|
|
Main menu for Browse IS/STAG
Course info
KMA / MA4
:
Course description
Department/Unit / Abbreviation
|
KMA
/
MA4
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Mathematical Analysis 4
|
Form of course completion
|
Exam
|
Form of course completion
|
Exam
|
Accredited / Credits
|
Yes,
5
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
|
Course credit prior to examination
|
Yes
|
Course credit prior to examination
|
Yes
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
YES
|
Language of instruction
|
Czech
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
0 / -
|
0 / -
|
0 / -
|
Included in study average
|
YES
|
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 |
1|2|3|4 |
Periodicity |
každý rok
|
Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
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:
|
The plane of complex numbers, sequences and series of the complex numbers. The complex variable theory. Differentiable and holomorphic functions, Cauchy harmonic functions, Cauchy´s integral theorem and formulas, the Taylor and Laurent series, singular points, the residue, the residues theorem and its use, the Laplace and Fourier transforms and their use, the discrete transforms and their use.
|
Requirements on student
|
During semester: Students have to write two assignments during semester.
The final examination: Demonstrate knowledge and undesrtanding of the material and ability to apply them in solving problems on the topics in syllabus and treated in the course.
|
Content
|
1) Complex numbers. Construction and algebraic characterization
2) Complex sequences and series. Extended complex plane. Construction and topologic characterization
3) Coplex functions.
4) Power series, the exponential function and complex trigonometric functions.
5) Derivatives in complex plane. Cauchy Riemann Equations
6) Integration in complex plane. Integration on path. The coplex integral.
7) Cauchy Theorem.
8) Taylor a Laurent series.
9) Singularities, residue theore. the index of point with respect to close curve.
10) Application of residual theory. Calculation of real intergral.
11) Laplace transform - definitions, using, properties and application.
12) Fourier transform - definitions, using, properties and application.
13) Z transform - definitions, using, properties and application.
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
-
Recommended:
Polák, Josef. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
-
Recommended:
Polák, Josef. Matematická analýza v komplexním oboru. 2., upr. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-923-0.
-
Recommended:
Polák, Josef. Matematická analýza v komplexním oboru II/. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-700-9.
-
Recommended:
Mašek, Josef. Sbírka úloh z matematiky : integrální transformace. 1. vyd. Plzeň : ZČU, 1993. ISBN 80-7082-117-5.
-
Recommended:
Mašek, Josef. Sbírka úloh z vyšší matematiky : funkce komplexní proměnné. 1. vyd. Plzeň : ZČU, 1992. ISBN 80-7082-074-8.
-
On-line library catalogues
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Contact hours
|
65
|
Preparation for an examination (30-60)
|
50
|
Preparation for formative assessments (2-20)
|
40
|
Total
|
155
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1 or KMA/MA1. Other broader knowledge of the apparatus of functional analysis would be an advantage. |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
By the end of the course, a successful student should be able to:
- set up space of complex numbers and extended complex space, derivate basic characteristic these spaces;
- deal with complex numbers;
- deal with complex functions;
- demonstrate knowledge of the definitions and fundamental theorems concerning complex sequences and complex series;
- give the definitions and use derivatives and integrals in complex space;
- deal with holomorphic (analytic) functions;
- demonstrate knowledge of the Cauchy theorem and applications of the Cauchy Theorem;
- deal with Laurent Series;
- demonstrate knowledge of the definitions and fundamental theorems concerning Fourier, Laplace and Z transform.
|
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Group discussion |
Self-study of literature |
|
|
|
|