After successful completion of the course, students are able to
- master elementary mathematical models and employ these models properly on according questions,
- understand mathematical language and formalism so that they can independently study mathematical textbooks and work their way into new subject areas,
- work sensibly with the subjects dealt with in the course and use them in other courses (e.g. Physics, Physical Chemistry, ...).
Graduates are acquainted with mathematical methods to systematically analyze, structure and investigate problems.

Mathematical methods and models from the following subjects:

• Algebra: logic and foundations, mathematical formalism; sets, relations, functions, permutations; groups, symmetry groups of molecules; number systems and fields; complex numbers; polynomials; calculating with (formal) power series; partial fraction decomposition
• Calculus in one variable: sequences, limits; series; convergence criteria; power series and radius of convergence; elementary functions; continuity, limits and differentiability; modelling of reaction kinetics; mean value theorem; de l'Hospital's rule; monotonicity and convexity criteria; Taylor' theorem; extremal values; Riemann integration; fundamental theorem of calculus; antiderivative and indefinite integration; integration technique; integration of rational functions; improper integral and Gamma function
• Ordinary differential equations (ODEs): introduction; approximate solution by power series expansion; methods of solution for specific 1st order ODEs (e.g., separable, linear); rate equation; theory for linear ODEs; existence and uniqueness of solutions; systems of 1st order ODEs and stability of equilibrium points; 2nd order linear ODEs with constant coefficients; Schrödinger equation, an easy case (optional)
• Elements of stochastics and statistics: basic notions in probability theory; random variables, distribution function, expected value, variance, quantile etc; basic inferential statistics; point and interval estimates; lineare regression; confidence intervals for the expected value of normally distributed random variables

 In the parts we include practical problems from chemistry or physics, respectively.

In the lecture the mathematical contents are presented mainly by data projection, it contains illustrations and several examples with reference to applications in chemistry.

From the students' side: active attendance during the lecture (livestream in the case of distance learning); preparation of written notes; reassessing, consolidating and expanding the range of understanding by autonomously solving problems of the corresponding exercise course.

############################################################################
############################################################################
##     Lecture 19 to 20 Dec 2022 (on-line, Zoom)                          ##
##     Zoom-ID: 969 9139 7739                                             ##
##     Password: will be mentioned in the lecture of 13 Dec 2022          ##
############################################################################
############################################################################

• Course assessment is done by written exam.
• usually 3 examination dates per semestre (roughly beginning, mid, end of term, cf. TISS)
• Registration for the exam is possible via TISS (consider the deadlines for registration or cancellation carefully); only registered students can take the exam (to be simply on the waiting list is not sufficient). Regarding examinations in front of a board of examiners, it is not possible to register in TISS. Instead the examinee has to notify, within the registration period, the main examiner as well as the dean's office of their intent to sit the exam.
• For organisational questions regarding the exams (registration, cancellation, announcement of sickness etc.) please refer to our secretary Ms Marietta Meszlenyi.
• There will be given 100 minutes (1 h 40 min) to complete the exam.
• The whole content of the lecture is subject to examination (not only the topics covered by the exercise sessions) [The term "content" describes the content of this lecture as given in the winter term of 2022; it does not apply and is perhaps unrelated to other content presented (by possibly other lecturers) in other semesters. It is the duty of the candidate to make sure they are aware of possible changes (if applicable) compared to previous semesters. Exams concerning the content of previous years (within the legal regulations) can be arranged on an individual basis.].
  As a general rule there will be 5 problems, each allowing to earn 16 out of 80 points total. There will be practical questions dealing with modelling or calculations similarly to the exercise sessions (usually 3/5), as well as theoretical questions concerning the definitions, concepts and theorems (including their proofs) covered in the lecture (usually 2/5). In general, the following marks are assigned for x out of 80 points: x<40: mark 5 (insufficient, fail), 40≤x<50: mark 4 (sufficient, pass), 50≤x<60: mark 3 (satisfactory), 60≤x<70: mark 2 (good), 70≤x≤80: mark 1 (very good). General rules regarding the distribution of questions and marks may be subject to exceptions (changes usually occur in favour of the examinees)! The content of the problems is randomly chosen from the topics of the lecture.
• Authorized resources:
  1) Collection of mathematical formulae: the collection "Mathematik für Chemiker" that is available at Institut 104 (https://tiss.tuwien.ac.at/adressbuch/adressbuch/orgeinheit/1669, genauere Kontaktinformationen) or a collection containing the endorsement "für die allgemeinbildenden höheren Schulen zur Abfassung der schriftlichen Reifeprüfung" authored by (a possibly proper subset of) {Götz, Bürger, Kraft, Unfried, Haschkovitz} published by öbv [other collections are explicity forbidden]; except for highlighting no additional notes in the collection of formulae are permitted.
  2) Calculators: calculators are admitted to perform the basic numerical operations (such as addition, subtraction, multiplication, division, square roots) and to calculate values of fundamental functions (trigonometric operations, exponentials and their inverses); calculators allowing for one of the following operations are not approved: numerical or symbolic integration, numerical or symbolic derivation, automated drawing or generation of value tables of graphs of real functions, matrix operations, integrated computer algebra system, programmable calculators, integrated regression
  FOR A LIST OF FORBIDDEN / ALLOWED CALCULATORS, please see the German version of this site.
• In case of doubt, it is the responsibility of the candidate to check the acceptability of the means he or she intends to use in advance.
  Student identity cards are to be presented upon the exam to permit identity verification.
• After confirmed registration, unexcused absence will be sactioned within the legal regulations. Announce withdrawal due to health conditions to the person supervising the exam before the exam starts, i.e., before you will be handed out the exam paper. Otherwise, after the exam has started, illness cannot be recognised as an excuse to resign from the examination and the test will be marked (resulting in a failed attempt as the case may be).
• Whenever possible the exam will take place in a lecture hall.
• Necessary technical equipment in case of an online-exam: Computer with video camera, speakers and microphone; reliable internet connection; access to TUWEL.
  Detailed information regarding on-line exams will be made available (in TISS, or via message to the registered participants) should the necessity arise. On-line examinations will usually be split up into a written and an oral part.
• Oral inquiry in order to authenticate the written exam is possible.

• D. Dorninger et al., "Mathematische Grundlagen für Chemiker", Bände I, II und III. Prugg Verlag, Eisenstadt, 1983.
• H. Zachmann & A. Jüngel, "Mathematik für Chemiker", Wiley-VCH, Weinheim, 2007.
• M. Drmota & B. Gittenberger & G. Karigl & A. Panholzer, "Mathematik für Informatik" Berliner Studienreihe zur Mathematik. Band 17. 438 Seiten. Heldermann, Lemgo, 2008
  ISBN 3-88538-117-4
• H. Heuser, "Lehrbuch der Analysis Teil 1" Mathematische Leitfäden. 17. Ausgabe. XI+632 Seiten. Vieweg+Teubner Verlag, Wiesbaden, 2009
  ISBN 978-3-8348-0777-9

Solid knowledge of mathematics as taught at school.

It is stongly recommended to attend the course "101.748 Harmonisation Course Mathematics" in order to freshen up (or improve) your knowledge of mathematics. Note that this course already starts towards the end of September.