# 714-0397/01 – Functions of Complex Variable (FKP)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 2 Subject guarantor doc. RNDr. Jarmila Doležalová, CSc. Subject version guarantor doc. RNDr. Jarmila Doležalová, CSc. Study level undergraduate or graduate Requirement Optional Year 2 Semester summer Study language Czech Year of introduction 2000/2001 Year of cancellation 2011/2012 Intended for the faculties FS Intended for study types Bachelor
Instruction secured by
DOL30 doc. RNDr. Jarmila Doležalová, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent

### 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

2 projekty (Fourierovy řady, FKP) test

### Prerequisities

Subject codeAbbreviationTitleRequirement
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
Project Project 40  0
Written exam Written test 60  0
Mandatory attendence parzicipation:

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2010/2011 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering P Czech Šumperk 2 Optional study plan
2010/2011 (B2341) Engineering (2301R002) Transport Equipment (10) Transport Equipment and Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (2301R003) Transport Equipment and Technology P Czech Ostrava 2 Optional study plan
2010/2011 (B2341) Engineering (3907R009) Operation of Energy Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Industrial Design P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (2301R040) Industrial Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2302R010) Design of Machines and Equipment (70) Earth, Mining and Building Machines P Czech Ostrava 2 Optional study plan
2009/2010 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Optional study plan
2009/2010 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering P Czech Ostrava 2 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2008/2009 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2007/2008 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2006/2007 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Šumperk 2 Optional study plan
2005/2006 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2004/2005 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2003/2004 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan
2002/2003 (B2341) Engineering (2341R888) Mechanical Engineering /not obligatory subject (70) Volitelné předměty P Czech Ostrava 2 Optional study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner