higher mathematics
The term higher mathematics comes from the language used by universities and forms a complement to both elementary mathematics in secondary education and university mathematics.
It includes, without being sharply defined, those sub-areas of mathematics that are taught as mathematical foundations in the natural sciences and engineering courses of study at universities . The intended increase in knowledge of mathematical concepts and methods certainly reaches a level that is not offered at secondary schools.
In contrast to the more in-depth content of mathematics studies and mathematical research, the emphasis here is more on the practical aspect. However, the scope and degree of abstraction vary between the individual universities.
meaning
Higher mathematics is regarded as the “ language ” of the specialist sciences for describing natural law processes in the environment and as an excellent means to train precise thinking .
This is why it is traditionally at the beginning of the curriculum in university courses - in certain university courses different parts are left out or offered as a later specialization .
structure
Which sub-areas of mathematics are part of the general range of courses at universities differs regionally and also as a result of scientific developments. For example, around 1980 the Vieweg manual "Higher Mathematics" was structured as follows:
- Analytical geometry in the plane and in space
- Basic concepts of mathematical analysis
- Differential calculus and integral calculus
- Plane and spatial curves
- Infinite rows
- Differential and integral calculus for functions of several variables
- Differential equations
- Function theory
- Parts of functional analysis such as Fourier analysis
- Vector analysis
In addition, there are now general chapters on linear algebra ( vectors and matrices ), basic numerical methods , knowledge of descriptive and inductive statistics and possibly an introduction to computer algebra systems .
literature
- Klaus Habetha : Higher Mathematics for Engineers , 3 volumes, Klett-Verlag, Stuttgart, 1976 to 1979
- A. Hoffmann, B. Marx, W. Vogt: Mathematics for engineers. Volume 1: Linear Algebra, Analysis, Theory and Numerics . Pearson studies, Munich et al. 2005, ISBN 3-827-37113-9 , ( electrical engineering - mathematics ).
- Kurt Meyberg, Peter Vachenauer: Higher Mathematics. Volume 1: differential and integral calculus, vector and matrix calculation . 6th corrected edition. Springer, Berlin et al. 2001, ISBN 3-540-41850-4 , (with 1 CD-ROM).
- Gerhard Merziger, Thomas Wirth: Repetition of higher mathematics. 5th edition. Binomi-Verlag, Springe 2006, ISBN 3-923923-33-3 .
- Hermann Schichl , Roland Steinbauer: Introduction to mathematical work. Springer, Berlin 2012, ISBN 978-3-642-28645-2 .
Web links
- Higher math formulary
- Higher Mathematics in Mathematica ( Memento from February 18, 2008 in the Internet Archive )