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

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 PRK
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_U14+ K_U15+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG P7S_WK
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_U08+ K_U10+ K_U15+ K_U17+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG
03	Can solve some first-order linear and quasi-linear PDEs.	lecture, solving classes	test	K_W01+ K_U06+ K_U16+ K_K01+ K_K02+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UU P7S_UW P7S_WG
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_U04+ K_U05+ K_U06+++ K_U13+ K_K02+ K_K04+ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UW P7S_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 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, W06, C01, C02, C03, C04, C05, C06	MEK01
3	TK02	Stability and asymptotic stability in tte sense of Lyapunov.	W06, W07, , W08, C06, C07, C08	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: 15.00 hours/sem. The preparation for a test: 10.00 hours/sem.	contact hours: 45.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Advice (sem. 3)		The participation in Advice: 2.00 hours/sem.
Exam (sem. 3)	The preparation for an Exam: 15.00 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	Presence on lectures.
Class	Two written tests on the dates agreed with the students. The tests contain the obvious exercises and the extra exercises. The obvious exercises must be solved.
The final grade	The final grade is the average of the exercises, written and oral 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	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	The Study of Options for Identification Stress Contrasts via Pumping History	2023
2	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	Evaluation of Rockburst Hazard by Accelerated Numerical Modeling of Stressed State and Induced Seismicity	2022
3	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	On accuracy of translations by kernel independent fast multipole methods	2022
4	A. Linkov; E. Rejwer-Kosińska; L. Rybarska-Rusinek	On evaluation of local fields by fast multipole method employing smooth equivalent/check surfaces	2021
5	A. Linkov; E. Rejwer; L. Rybarska-Rusinek	On speeding up nano- and micromechanical calculations for irregular systems with long-range potentials	2020
6	L. Rybarska-Rusinek	On evaluation of influence coefficients for edge and intermediate boundary elements in 3D problems involving strong field concentrations	2019
7	L. Rybarska-Rusinek	Opracowanie metod i procedur numerycznych do modelowania obszarów o silnej koncentracji pól fizycznych	2019