Module also offered within study programmes:
General information:
Annual:
2013/2014
Code:
AMA-2-039-MN-s
Name:
Mathematics in Science and Engineering
Faculty of:
Applied Mathematics
Study level:
Second-cycle studies
Specialty:
Matematyka w naukach technicznych i przyrodniczych
Field of study:
Mathematics
Semester:
0
Profile of education:
Academic (A)
Lecture language:
Polish
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
prof. dr hab. Prykarpatski Anatolij (prykanat@agh.edu.pl)
Academic teachers:
prof. dr hab. Prykarpatski Anatolij (prykanat@agh.edu.pl)
Descriptions of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Students are able to accurately formulate questions that deepen understanding of the considered topic MA2A_K02 Activity during classes,
Examination,
Oral answer
M_K002 Students understand the need for a popular presentation of selected higher mathematics achivement MA2A_K05 Activity during classes,
Examination,
Oral answer
Knowledge
M_W001 Students known the foundations of catastrophe theory and the mathematical description of catastrophies MA2A_W02, MA2A_W04 Activity during classes,
Examination,
Oral answer
M_W002 Students known some models of the catastrophe theory and selected applications MA2A_W02, MA2A_W04 Activity during classes,
Examination,
Oral answer
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Others
E-learning
Social competence
M_K001 Students are able to accurately formulate questions that deepen understanding of the considered topic + + - - - - - - -
M_K002 Students understand the need for a popular presentation of selected higher mathematics achivement + + - - - - - - -
Knowledge
M_W001 Students known the foundations of catastrophe theory and the mathematical description of catastrophies + + - - - - - - -
M_W002 Students known some models of the catastrophe theory and selected applications + + - - - - - - -
Module content
Lectures:

1. Introduction to mathmatical descryptions of catastrophes.

2. Examples of soft and rigid models

3. The Lancaster’s war and battle model – Napoleon and Hitler lost battles and Khan Baty’s victory.

4. Optimization and saturation systems – Maltus and logistic models and their predictions.

5. Ecological and social evolution rigid and soft models – fishing in lake, tax system and the optimization-stability problem.

6. Rigid models and structural instability – the famous Lottki-Volterra prey-predator model for pikes and crucians and political parties elections

7. Many-stages management and production system – its modeling and the dangerous instability

8. Ergodic principle in evolution studies – “for a one tree temporal evolution in forest it is not necessary to wait for this tree to get grown from a seed and died, it is enough simply to look at ather trees of diverse ages”.

9. Modeling of intellectual and phsychical human states –geniuses, crazious and maniacs (idiots).

10. Conclusions and further readings.

Auditorium classes:

The problems considered during lectures are completed and discussed.

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 162 h
Module ECTS credits 6 ECTS
Udział w wykładach 15 h
Udział w ćwiczeniach audytoryjnych 30 h
Samodzielne studiowanie tematyki zajęć 85 h
Przygotowanie do zajęć 30 h
Egzamin lub kolokwium zaliczeniowe 2 h
Additional information
Method of calculating the final grade:

Ocena z egzaminu

Prerequisites and additional requirements:

Mathematical analysis, mesure theory and Lebesgue integral

Recommended literature and teaching resources:

1) “Catastrophe Theory” (Vladimir Igorevich Arnold)

2) “Catastrophe Theory” (Domenico P. L. Castrigiano, Sandra A. Hayes)

3) “Catastrophe Theory and Its Applications” (Tim Poston,Ian Stewart)

Additional information:

None