# COURSE UNIT TITLE

: COMPLEX ANALYSIS

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EED 2007 COMPLEX ANALYSIS COMPULSORY 3 0 0 5

#### Offered By

Electrical and Electronics Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

ASISTANT PROFESSOR SERKAN GÜNEL

#### Offered to

Electrical and Electronics Engineering

#### Course Objective

The fundamentals, main methods and techniques of complex analysis, including complex algebra, complex functions, complex integration, differentiation and series, is to be introduced.

#### Learning Outcomes of the Course Unit

 1 To be able to express the fundamental concepts of complex analysis. 2 Concrete understanding of the analytic functions concept. 3 To be able to use exponential functions, trigonometric and hyperbolic functions, logarithm and their properties in analysis 4 To grasp and use the concept of poles, zeros and essential singularities of functions. 5 To be able to use the power and Laurent series techniques, and to be able to calculate residues of functions 6 To be able to calculate complex integrals and use them in analysis. 7 To be able to use the complex integration techniques for calculation of improper integrals arising in electrical engineering.

Face -to- Face

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#### Course Contents

 Week Subject Description 1 Properties, Addition, Subtraction, Multiplication, Conjugate operations, Complex plane, Modulus and argument of a complex number, triangular inequality, Powers and roots, Set of points in complex plane 2 Real and Imaginary parts, Complex Exponential Function, Complex trigonometric and hyperbolic functions 3 Parametric curves in Complex plane, Limits, Continuity 4 Differentiability, Analyticity, Entire Functions 5 Conditions for analyticity, Cauchy-Riemann Equations, Conditions for non-analyticity 6 Sufficient conditions for analyticity and differentiability, Harmonic Functions 7 Line integrals in complex plane 8 Cauchy and Morera Integral Theorems, Cauchy Integral Formula 9 Visa I, Derivatives of analytic functions, Power Series, Radius of Convergence, Taylor Series, Integration of Power series 10 Laurent Series, Singularities and Zeros 11 Residue 12 Visa II, Residue Integration Method 13 Evaluation of Real Integrals using the residue theorem 14 Residue integration of real integrals

Textbook: Denis G. Zill, Patric D. Sahanahan, A first course in complex analysis with applications, Jones & Barlett Publications, 2003

Erwin Kreyszig, Advanced Engineering Mathematics, 8th Ed.,John
Wiley & Sons Inc., 2001

James Ward Brown and Ruel V. Churchill, Complex variables and
applications, McGraw-Hill, 2004

References:
Other course materials: PDF files of lecture notes

#### Planned Learning Activities and Teaching Methods

Lectures with active discussions, homeworks, examinations

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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Examinations

English

To be announced.

To be announced.

To be announced.

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