Plans (will be posted when ready):

Welcome to the course.

Lecture plan for the first block.

Lecture plan for the second block.

Lecture plan for the third block.
### Lecturers:

Morten Nielsen. and Lisbeth Fajstrup.
### Literature

[A]: Tom. M. Apostol: Mathematical Analysis, Second Edition, Addison Wesley, 1974.

[DS]: D.A.Santos, Linear Algebra Notes, Chapters 5 and 6. Available
here

Notes on Kuhn Tucker

Sections 2.1-2.3 of these notes by Gerald Teschl: ps-file

Last modified: Mon Nov 14 13:25:01 CET 2005