Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - Department of Chemistry

(1st semester)

Sets and mappings, Combinatorics, Elementary functions, limits of sequences, series and functions.

Calculus: differentiation and integration of functions, functions of several variables, partial derivatives, implicit functions, homogeneous functions (intensive and extensive state variables), differential forms, total differential, theorem of Schwarz and it's consequences, extremal values.

(2nd semester)

Vectors and matrices, geometry linear algebra, vector spaces and linear mappings, systems of linear equations, linear independence of vectors, systems of reference, dimension, matrix multiplication, inverse of a matrix, orthogonal bases - application for linear fit and Fourier series, determinants, representing linear transformations by matrices, groups of matrices, eigenvalues and eigenvectors.

(3rd semester)

Ordinary differential equations, separation of variables, linear differential equations, numerical methods, existence and unicity of solutions - initial values, linear differential equations, systems of linear differential equations - eigenvalue method, partial differential equations (especially Schrödinger- and diffusion equation), applications in chemistry and physics

L. Papula, Mathematik für Chemiker, Ferdinand Enke Verlag Stuttgart, 1991.
H. G. Zachmann, Mathematik für Chemiker, VCH, Weinheim.
N. Rösch, Mathematik für Chemiker, Springer Verlag, 1993.
H. Margenau; G. M. Murphy, Die Mathematik für Physik und Chemie.
L. Papula, Mathematik für Ingenieure und Naturwissenschaftler,
       Band 1: Vektoren, Funktionen, Differential- und Integralrechnung für Funktionen einer Veränderlichen, Potenzreihenentwicklung von Funktionen
       Band 2: Matrizen, Determinanten, lineare Gleichungssysteme, Eigenwerte und Eigenvektoren, komplexe Zahlen und Funktionen, Differential- und Integralrechnung für Funktionen mehrerer Veränderlicher.
       Band 3: Vektoranalysis, Wahrscheinlichkeitsrechnung, mathematische Statistik.
W. Göhler, Formelsammlung höhere Mathematik, Harri-Deutsch Verlag.
I. N. Bronstein; K. A. Semendjajew, Taschenbuch der Mathematik, Teubner Verlag.
E.-A. Reinsch, Mathematik für Chemiker, B. G. Teubner Verlag 2004.
MINÖL-series: about 30 volumes written by different authors, devoted to selected topics of applied mathematics for students of mathematics, engineering, science, economy, science, and agronomy. To our course, volumes 0, 1, 2, 3, 4, 7/1, 7/2, 13 are related.