The aim of studying and bibliography

The main aim of study: To familiarize students with the fundamentals of ODEs theory.

The general information about the module: To acquaint students with basic methods of solving of ordinary differential equations and linear systems of ordinary differential equations.

Bibliography required to complete the module

Bibliography used during lectures

1	J.Kłopotowski, J.Winnicka	Równania różniczkowe zwyczajne. Teoria i zadania.	BEL Studio Warszawa.	2017
2	J.Myjak	Równania różniczkowe	AGH.	2016
3	B.P.Conrad	Differential Equations With Boundary Value Problems: A Systems Approach	Upper Saddle River, NJ : Pearson Education, Inc..	2003

Bibliography used during classes/laboratories/others

1	N.M. Matwiejew	Zadania z równań różniczkowych zwyczajnych	PWN.	1976
2	W.Krysicki, L.Włodarski	Analiza matematyczna w zadaniach 2	PWN.	2008

Bibliography to self-study

1	M.Gewert, Z.Skoczylas	Równania różniczkowe zwyczajne. Teoria, przykłady, zadania.	GiS Wrocław.	2003
2	J.Stankiewicz, K.Wilczek	Rachunek różniczkowy i całkowy funkcji wielu zmiennych	Oficyna Wyd. PRz.	2005
3	A.Palczewski	Równania różniczkowe zwyczajne	WNT.	2004

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: Student can calculate derivatives and integrals of real functions of one variable.He knows basic facts concerning theory of metric spaces and linear algebra.

Basic requirements in category skills: Student is able to calculate derivatives and integrals.

Basic requirements in category social competences: Student understands the necessity of systematic acquisition of knowledge and its preservation.

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	Can solve some first-order differential equations.	lecture, solving classes	test, written exam	K_W01+ K_W02+ K_W03+ K_W05+ K_U21+ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
02	Can solve some second order differential equations.	lecture, solving classes	test, written exam	K_W01+ K_W02+ K_W03+ K_W04+ K_U21++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
03	Can solve linear differential equations of order n.	lecture, solving classes	test, written exam	K_W01+ K_W04++ K_W05+ K_U21++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
04	Student can solve simply first-order linear systems of ODEs.	lecture, solving classes	test, written exam	K_W01+ K_W05+ K_U21+ K_U22++ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK

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
4	TK01	The concept of differential equation and its solution. Seperable differential equations and differential equations which can be transformed into a separable equations. Linear first order differential equation and the structure of its solutions.The Bernoulli differential equation, The Riccati differential equation, The Clairaut differential equation and the complete differential equation.	W01- W05, C01-C05	MEK01
4	TK02	Second-order differential equations which are convertible to first-order differential equations. Second-order linear differential equations. Second-order Euler differential equation.	W06- W09, C06- C09	MEK02
4	TK03	Linear differential equations of order n.	W10, C10, C11	MEK03
4	TK04	First-order linear systems of ODEs. Methods of solving of first-order homogeneous linear systems with constant coefficients and method of variation of constants to solve nonhomogeneous linear system of ODEs.	W11-W13, C12-C14	MEK04
4	TK05	Basic problems of the theory of ordinary differential equations. Existence and uniqueness. Peano theorem, Picard theorem. Local theorems on existence. Global theorems on existence. Uniqueness theorems.	W14, W15, C15	MEK01

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 4)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 5.00 hours/sem. Studying the recommended bibliography: 5.00 hours/sem.
Class (sem. 4)	The preparation for a Class: 15.00 hours/sem. The preparation for a test: 15.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 4)		The participation in Advice: 1.00 hours/sem.
Exam (sem. 4)	The preparation for an Exam: 15.00 hours/sem.	The written exam: 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	Written exam. Exam only after the credit of classes. There is a possibility of exemption from the written exam based on a credit for the tutorials.
Class	Two written tests and activity during classes.
The final grade	The final grade is the average of grade of classes and grade of the exam.

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	U. Bednarz; M. Wołowiec-Musiał	Generalized Fibonacci–Leonardo numbers	2024
2	U. Bednarz; A. Włoch; M. Wołowiec-Musiał	New Types of Distance Padovan Sequences via Decomposition Technique	2022
3	U. Bednarz; I. Włoch	Fibonacci numbers in graphs with strong (1, 1, 2)-kernels	2021
4	U. Bednarz; M. Wołowiec-Musiał	Distance Fibonacci Polynomials—Part II	2021
5	U. Bednarz	Strong (1,1,2)-kernels in the corona of graphs and some realization problems	2020
6	U. Bednarz; I. Włoch	On strong (1,1,2)-kernels in graphs	2020
7	U. Bednarz; M. Wołowiec-Musiał	Distance Fibonacci Polynomials	2020
8	U. Bednarz; M. Wołowiec-Musiał	On a new generalization of telephone numbers	2019