# 714-0322/01 – Functions of Complex Variable (FKP)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor doc. RNDr. Jarmila Doležalová, CSc. Subject version guarantor doc. RNDr. Jarmila Doležalová, CSc. Study level undergraduate or graduate Requirement Choice-compulsory Year 4 Semester summer Study language Czech Year of introduction 1990/1991 Year of cancellation 2010/2011 Intended for the faculties FS Intended for study types Master
Instruction secured by
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 12+2

### Subject aims expressed by acquired skills and competences

Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.

### Teaching methods

Lectures
Individual consultations
Tutorials
Project work

### Summary

Fourier series: periodic functions, Fourier coefficients, functions of the period 2pi, functions of the period T, even and odd functions, half - range cosine and sine series, convergence of Fourier series. Functions of a complex variable: complex numbers, complex functions of a real variable, Fourier series at a complex form, complex functions of a complex variable and mappings, complex differentiation, Cauchy - Riemann equations, complex series, Taylor and Laurent series, singularities, zeros and residues, integration Cauchy theorem.

### Compulsory literature:

James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456

### Way of continuous check of knowledge in the course of semester

zápočet Účast ve cvičení je povinná, 20 % neúčasti lze omluvit - za splnění podmínek získá student 5 b., odevzdání programů zadaných vedoucím cvičení v předepsané úpravě, absolvování 3 písemných testů po 5 bodech - za testy lze získat 0 - 15 b. Celkem maximálně 20 bodů zkouška Kombinovanou zkoušku tvoří praktická část (60 minut, příklady) a teoretická část (20 minut, teoretické otázky). Praktická část je hodnocena 0 - 60 body, teoretická část 0 - 20 body. Aby student u zkoušky uspěl musí získat v praktické části nejméně 25 bodů a v teoretické části nejméně 5 bodů. klasifikace získané body známka 86 - 100 výborně 66 - 85 velmi dobře 51 - 65 dobře 0 - 50 nevyhověl Otázky k teoretické části zkoušky 1. Fourierovy řady v reálném oboru 2. Řada sinová a kosinová 3. Komplexní čísla 4. Posloupnosti a řady komplexních čísel 5. Komplexní funkce reálné proměnné 6. Fourierovy řady v komplexním oboru 7. Komplexní funkce komplexní proměnné - definice, limita, spojitost 8. Elementární funkce komplexní proměnné - jednoznačné (polynom, racionální, exponenciální, goniometrické a hyperbolické funkce, Eulerovy vzorce) 9. Elementární funkce komplexní proměnné - mnohoznačné (přirozená logaritmická funkce, obecná exponenciální funkce, cyklometrické a hyperbolometrické funkce) 10. Derivace funkce komplexní proměnné - definice, Cauchy - Riemannovy podmínky, význam 11. Integrál funkce komplexní proměnné 12. Cauchyovy věty 13. Singulární body, Taylorova a Laurentova řada 14. Rezidua a jejich použití

### Prerequisities

Subject codeAbbreviationTitleRequirement
714-0366 MI Mathematics I Compulsory
714-0367 MII Mathematics II Compulsory

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Syllabus of lecture 1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions 2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series 3. Complex numbers 4. Infinite complex number series 5. Complex functions of a real variable 6. Fourier series at a complex form 7. Complex functions of a complex variable and mappings 8. Elementary functions of complex variable 9. Complex differentiation Cauchy - Riemann equations 10. Integration of complex variable function 11. Cauchy´s theorems 12. Singularities, Taylor´s and Laurent´s series 13. Residues, applications 14. Reserve

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Examination Examination 55  0
Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2005/2006 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2005/2006 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2005/2006 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2005/2006 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment P Czech Ostrava 4 Choice-compulsory study plan
2005/2006 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2005/2006 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment P Czech Ostrava 4 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2302T032) Minig Equipment P Czech Ostrava 4 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2004/2005 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling P Czech Ostrava 4 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment P Czech Ostrava 4 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2302T032) Minig Equipment P Czech Ostrava 4 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2003/2004 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling P Czech Ostrava 4 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment P Czech Ostrava 4 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2302T032) Minig Equipment P Czech Ostrava 4 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2002/2003 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling P Czech Ostrava 4 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment P Czech Ostrava 4 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2302T032) Minig Equipment P Czech Ostrava 4 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2001/2002 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling P Czech Ostrava 4 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2303T002) Mechanical Technology K Czech Ostrava 5 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2303T002) Mechanical Technology P Czech Ostrava 4 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment K Czech Ostrava 5 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment (10) Production Machines and Equipment in Meallurgy P Czech Ostrava 4 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2302T010) Design of Machines and Equipment (20) Metal Forming Machines P Czech Ostrava 4 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2302T032) Minig Equipment K Czech Ostrava 5 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2302T032) Minig Equipment P Czech Ostrava 4 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling K Czech Ostrava 5 Choice-compulsory study plan
2000/2001 (M2301) Mechanical Engineering (2301T001) Transport and Material Handling P Czech Ostrava 4 Choice-compulsory study plan

### Occurrence in special blocks

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