Karta przedmiotu

Monographic lecture I - Basics of mathematical modelling

Some basic information about the module

Cycle of education:

2018/2019

The name of the faculty organization unit:

The faculty Mathematics and Applied Physics

The name of the field of study:

Mathematics

The area of study:

sciences

The profile of studing:

The level of study:

second degree study

Type of study:

full time

discipline specialities :

Applications of Mathematics in Computer Science, Applications of Mathematics in Economics

The degree after graduating from university:

The name of the module department :

Departament of Mathematical Modelling

The code of the module:

1495

The module status:

mandatory for teaching programme with the posibility of choice Applications of Mathematics in Economics

The position in the studies teaching programme:

sem: 2 / W30 / 2 ECTS / Z

The language of the lecture:

Polish

The name of the coordinator:

Bohdan Datsko, DSc, PhD

office hours of the coordinator:

Pon. 17.15-18.45, Wt. 14.30-16.00, TEAMS

The aim of studying and bibliography

The main aim of study:
Introduction to the basics of mathematical modeling and selected sections of numerical methods.

The general information about the module:
The subject matter of the classes chosen by students. In the second semester, 30 hours of lectures are realized.

Teaching materials:
podane na stronie https://wojciechjablonski.v.prz.edu.pl/

Bibliography required to complete the module

Bibliography used during lectures
1	A. Witecek, L.Cedro, R. Farana	Modelowanie matematyczne. Podstawy.	Pol. Swiętokrzyska, Kielce, .	2010
2	M.Holodniok, M.Kubiczek	Metody analizy nelinearnich dynamickich modelu	Academia, Praha.	1986
3	U. Foryś	Modelowanie matematyczne w biologii i medycynie	Uniwersytet Warszawski.	2011
4	S.J.Farlow	Partial differential equations for Scientists and Engineers	Wiley, Inc..	1982
5	Lawrence C. Evans	Równania różniczkowe cząstkowe	PWN Warszawa.	2002
6	P. Strzelecki	Krótkie wprowadzenie do równań różniczkowych cząstkowych.	PWN Warszawa.	2006
7	A. Turowicz	Teoria macierzy	Uczel. Wyd. Nauk.-Dydakt. Kraków.	2005

Bibliography to self-study
1	H. Guściowa, M. Sadowska	Repetytorium z algebry liniowej	PWN Warszawa 1977.	-
2	J. Klukowski, I. Nabiałek	Algebra dla studentów	PWN Warszawa.	1999
3	A. I. Kostrykin	Zbiór zadań z algebry	PWN Warszawa.	1995
4	I. Nabiałek	Zadania z algebry liniowej	WNT Warszawa.	2006
5	J. Rutkowski	Algebra liniowa w zadaniach	PWN Warszawa.	2012

Basic requirements in category knowledge/skills/social competences

Formal requirements:

Basic requirements in category knowledge:
Mastering the basics of mathematical analysis, matrix calculus, differential equations and computational packages.

Basic requirements in category skills:
Passing courses in mathematical analysis 1,2, linear algebra, differential equations, and computational packages.

Basic requirements in category social competences:
ability to acquire knowledge, ability to work in a group

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with OEK
MEK01	The student has knowledge concerning algebraic structures (group, ring, field, linear space, algebra) and can apply it in problems and exercises.	lecture	written test	K-W01+ K-W02++ K-W03++ K-W04++ K-U01++ K-K02+ K-K04+ K-K07+	W01 W03 W06 U01 U02 U05 K01 K02 K03 K04 K06
MEK02	The Student is familiar with advanced concepts and tools of linear algebra (algebra of operators, dual space, invariant subspace and eigenvector, Jordan canonical form) and can apply it in problems and exercises.	lecture	written test	K-W01+ K-W02+ K-W03+ K-W04++ K-W05++ K-W07++ K-U01+ K-U02++ K-U03+ K-K01+	W01 W02 W03 W06 U01 U02 U03 U05 U07 K01

The syllabus of the module

Sem.	TK	The content	realized in	MEK
2	TK01	Introduction: mathematical modeling - the art of applying mathematics. Principles and main features of modeling. Computer experiment - stages, features and functions. Technical support and software in a computational experiment.	W01-W03	MEK01
2	TK02	Mathematical models that are reduced to algebraic equations. Static issues. Mathematical equilibrium models. Issues of approximation and optimization. Methods of solving systems of linear and nonlinear equations.	W04-W07	MEK02
2	TK03	Mathematical models that are reduced to systems of ordinary differential equations. Mathematical models of the dynamics of a material point. Free and forced vibrations. Nonlinear oscillatory systems. Analysis methods and solutions of initial-boundary problems for ordinary differential equations.	W7-W10	MEK02
2	TK04	Mathematical models that are reduced to partial differential equations. Classification of partial differential equations and appropriate basic mathematical models. Systems of partial non-linear equations.	W11-W15	MEK01 MEK02

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 2)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 10.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Credit (sem. 2)	The preparation for a Credit: 10.00 hours/sem.	The written credit: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	the execution of problems proposed after lectures and the positive evaluation of written test
The final grade

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile no