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.Myjak	Równania różniczkowe	AGH.	2016
2	J.Kłopotowski, J.Winnicka	Równania różniczkowe zwyczajne. Teoria i zadania.	BEL Studio Warszawa.	2017
3	R. Filipów, J. Gulgowski	Zastosowanie pakietu Maxima w Analizie Matematycznej	https://inf.ug.edu.pl/kierunkizamawiane/ materialy.matematyka/skrypt_maxima/ Maxima.pdf.

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

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: Knowledge of differential and integral calculus of functions of one variable and the basics of differential calculus of functions of two variables.

Basic requirements in category skills: Ability to calculate derivatives, indefinite integrals and partial derivatives of functions of two variables. Computer literacy.

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 seperable differential equations and differential equations which can be transformed into separable equations. Linear first order differential equation .	lecture, solving classes	written test (two tests)	K_W01+ K_W02+ K_U01+ K_U03+ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
02	Can solve linear differential equations of order n (n>1) with constant coefficients.	lecture, solving classes	written test (two tests)	K_W01+ K_W02+ K_U01+ K_U03+ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG
03	In CAS Maxima, can solve differential equations and systems of differential equations, generate graphs of solutions.	laboratory	practical test on a computer	K_W01+ K_W02+ K_U01+ K_U03+ K_K01+ K_K02+	P6S_KK P6S_KO P6S_UW P6S_WG

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
3	TK01	The concept of differential equation and its solution. Seperable differential equations and differential equations which can be transformed into separable equations. Linear first order differential equation.	W1-W4, C1-C10	MEK01
3	TK02	Nonlinear differential equations : Bernoulli differential equation, Riccati differential equation, Clairaut differential equation and the complete differential equation.	W5-W9, C11-C18	MEK01
3	TK03	Second-order differential equations which are convertible to first-order differential equations. Second-order linear differential equations. Second-order Euler differential equation.	W10-W13, C19-C26	MEK02
3	TK04	Linear differential equations of order n with constant coefficients.	W14, C27-C28	MEK02
3	TK05	First-order linear systems of ODEs with constant coefficients .	W15, C29-C30	MEK01
3	TK06	Solving ordinary differential equations of the 1st order using the CAS Maxima program - transforming expressions, integrating, creating graphs.	L1-L2	MEK03
3	TK07	Solving ordinary differential equations of the 2nd order using the CAS Maxima program - transforming expressions, solving systems of equations, integrating, creating graphs.	L3-L6	MEK03
3	TK08	Solving systems of differential equations with the CAS Maxima program.	L7-L10	MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 3)		contact hours: 15.00 hours/sem.	complementing/reading through notes: 1.00 hours/sem. Studying the recommended bibliography: 1.00 hours/sem.
Class (sem. 3)	The preparation for a Class: 5.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem.
Laboratory (sem. 3)	The preparation for a Laboratory: 5.00 hours/sem.	contact hours: 10.00 hours/sem.	Finishing/Making the report: 3.00 hours/sem.
Advice (sem. 3)
Credit (sem. 3)	The preparation for a Credit: 3.00 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	Completion of the lecture is based on the completion of exercises and laboratories.
Class	Two written tests and activity during classes.
Laboratory	Completion of the laboratory is based on the assessment of the practical test at the computer, verifying the practical ability to solve differential equations using symbolic calculations in the CAS Maxima program.
The final grade	The final grade is the weighted mean of grades of the class - weight 0,7 and the laboratory - weight 0,3.

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