1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Mathematics - drugiego stopnia z tyt. magistra
5. Selected Problems of Mathematical Modeling

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Selected Problems of Mathematical Modeling - opis przedmiotu

Cel przedmiotu

The aim of the course are general rules of mathematical modeling basing on selected parts of applied. They are ilustrated by selected problems of economy, mathematics, engineering, physics and chemistry.

Wymagania wstępne

Zapisz zmiany

Courses of ordinary differential equations and elements of optimal control theory.

Zakres tematyczny

The lecture is devoted to presentation of the general pattern of progressive dealing with modeling of selected problems of economics, engineering, physics and chemistry, with application of computer technology of calculations. Presented examples of modeling of selected non - mathematical problems contains the essential compendium knowledge of selected branches of sciences dealing with modeling problems. Important elements of lecture are analysis of computer calculations of solutions modeled problems. Lectures are realized by conversational forms. The aim of such parts of lecture is showing for reach possibilities of forecasting and projecting of getting solutions.

Classes to presented subject pose a continuation investigations of selected mathematical models presented on lectures. Students solve under guidance of the leader problems keeping to construction of mathematical models, solving them and analysis of getting results. Problems of exercises deals with complex dynamical and statical systems, which require compilation of differentiated mathematical methods.

Laboratory, realized by projection form, should be devoted to study by students of a project of a selected problem describing of non - mathematical problem. Project needs construction of the proper mathematical model, its solution and complex analysis getting results including an information dealing with a possibility of practical them application. As examples of projection classes can be tasks dealing with pointed out of path of rear weels of the bus and the trailer - truck jackknifing, mechanics describing of slowing down of the hovercraft, conditions of the slowest descent to the Moon. As the final result of projection classes of the mathematical modeling should be the written study of solution of the problem.

Metody kształcenia

The basing methods of teaching is a lecture, realized in small groupes. Classes and laboratory are  integrated parts of teaching mthematical modeling, devoted to solving selected problems and verification of thir outcomes.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The basic form of passing a course is passing its individual forms of implementation. The basis for passing project classes is a positive assessment of the student's report. A positive assessment of the student's activity and participation in classes are the basis for passing the exercises. The student's activity in the conversational part of the lecture is the basis for passing the lecture.

The grade for the course consists of the grade for the laboratory (35%), exercises (35%) and lecture (30%). The condition for passing the course is a positive grade in all forms of classes.

Literatura podstawowa

1. W. I. Arnold, Orgdinary Differential Equations, PWN (1975) .

2. K.K. Ponomariew, Constructions and Solving Differential Equations in engineering Problems, WNT Warszawa (1965).

3. M.S. Klamkin, Modeling: Clasroom Notes in Applied Mathemaics, Society Ind. Appl. Math.  (1995).

Literatura uzupełniająca

1. M. Piekara, General Mechanics, Warszawa (1961).

2. E. Kreyszig, Advanced Engineering Mathemtics, J. Wiley and Sons Inc. New York (1993).

Uwagi

Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 10-04-2024 16:09)