Winter 2022 — Engineering Mathematics (VU)

The instructor for this course is Marc Technau ().

The contents of this website is subject to change. Please mind the time stamp at the bottom of this website. Dates are written in DD.MM.YYYY format (e.g., “01.02.2022” means “February 1st 2022”).


The first lecture takes place on Monday, 03.10.2022.

Tue., 08:15–09:45, room HS·H “Ulrich Santner”.

Exceptions: due to 01.11.2022 being a public holiday, the lecture in that week will take place on Friday, 04.11.2022, 08:15–09:45, in HS·P2 in Petersgasse 16. Due to a blocked room, the lecture on the 22.11.2022 moves to room NT·02·008 in Kopernikusgasse 24/II (same time slot; 08:15–09:45).

For a complete list of the scheduled appointments, please see TUGonline.


This course is aimed at students entering the master's programme “Chemical and Pharmaceutical Engineering” and having a background in chemistry. Given the time constraints, basic familiarity with mathematics at the level of the lectures Mathematik für ChemikerInnen 1 and Mathematik für ChemikerInnen 2 will be assumed. However, there is a substantial overlap with the aforementioned courses.

The syllabus is not completely fixed yet. Curious students may consult the syllabus for the lecture Mathematics for advanced materials science which is similar and has a large overlap. However, the focus for this course will be slightly different.

Online teaching

It is planned to record the lecture-part of the course (see below). Please take note that, although the camera equipment is primarily focused at recording the lecturer and the blackboard area, it may not be possible to prevent that you appear on the recordings (sound or picture). By attending the lecture you automatically agree to these circumstances and agree to the publication of the recordings. In case you feel that a part of the recordings constitutes an infringement towards your personal rights, please contact (in well-founded cases, the relevant parts of the recordings can be cut out).

Grading policy

The final grade is derived from two aspects:

bi-weekly electronic submission of solutions to exercises, and
score from the written exam.

Details on these two aspects are expounded below. Given your score in each of the two aspects, and assuming that you have scored at least 30% of the points in the written exam, your final score η is calculated via the following formula:

η = 60% · (E) + 40% · (W).

(Here your score for each of the two aspects is understood to be the quotient of the points you have accumulated in that particular aspect and the maximum number of points attainable there.) Your grade is then determined from η and the following table:

Range for η Grade
85% ≤ η „Sehr gut“ (1)
70% ≤ η < 85% „Gut“ (2)
60% ≤ η < 70% „Befriedigend“ (3)
50% ≤ η < 60% „Genügend“ (4)
00% ≤ η < 50% „Nicht genügend“ (5)

Important note #1: If you score less than 30% in the written exam, then η = 0 (that is, your grade is „nicht genügend“).

Important note #2: Showing up for the lectures is not necessary for passing the course. To pass, you need only hand in (correct) solutions to sufficiently many exercises and score at least 30% in the written exam. (The last part obviously requires physical attendance.)

Submission of solutions for exercises and having enrolled for the course via TUGonline implies the receipt of a grade for the course, unless the enrollment in cancelled before the end of October 31st via TUGonline. Conversely, staying enrolled beyond October 31st is necessary for receiving a grade for this course.

(E): Solving exercises

Exercise sheets will be posted on this website every Thursday if there was a lecture during that week. Solutions to every other sheet (2nd sheet, 4th sheet, 6th sheet etc.) are to be submitted online via the TeachCenter by Thursday of the following week. The solutions will then be graded.

The solutions you submit must be your own. In this regard, please ensure take into account the plagiarism statute of the TU Graz (see here for an English version). The right to award a failing grade in case of violations to the above statute shall remain reserved.

The exercise sheets not due for submission (1st sheet, 3rd sheet etc.) also contain material important for the written exam. It is strongly suggested that participants of the course also try to work on these exercise sheets.

(W): Written exam

There are two chances for taking the written exam: 06.02.2023 and 20.02.2023, both taking place from 12:15 until 13:45 (90 minutes) in room NT·02·008 in Kopernikusgasse 24/II.

If one takes part in both exams, then the score achieved in the second exam replaces the score from the previous one (regardless if it is higher or lower).

The students are allowed to bring two DIN-A4 sheets with notes (both sides of a sheet may contain notes). Further aids (e.g., calculators, smart watches, phones etc.) are not admissible.



Please note that all of the above books (excluding only Jänich's Analysis and the book by Kreyszig) are freely available online. (For downloading the Springer books you should be accessing the internet from the university's IP range.)

The books of Jänich are arguably quite advanced in that they aim at expounding a high-brow view on the subject matter (although they start from scratch). They do, however, have a quite unique style of giving a real explanation of why various results are true in a very insightful fashion that is hard to find anywhere else. They are especially recommended.
The book of Bärwolff contains essentially all of the material of this course (and more), but takes a rather more calculative approach that may serve some readers better.
The present course shall attempt to combine aspects of both approaches.

Lecture notes

The lecture notes are for personal use only and are not to be distributed! Here are the various chapters:

The complete lecture notes are available here as one PDF file.

Exercise sheets

The following list will be updated regularly. New sheets generally become available every Tuesday (exceptions may occur) and written solutions for exercise sheets with even numbers are due on the following Tuesday (to be handed in online via the TeachCenter). There will probably be 15 exercise sheets.

Sheet Due date …
Sheet 1
Sheet 2 18.10.2022
Sheet 3
Sheet 4 01.11.2022
Sheet 5
Sheet 6 15.11.2022
Sheet 7
Sheet 8 29.11.2022
Sheet 9
Sheet 10 13.12.2022
Sheet 11
Sheet 12 10.01.2023
Sheet 13
Sheet 14 24.01.2023
Sheet 15