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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

PROFESSOR DOCTOR UTKU KÂNOĞLU

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.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

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

Recomended or Required Reading

Textbook: Denis G. Zill, Patric D. Sahanahan, A first course in complex analysis with applications, Jones & Barlett Publications, 2003 Recommended Readings: 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 1 MIDTERM EXAM 1 2 MTE 2 MIDTERM EXAM 2 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE 1 * 0.30 + MTE 2 * 0.30 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE 1 * 0.30 + MTE 2 * 0.30 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Examinations

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparations before/after weekly lectures 14 3 42 Preparation for midterm exam 2 6 12 Preparation for final exam 1 20 20 Midterm 2 2 4 Final 1 3 3 TOTAL WORKLOAD (hours) 123

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 5 4 4 LO.2 5 5 4 4 LO.3 5 5 4 4 LO.4 5 5 4 4 LO.5 5 5 4 4 LO.6 5 5 4 4 LO.7 5 5 4 4