Print syllabusMathematical methods in natural and social sciences
General data
| Course ID: | 1000-135MMN |
| Erasmus code / ISCED: |
11.1
|
| Course title: | Mathematical methods in natural and social sciences |
| Name in Polish: | Metody matematyczne nauk przyrodniczych i społecznych |
| Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
| Course groups: |
(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics |
| ECTS credit allocation (and other scores): |
6.00
|
| Language: | English |
| Main fields of studies for MISMaP: | computer science |
| Type of course: | elective courses |
| Short description: |
The aim of the lecture is to present some basic methods of dynamical systems and partial differential equations that are essential in the modern description of natural and social processes. |
| Full description: |
The aim of the lecture is to present some basic methods of dynamical systemsand partial differential equations that are essential in the modern description of natural and social processes. In the past Mathematical Methods of Physics were a basis for description of physical processes. Nowadays it is important to know modern mathematical methods used in description of processes in Natural and Social Sciences. The methods refer to typical nonlinear equations that are used in description. The plan of the lecture is as follows: Poincar´ e–Bendixson Theorem; Grobman–Hartman Theorem; Methods of Small Parameter, Singular Perturbations; Conservation Laws, Methods of Characteristics; Diffusion Processes; Reaction–Diffusion Equations; Semigroups theory; Deterministic chaos. The theory is illustrated by numerous examples including those in Economy, Biology, Medicine, Social Sciences and Technology. |
| Bibliography: |
1. J. Banasiak, M. Lachowicz, Methods of small parameter in mathematical biology, Birkhüser 2014. 2. M.W. Hirsch, S. Smale, R.L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, Academic Press 2004. 3. J.D. Logan, An Introduction to Nonlinear Partial Differential Equations, Wiley Interscience 2008. 4. L. Perko, Differential Equations and Dynamical Systems, Springer 2001. |
| Learning outcomes: |
1. The knowledge of basic mathematical structures corresponding to processes in biology, medicine and social sciences 2) The knowledge of mathematical technics in analysis of models (a) The Poincare'-Bendixson theorem, (b) The Grobman-Hartman theorem, (c) Methods of small parameter, singular perturbation, (d) Initial layer, Boundary layer, shock waves, (e) Tikhonov-Vasil'eva theory, (f) The characteristic methods, (g) The similiaryty methods, (h) Travelling waves, (i) Existence, uniqueness, Maximum Principle, (j) Energy estimates and asymptotic behaviour, (k) Patterns (l) Semigroup theory (m) Deterministic Chaos |
| Assessment methods and assessment criteria: |
score system and a written exam |
Classes in period "Winter semester 2023/24" (past)
| Time span: | 2023-10-01 - 2024-01-28 |
 
MO TU W CW
WYK
TH FR |
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
| Coordinators: | Mirosław Lachowicz | |
| Group instructors: | Marcin Choiński, Mirosław Lachowicz | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Classes in period "Winter semester 2024/25" (future)
| Time span: | 2024-10-01 - 2025-01-26 |
MO TU W TH FR |
| Type of class: |
Classes, 30 hours
Lecture, 30 hours
|
|
| Coordinators: | Mirosław Lachowicz | |
| Group instructors: | Marcin Choiński, Mirosław Lachowicz | |
| Students list: | (inaccessible to you) | |
| Examination: | Examination |
Copyright by University of Warsaw.
