TYPE OF COURSE UNIT	Elective Course
LEVEL OF COURSE UNIT	Bachelor's Degree
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	4
NAME OF LECTURER(S)	-
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) Understands the definition of complex numbers and knows their properties. 2) Defines complex functions. 3) Knows functions of complex variables and can make applications related to these functions. 4) Understands differentiability of complex functions. 5) Knows the concept of integral in complex functions.
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	Calculus
COURSE DEFINITION	Complex numbers, Complex functions, Complex sequence, Limit and continuity in complex functions, Exponential, logarithm, trigonometric, hyperbolic, inverse trigonometric functions, Differentibility in complex functions, Analytical functions, Harmonic functions, Integration of Complex functions, Cauchy integral theorem and Cauchy Derivative formula.
COURSE CONTENTS	WEEK TOPICS 1st Week Complex numbers, geometric representations 2nd Week Some elamanter complex functions, Inverse trigonometric and inverse hyperbolic functions 3rd Week Limit and continuity in complex functions 4th Week Differentiability of complex functions 5th Week Analytical functions, Cauchy-Rieman Equations 6th Week Determining analytic sets of functions 7th Week Integral of complex functions, line integral 8th Week MIDTERM EXAM 9th Week Cauchy Theorem and its applications, Cauchy Integral formula and its results 10th Week Harmonic functions 11th Week Cauchy integral formula and applications 12th Week Results of the Cauchy integral formula 13th Week Complex number series 14th Week Laurent's Theorem and its applications
RECOMENDED OR REQUIRED READING	Basic Complex Analysis - Jerrold E. Marsden Complex Variables - Schoum's Outline Series - Murray R. Spigel
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS	Lecture,Questions/Answers
ASSESSMENT METHODS AND CRITERIA	Quantity Percentage(%) Mid-term 1 40 Quiz 2 10 Total(%) 50 Contribution of In-term Studies to Overall Grade(%) 50 Contribution of Final Examination to Overall Grade(%) 50 Total(%) 100
ECTS WORKLOAD	Activities Number Hours Workload Midterm exam 1 2 2 Preparation for Quiz 2 3 6 Individual or group work 13 2 26 Preparation for Final exam 6 3 18 Course hours 13 3 39 Preparation for Midterm exam 7 3 21 Laboratory (including preparation) Final exam 1 2 2 Homework Total Workload 114 Total Workload / 30 3,8 ECTS Credits of the Course 4
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No