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 the mathematical method to systematically analyze, structure and investigate problems.

Mathematical methods and models from the following subjects:

• Numerical methods: polynomial interpolation, approximating methods for computin integrals, for solving equations and differential equations
• Linear algebra:vector spaces (subspaces, linear independence, generating systems, basis, dimension), inner product and Euclidian spaces, cross product, matrices (rank, matrix operations, regular/singular matrices, inverse matrix), determinants (computation and interpretation), linear functions (rank, kernel, coordinatization), orthogonal transformations (application to symmetry operations of molecules), systems of linear equations (Gauß algorithm, Cramer-method), linear optimization, eigenvalues and -vectors, diagonalization, basics in Hückel's molecular orbital theory, 
• Analysis of functions in several variables: various types of functions in several variables (curves, skalar and vector fields), limits and continuity, partial derivatives, differentiability and total derivative, chain rule and implicit functions, exact differential forms, differential operators (gradient, divergence, curl, Laplace operator), scalar potential of a vector field, integrability conditions, Taylor expansion in several variables, propagation of uncertainty (Gauß's law), extrema of functions in several variables with/without equality constraints, Lagrange multiplier method, multiple integras, line integrals of a vector field, path independence, line integral of a scalar field

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 students' side: active attendance during the lecture/livestream; preparation of written notes; reassess, consolidate and expand the range of understanding by autonomously solving problems of the corresponding  exercise course.

According to the pandemic situation the procedure of the course may vary.

Written exam, duration 100 minutes, consisting of 5 questions 3 of which are of computational nature similar to the questions in the corresponding exercise course, 2 questions concern definitions, theorems, (sketches of) proofs and interrelationship among the topics dealt with in the lecture.

The total amount of points to be gained is 40, the grading scale is as follows:
0-19 points: Not Sufficient (grad 5)
20-24 points: Sufficient (grade 4)
25-29 points: Satisfactory (grade 3)
30-34 points: Good (grade 2)
35-40 points: Excellent (grade 1)

Assistive equipment allowed during exam:
1) A mathematical formulary: two particular formularies are allowed, the "Formelsammlung zu Mathematik für Chemiker" edited at Institute for Discrete Mathematics and Geometry, and the  „Mathematische Formelsammlung“ authored by Götz, Kraft, öbv, 13th edition (or earlier editions with other/additional authors).
2) A calculator evaluating only basic operations and functions, not programmable, no graphic representation of functions, no computer algebra system, no (numerical) integration/differentiation.

Whenever possible the exam will take place in a lecture room.

Necessary technical equipment in case of an online-exam: Computer with camera, loudspeaker and microphone; reliable internet connection, printer.

For detailed regulations regarding online exams we refer to the homepage of the course.

Oral inquiry  in order to authenticate the written exam is possible.

Further reading: 

• H. Zachmann & A. Jüngel, "Mathematik für Chemiker", Wiley-VCH, Weinheim, 2007.
• J. Michael Fried," Mathematik für Ingenieure I und II -Für Dummies", Wiley-VCH, Weinheim, 2010 and 2013.
• H.-G. Roos & H. Schwetlick, "Numerische Mathematik. Das Grundwissen für jedermann." Mathematik für Ingenieure und Naturwissenschaftler. 220 pages. Teubner, Stuttgart/Leipzig, 1999
  ISBN 3-519-00221-3
• M. Drmota & B. Gittenberger & G. Karigl & A. Panholzer, "Mathematik für Informatik" Berliner Studienreihe zur Mathematik. Volume 17. 438 pages. Heldermann, Lemgo, 2008
  ISBN 3-88538-117-4
• Helmut Länger, "Grundlagen der Analysis und Linearen Algebra", TU-MV Media Verlag, Wien, 2018. ISBN 978-3-903024-83-0

Additional material (multimedia resources):

• Grant Sanderson (3Blue1Brown), "Essence of linear algebra".
• Grant Sanderson (3Blue1Brown), "Essence of calculus".
• Khan Academy, "Multivariable calculus".

It is recommended to complete "Mathematics for Chemists I".