Analysis 3

Webpage of the Course MAT.202UB WS 2022/23

General Information

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.

Lectures Calendar

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:

Assessment Rules

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.

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.


Exercise Sheets

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