Webpage of the Course MAT.202UB WS 2022/23
Welcome to the Practical Course of Analysis 3 MAT.202UB for the Bachelor Degree in Mathematics at the University of Graz. This is the companion module to the theoretical Course of Analysis 3 MAT.201UB. Exercise sheets will be released every week which will cover practical aspects of the topics covered in MAT.201UB.
Please do not hesitate to email me with any questions you have regarding the module or the exercises.
There will be 13 classes in Room 11.32. The times are 10:00-11:30 for Group 1 and 11:45-13:15 for Group 2. These are the dates:
To each Lecture will correspond one Exercise Sheet. This will be uploaded 1 week before the Lecture, and is due for Crossing and Presentation on the day
of the Lecture.
Crossing: At the beginning of each Lecture, a form will be handed out in which you should declare the problems you solved. This is referred to as Crossing. You will be awarded points for each cross, according to the amount specified on the Exercise Sheet for the corresponding problem. The total is always 100 points. The final Crossing Percentage will then be computed by averaging the best 12 crossing percentages, that is, by summing the best 12 scores out of the 13 sessions, and dividing the obtained sum by 12.
Presentation: Based on the crossing, some students will be called at the blackboard to solve one of the exercises they declared. A presentation is given a grade between 0 and 5, with 5 being highest. Ideally each student should present at least 2 times during the course. The final Presentation Percentage is averaged and scaled to a number out of 100.
The Final Percentage is computed by averaging Presentation Percentage and Crossing Percentage. The Final Percentage will be converted into a Final Grade according to the table below. A pass will be granted for a grade of 4 or better.
| Percentage | 0-49% | 50-59% | 60-74% | 75-89% | 90-100% |
|---|---|---|---|---|---|
| Grade | 5 | 4 | 3 | 2 | 1 |
If you cannot attend a session, please email your solutions to the tutor responsible for the class before 10AM on the day of the class. Your Crosses will be filled according to the solutions submitted. If you are absent and do not email the solutions, the Crossing Percentage for that session will be zero.
| Due date | Exercises | Topics |
|---|---|---|
| 5 Oct | Sheet 1 | Some revision. Warming up! |
| 12 Oct | Sheet 2 | Local maxima/minima. Constrained minimization |
| 19 Oct | Sheet 3 | Saddle points. Directional derivatives. Implicit Function Thm |
| 9 Nov | Sheet 4 | Continuous \(\nabla\) vs differentiability. Taylor. Directional derivative |
| 16 Nov | Sheet 5 | Schwarz Thm. Inverse Function Thm |
| 23 Nov | Sheet 6 | Inverse Function Thm. Topology: continuity, connectedness |
| 30 Nov | Sheet 7 | Continuity. Path-connectedness |
| 7 Dec | Sheet 8 | Unitary matrices. Surfaces: tangent space |
| 14 Dec | Sheet 9 | Curves and surfaces |
| 11 Jan | Sheet 10 | Curves and surfaces |
| 18 Jan | Sheet 11 | Curves and surfaces |
| 25 Jan | Sheet 12 | Curves and surfaces |
| 1 Feb | Sheet 13 | Gauss’ Theorem |