Course objectives:
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The objectives of the course is to extend and deepen to the participants knowledge of the theory of complex functions. The course develops and complements knowledge of subject An introductionary course of Complex Analysis (KMA/ZKA).The focus will be placed on the explanation of proofs of basic theorems and also on the possibilities of application of complex analysis. Integral (Laplace and Fourier) and discrete (Z-transform)) transforms, its properties. Use the transforms and the residue calculus to solutions of difference, differential and integral equations.
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Requirements on student
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During semester: Students have to write 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.
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Content
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The residue theorem and its consequences, calculations of the values of real integrals over the intervals using resudues.
Holomorphic, conformal and analytic functions, complex analytic extension of functions and complete analytic function and its Riemann surface.
Integral transforms (Laplace and Fourier transform) and Z-transform. Solution of ordinary differential equations, the Volterra integral equations and difference equations.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Basic:
trial.kma.zcu.cz
(kolektiv autorů)
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Recommended:
Polák,J. Integrální a diskrétní transformace. ZČU Plzeň, 1995.
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Recommended:
Polák, J. Matematická analýza v komplexním oboru, ZČU Plzeň 1994. 1996.
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Recommended:
Polák, J. Matematická analýza v komplexním oboru 1,2. ZČU Plzeň, 1996.
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Recommended:
Mašek, J. Sbírka úloh z matematiky. Funkce komplexní proměnné. ZČU Plzeň, 1996.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Preparation for formative assessments (2-20)
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30
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Preparation for an examination (30-60)
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50
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Total
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132
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
define basic notions of complex analysis from the course Základy komplexní analýzy |
state basic theorems of complex analysis from the course Základy komplexní analýzy |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
use single-valued complex functions |
use and generalize tools and notions from real analysis to the complex framework |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
multi-valued complex functions |
use of complex analysis in solving the problems from real analysis |
various complex transforms and their use in solving of differential and difference equations |
Skills - skills resulting from the course: |
work with set-valued complex functions |
apply methods and tools from complex analysis to solve the problems of real analysis |
apply integral transforms to find a solution of differential and difference equations |
Competences - competences resulting from the course: |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Group discussion |
Self-study of literature |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Task-based study method |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Practicum |
Seminar |
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