|
|
Main menu for Browse IS/STAG
Course info
KMA / DRTS
:
Course description
Department/Unit / Abbreviation
|
KMA
/
DRTS
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Difference Equations and Time Scales
|
Form of course completion
|
Pre-Exam Credit
|
Form of course completion
|
Pre-Exam Credit
|
Accredited / Credits
|
Yes,
2
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Tutorial
2
[Hours/Week]
|
Course credit prior to examination
|
No
|
Course credit prior to examination
|
No
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
NO
|
Language of instruction
|
Czech
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
0 / -
|
0 / -
|
0 / -
|
Included in study average
|
NO
|
Winter semester
|
0 / -
|
0 / -
|
0 / -
|
Repeated registration
|
NO
|
Repeated registration
|
NO
|
Timetable
|
Yes
|
Semester taught
|
Summer semester
|
Semester taught
|
Summer semester
|
Minimum (B + C) students
|
1
|
Optional course |
Yes
|
Optional course
|
Yes
|
Language of instruction
|
Czech
|
Internship duration
|
0
|
No. of hours of on-premise lessons |
|
Evaluation scale |
S|N |
Periodicity |
každý rok
|
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
S|N |
Substituted course
|
None
|
Preclusive courses
|
N/A
|
Prerequisite courses
|
N/A
|
Informally recommended courses
|
N/A
|
Courses depending on this Course
|
N/A
|
Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
|
This seminar will enable a student to learn to solve elementary difference equations. Several common techniques will be introduced. The analysis of solutions will be closely studied in connection with the solutions of corresponding differential equations. Problems, which arise in discretization of continuous models (or in the opposite direction), will be discussed. Finally, the time scales will be introduced, i.e. the theory which unifies the discrete and continuous calculus and enables better analysis of the distinct behaviour of difference and differential equations.
The seminar assumes the knowledge of ordinary differential equations within the range of KMA/ODR.
|
Requirements on student
|
small research project or exercise sheets
|
Content
|
Week 1: motivation, simple examples
Week 2: difference calculus, comparison with differential calculus
Week 3-5: linear difference equations and methods of their solutions
Week 6: stability theory
Week 7-8: nonlinear systems and chaos
Week 9-10: basic properties of partial difference equations
Week 11-13: time scales calculus and applications, dynamic equations
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
-
Recommended:
Kelley, Walter G.; Peterson, Allan C. Difference equations : an introduction with applications. 2nd ed. San Diego : Harcourt Academic Press, 2001. ISBN 0-12-403330-X.
-
Recommended:
Agarwal, Ravi P. Difference equations and inequalities : theory, methods and applications. 2nd ed., rev. New York : Marcel Dekker, 2000. ISBN 0-8247-9007-3.
-
Recommended:
Bohner, Martin; Peterson, Allan. Dynamic equations on time scales : an introduction with applications. Boston : Birkhäuser, 2001. ISBN 0-8176-4225-0.
-
On-line library catalogues
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Graduate study programme term essay (40-50)
|
26
|
Contact hours
|
26
|
Total
|
52
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
The seminar assumes the knowledge of ordinary differential equations within the range of KMA/ODR. |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
This seminar will enable a student to learn to solve elementary difference equations. Several common techniques will be introduced. The analysis of solutions will be closely studied in connection with the solutions of corresponding differential equations. Problems, which arise in discretization of continuous models (or in the opposite direction), will be discussed. |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Seminar work |
Continuous assessment |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Seminar |
Multimedia supported teaching |
Textual studies |
Individual study |
|
|
|
|