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:
- Algebra: groups, symmetry groups of molecules; number systems (rational, real, complex numbers); basic notions in probability; polynomials, partial fraction decomposition of rational functions; sequences, series, power series and Fourier series
- Calculus in one variable: elementary functions; differentiable functions; mean value theorem and its consequences; definite and indefinite integration; calculating integrals; chemical kinetics; improper integral
- Elements of statistics: random variables, distribution function, expected value, variance, etc; basic inferential statistics
- Ordinary differential equations: introduction; approximate solution by power series expansion; first order differential equations, methods of solution, general theory; second order linear differential equations with constant coefficients; Schrödinger equation, an easy case
In all parts we include practical problems from chemistry and 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 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.
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.
