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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS LME 5004 COMPLEX ANALYSIS ELECTIVE 2 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR BERNA TATAROĞLU TAŞDAN

Offered to

Mathematics Teacher Education

Course Objective

To introduce the concept of complex numbers and complex plane, to give concepts of single real-valued functions for complex variable functions, to compare these concepts

Learning Outcomes of the Course Unit

1   To be able to understand the relationship between the plane IR2 and a complex plane (Gauss's plane) 2   To be able to understand and apply the differences and similarities between concepts of single real-valued functions and complex variable functions.concepts of calculus, to apply 3   To be able to acquire the concept of complex function 4   To be able to acquire and apply the concept of complex integral 5   To be able to make generalizations

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 The axiomatic structure of complex numbers 2 The complex exponential functions, trigonometric functions, hyperbolic and inverse function 3 Logarithm function, inverse trigonometric and inverse hyperbolic functions 4 Limit and continuity of complex functions 5 Derivative of complex functions 6 The concept of analytic function 7 Conform transformations 8 Course overview, evaluation and midterm examination 9 Definition of complex curved integral, its properties, Cauchy's theorem 10 Cauchy's integral formula and its results 11 Introduction to series of complex numbers sequences and series of functions 12 Exact functions 13 Analytical continuation 14 Algebraic functions 15 Final exam

Recomended or Required Reading

Matematik Analiz, Cilt II, Mustafa Balcı; Yüksek Matematik 2. Cilt, H. Halilov, A. Hasanoğlu, M. Can; Matematik Analiz ve Analitik Geometri, Cilt II Çeviri Editörü: Ömer Akın

Planned Learning Activities and Teaching Methods

lecture, question-answer, group working

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Midterm 2 FN Semester final exam 3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60 4 BUT Make-up note 5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Midterm exam and final exam

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

adem.celik@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 2 26 Preparations before/after weekly lectures 13 2 26 Preparation for midterm exam 1 18 18 Preparation for final exam 1 18 18 Preparing assignments 1 6 6 Preparing presentations 1 2 2 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 100

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 PO.14 PO.15 PO.16 PO.17 PO.18 LO.1 5 5 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 LO.2 5 5 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 LO.3 5 5 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 LO.4 5 5 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 LO.5 5 5 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1