Item card
Monographic lecture I - Difference equations
Some basic information about the module
Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Engineering and data analysis
The area of study:
sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
The degree after graduating from university:
engineer
The name of the module department :
Departament of Discrete Mathematics
The code of the module:
12332
The module status:
mandatory for teaching programme with the posibility of choice
The position in the studies teaching programme:
sem: 3 / W15 L15 / 4 ECTS / E
The language of the lecture:
Polish
The name of the coordinator:
Dorota Bród, PhD
office hours of the coordinator:
podane na stronie domowej
semester 3:
Adrian Michalski, PhD , office hours on the home-page
semester 3:
Paweł Bednarz, PhD , office hours on the home-page
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
| 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 |
| 1 | S. Kanas | Podstawy ekonomii matematycznej | Warszawa, PWN. | 2011 |
| 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 |
|---|---|---|---|---|---|
| MEK01 | 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 |
| MEK02 | 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 |
| MEK03 | 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 |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 3 | TK01 | W1-W4, L1-L4 | MEK01 | |
| 3 | TK02 | W5-W8, L5-L7 | MEK02 MEK03 | |
| 3 | TK03 | W9-W10, L8-L9 | MEK02 | |
| 3 | TK04 | W11-W13, L10-L11 | MEK02 MEK03 | |
| 3 | TK05 | W14-W15, L12-L13 | MEK01 MEK02 | |
| 3 | TK06 | 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 |
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