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. The module includes content in the field of mathematical modeling methods: a computer experiment, its stages, features, functions, technical support and software. The aim of the course is also the construction and analysis of mathematical models using a computational experiment. The module includes consideration of various types of mathematical models, which are reduced to equations and systems of algebraic, ordinary and partial differential equations as well as basic methods of analysis and solutions of various types of mathematical problems.

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: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: K_W01,K_W02,K_W03,K_W04,K_W05,K_W07

Basic requirements in category skills: K_U01,K_U02,K_U03

Basic requirements in category social competences: K_K01,K_K02,K_K04,K_K07

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 PRK
01		lecture		K_W01+ K_W02++ K_W03++ K_W04++ K_U01++ K_K02+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UW P7S_WG P7S_WK
02		lecture		K_W01+ K_W02+ K_W03+ K_W04++ K_W05++ K_W07++ K_U01+ K_U02++ K_U03+ K_K01+	P7S_KK P7S_UK P7S_UO P7S_UW P7S_WG P7S_WK
03				K_U01+ K_U02+ K_U03+ K_K02+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UW

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

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, Cw01	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,Cw02-Cw03	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, Cw04-Cw05	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, Cw06-Cw07	MEK03

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.
Class (sem. 2)		contact hours: 15.00 hours/sem.
Advice (sem. 2)
Credit (sem. 2)

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

The type of classes	The way of giving the final grade
Lecture	Performing the tasks proposed after the lecture and during the tutorial classes with a positive grade for a written test. Average grade: written work (70%), classwork (30%)
Class	Performing tasks during classes with a positive grade for a written test.
The final grade	Average rating: written work(70%), work in the classroom (30%)

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: yes

1	B. Datsko; M. Kutniv	Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	2024
2	B. Datsko; V. Gafiychuk; C. Naconechna	Pattern Formation in Activator-Inhibitor Fractional Reaction-Diffusion Systems	2022
3	B. Datsko	Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion	2021
4	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	New explicit high‐order one‐step methods for singular initial value problems	2021
5	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations	2020
6	B. Datsko; M. Kutniv; A. Włoch	Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion	2020
7	B. Datsko; I. Podlubny; Y. Povstenko	Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact	2019