TYPE OF COURSE UNIT	Elective Course
LEVEL OF COURSE UNIT	Master's Degree With Thesis
YEAR OF STUDY	-
SEMESTER	-
NUMBER OF ECTS CREDITS ALLOCATED	10
NAME OF LECTURER(S)	-
LEARNING OUTCOMES OF THE COURSE UNIT	At the end of this course, the students; 1) Students will find the solution of the given differential equations 2) Also, students will understand the theory of complex functions and to associate in real numbers.
MODE OF DELIVERY	Face to face
PRE-REQUISITES OF THE COURSE	No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT	There is no recommended optional programme component for this course.
COURSE DEFINITION	Transcendantal functions: logarithms and exponentials. Arc lengths, areas of surfaces of revolution, volumes of solids of revolution, physical applications. Sequences and series, power series, Taylor and Maclaurin series. Functions of several variables, partial derivatives, multiple integration, curves in space.
COURSE CONTENTS	WEEK TOPICS 1st Week Vectors in plane and in three dimensional space. Algebra of vectors. Lines, planes and curves in space. Line integrals. Surfaces and surface integrals. Green's and Stoke's theorems. 2nd Week Differential equations, Seperable equations, Homogeneous equations 3rd Week Exact equations and integrating factors, Firs-order Linear equations. 4th Week Bernoulli's equation, Riccatti's equation, Clairaut's equations 5th Week Second order differential equations of constant coefficients 6th Week Complex numbers , Properties, Geometric representation, Complex conjugates, The polar form, Product, Powers, and Quotients, Extraction of roots, Regions in the complex plane. 7th Week Functions of a Complex variable, Limits, Theorems on limits and continuity, The Derivative, Differentiation formulas, The Cauchy-Riemann conditions 8th Week MIDTERM I 9th Week The Exponential function, The Trigonometric functions,The Hyperbolic funtions, The Logatrithmic function, The Root function, The İnverse trigonometric functions and properties 10th Week Trible integrals in Cartesian Coordinates 11th Week Integrals, Properties of integrals, Line integrals, The Cauchy integral theorem, The Cauchy integral formula 12th Week MID TERM II 13th Week Complex number's series, Taylor's series, Laurent' series and examples. 14th Week Rezidues, Singuler points, The rezidue theorem, İmproper integrals involving trigonometric functions.
RECOMENDED OR REQUIRED READING	"Calculus, 6th Edition", Robert A. Adams, 2006. "Complex variables and Applications", second edition, Ruel V. Churchill
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS	Lecture,Questions/Answers,Case Study,Problem Solving
ASSESSMENT METHODS AND CRITERIA	Quantity Percentage(%) Mid-term 2 40 Quiz 5 10 Total(%) 50 Contribution of In-term Studies to Overall Grade(%) 50 Contribution of Final Examination to Overall Grade(%) 50 Total(%) 100
LANGUAGE OF INSTRUCTION	Turkish
WORK PLACEMENT(S)	No