The aim of studying and bibliography

The main aim of study: Extension of knowledge about differential equations.

The general information about the module: Training of basic methods of solving systems of ordinary differential equations and research of stability of their solutions.To familiarize students with the fundamentals of theory linear partial differential equations first and second order.

Bibliography required to complete the module

Bibliography used during lectures

1	N.M. Matwiejew	Metody całkowania równań różniczkowych zwyczajnych	PWN.	1972
2	A. Palczewski	Równania różniczkowe zwyczajne	WNT.	2004
3	H. Marcinkowska	Wstęp do teorii równań różniczkowych cząstkowych	PWN.	1972

Bibliography used during classes/laboratories/others

1	N.M. Matwiejew	Zadania z równań różniczkowych zwyczajnych	PWN.	1976
2	M.M. Smirnow	Zadania z równań różniczkowych cząstkowych	PWN.	1970

Bibliography to self-study

1

W.W. Stiepanow

Równania różniczkowe

PWN.

1964

Basic requirements in category knowledge/skills/social competences

Formal requirements: Requirements accordant with Rules and Regulations of studies

Basic requirements in category knowledge: It can calculate derivatives and integrals of real functions of one and several variables.He knows basic facts concerning ODE, theory of metric spaces, linear algebra and functional analysis.

Basic requirements in category skills: Student is able to solve basic types of scalar ODEs and linear first-order systems ODEs with constant coefficients.

Basic requirements in category social competences: The student is prepared to undertake objective and justified actions in order to solve the posed exercise.

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
01	Knows fundamental theorems on existence and uniqueness of solutions of systems ODEs. Can solve some systems of such equations use the matrix method or first integral method.	lecture, solving classes	test	K_W01+ K_W02++ K_W03+ K_W04++ K_W05++ K_U02+ K_U03+ K_U07+ K_U08+ K_U09+ K_U13+ K_U15+ K_K02+ K_K04+	X2A_W02 X2A_W03 X2A_U01 X2A_U02 X2A_U03 X2A_U05 X2A_U06 X2A_U08 X2A_U09 X2A_K01 X2A_K02 X2A_K03 X2A_K04
02	Knows the notion of stability and asymptotic stability in tte sense of Lyapunov. Can investigate the stability of system of ODEs.	lecture, solving classes	test	K_W01+ K_W08+ K_W10+ K_U01+ K_U02+ K_U03+ K_U04+ K_U08+ K_U10+ K_U13+ K_U14+ K_K02+ K_K07+	X2A_W03 X2A_U01 X2A_U02 X2A_U03 X2A_U05 X2A_K01 X2A_K02 X2A_K06
03	Can solve some first-order linear and quasi-linear PDEs.	lecture, solving classes	test	K_W01+ K_U02+ K_U04+ K_U05+ K_U13+ K_U14+ K_U15+ K_U16+ K_K04+	X2A_U01 X2A_U02 X2A_U03 X2A_U05 X2A_U06 X2A_U08 X2A_U09 X2A_K03 X2A_K04
04	Knows classification of second-order linear PDEs and can reduce such equation to canonical form. Can solve some second-order linear PDEs.	lecture, solving classes	written exam	K_W01+ K_W07+ K_U05+ K_U06+++ K_U13+ K_U14+ K_U15+ K_U17+ K_K01+ K_K02+ K_K04+	X2A_W02 X2A_U01 X2A_U02 X2A_U04 X2A_U05 X2A_U06 X2A_U07 X2A_U08 X2A_U09 X2A_K01 X2A_K02 X2A_K03 X2A_K04

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 Cauchy (initial value) problem, existence and uniqueness of solutions of first-order systems of ODEs. Scalar n-order ODE and first-order system ODEs. General methods of solving of first-order system ODEs. Matrix method and first integral method.	W01, W02, W03, W04, W05,C01, C02, C03, C04, C05	MEK01
3	TK02	Stability and asymptotic stability in tte sense of Lyapunov.	W06, W07, C06, C07	MEK02
3	TK03	Initial-value and boundary-value problems for PDEs. First-order linear and quasi-linear PDEs.	W08, W09, W10, W011, C08, C09, C10, C011	MEK03
3	TK04	Canonical forms of second-order linear PDEs. Method of Separation of Variables for PDEs. The vibrating string and the wave equation. The heat equation. The Laplace's equation.	W12, W13, W14, W15, C12, C13, C14, C15	MEK04

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: 30.00 hours/sem.	complementing/reading through notes: 10.00 hours/sem. Studying the recommended bibliography: 5.00 hours/sem.
Class (sem. 3)	The preparation for a Class: 10.00 hours/sem. The preparation for a test: 15.00 hours/sem.	contact hours: 30.00 hours/sem.
Advice (sem. 3)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Exam (sem. 3)	The preparation for an Exam: 20.00 hours/sem.	The written exam: 2.00 hours/sem. The oral exam: 1.00 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.
Class	Two written tests on dates agreed with the students. To obtain the pass the student must attend classes, and pass both tests.
The final grade	After the credit of all types of classes the final grade is the average of grade of classes and grade of 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: no