| Course title |
Mathematics IV |
| Lecturer |
prof. dr hab. Maciej M±czyński |
| Semester |
Winter |
| Description |
The course develops some advance methods of mathematics supplementary to Mathematics III. In particular, distribution theory used for heat equation is developed, as well as Fourier transform, Laplace transform in application to partial differential equation, foundations of functional analysis, linear operators and hermitean operators with eigenvalues. |
| Prerequisites |
Mathematics III, in particular linear partial differential equations solved by Fourier method, linear algebra and matrices. |
| Course content |
Elements of the theory of distribution - functional (Schwartz) and sequential (Sikorski-Mikusiński) approach, Delta-Dirac distribution and its properties, Fourier transform, connection with Laplace transform, application to solving the heat equation, linear vector spaces, Banach and Hilbert spaces, linear operators, expression by matrices, hermitean operators, eigenvalues and eigenvectors, application to the theory of chemical orbitals and quantum compound systems. |
| Recommended books |
- Laurent Schwartz "Mathematics for Physical Sciences", Paris, Hermann 1996.
- B. Friedman "Lectures for Application-oriented Mathematics", Holden-Day Chicago 1969.
- M. Franklin "Matrix Theory", Academic Press 1969.
- K. Mathiak, Peter Stingl "Teoria Grup dla chemików", PWN 1990 |
| Examination type |
written + oral |
| Level |
4th year |
| Credits |
3 |
| Language |
Polish |
| Faculty |
Chemical and Process Engineering |
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