The aim of studying and bibliography

The main aim of study:

The general information about the module: An introduction to difference equations. Main methods of solving difference equations and systems of difference equations.

Bibliography required to complete the module

Bibliography used during lectures

1	H. Levy, F. Lessman	Równania różnicowe skończone	Warszawa, PWN.	1966
2	S. Kanas	Podstawy ekonomii matematycznej	Warszawa, PWN.	2011
3	V. Bryant	Aspekty kombinatoryki	Warszawa, WNT.	1997

Bibliography used during classes/laboratories/others

1

S. Kanas

Podstawy ekonomii matematycznej

Warszawa, PWN.

2011

Bibliography to self-study

1

S. Elaydi

An introduction to difference equations

New York, Springer.

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: Student should know operations on matrices and theory of complex numbers.

Basic requirements in category skills: The student should know basic methods of solving polynomial equations in the set R and C.

Basic requirements in category social competences: Student understands the necessity of the systematic learning.

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	Student knows basic properties of difference operator and antidifference operator.	lecture, laboratory, e-learning	practical test, test, exam	K_W01++ K_K01++	P6S_KK P6S_WG
02	Student knows methods of solving of linear difference equation of first and higher order.	lecture, laboratory, e-learning	practical test, test, exam	K_K02++	P6S_KK P6S_KO
03	Student knows the method undetermined coefficients of solving linear nonhomogeneous difference equations.	lecture, laboratory, e-learning	practical test, test, exam	K_W02++ K_U03++	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	Difference calculus - notion preliminary. Difference equations. Linear first-order difference equations.	W1-W4, L1-L4	MEK01
3	TK02	Linear nonhomogeneous equations with constant coefficients: method of undetermined coefficients, method of variation of constants.	W5-W8, L5-L7	MEK02 MEK03
3	TK03	Nonlinear equations transformable to linear difference equations.	W9-W10, L8-L9	MEK02
3	TK04	Aplications of difference equations (in economy, graph theory).	W11-W13, L10-L11	MEK02 MEK03
3	TK05	Systems of linear difference equations and their applications.	W14-W15, L12-L13	MEK01 MEK02
3	TK06	Test.	L14-L15	MEK01 MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 3)	The preparation for a test: 20.00 hours/sem.	contact hours: 15.00 hours/sem.	complementing/reading through notes: 6.00 hours/sem. Studying the recommended bibliography: 8.00 hours/sem.
Laboratory (sem. 3)	The preparation for a Laboratory: 20.00 hours/sem. The preparation for a test: 8.00 hours/sem.	contact hours: 15.00 hours/sem.
Advice (sem. 3)	The preparation for Advice: 4.00 hours/sem.	The participation in Advice: 4.00 hours/sem.
Exam (sem. 3)	The preparation for an Exam: 6.00 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	Passing the lecture is based on the exam.
Laboratory	Reports and test with using the computer (using software such as CAS Maxima).
The final grade	The final grade is the grade from the laboratory and 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 : yes

Available materials : the list of formulas

The contents of the module are associated with the research profile: no