GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
Elective Course-4 (Complex Analysis/Calculus)/MTÖ310
Course Title: Elective Course-4 (Complex Analysis/Calculus)
Credits 2 ECTS 4
Course Semester 6 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
Manipulate and calculate with complex numbers, complex functions (polynomials, rational functions, exponential and trigonometric functions) and multi-valued functions (argument, logarithm and square root).
Identify subsets of the complex plane and their geometric and topological properties (open, closed, connected, bounded etc).
Determine if a sequence of complex numbers is convergent, compute the limit of a given sequence.
Define the limit of a complex function at a point and apply properties of limits. Compute the limit of a complex function at a point and determine whether a given complex function is continuous.
Define the derivative of a complex function, state and prove properties of the derivative and compute the derivative of a given complex function. Derive the Cauchy-Riemann equations for a complex differentiable function and identify whether a function is complex differentiable at a point.
Determine if an infinite series of complex numbers is convergent. Describe the convergence properties of a complex power series, derive formulae for and compute the radius of convergence.
Identify and construct examples of paths satisfying prescribed properties. Evaluate complex path integrals and state and prove properties of such integrals.
State versions of Cauchy's theorem and its consequences including Cauchy's integral formula, the power series representation for analytic functions, Liouville's theorem and the Fundamental Theorem of Algebra.
Find Taylor and Laurent series for a complex function, compute residues and apply the residue theorem to evaluate integrals.
Find suitable conformal mappings to map regions onto upper-half plane or unit circle.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face.
 --WEEKLY SCHEDULE
1. Week  Introduction, Definitions and importance of the subject, Complex numbers and complex plane. Algebraic operations
2. Week  Complex Exponential, powers, roots
3. Week  Functions, Limit and continuity, analyticity
4. Week  Derivative, Cauchy Riemann equations, harmonic functions
5. Week  Elementary Functions and Inverses
6. Week  Sequences, Series
7. Week  Introduction to complex Integration, contours
8. Week  Midterm Exam
9. Week  Cauchy theorem, Cauchy`s formula and its consequences
10. Week  Integral Theorems, Laurent Series
11. Week  Singularities, Residue Theorem
12. Week  Residue theorem
13. Week  Trigonometric Integrals
14. Week  Improper Integrals
15. Week  Final Exam
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
40
 Assignment
0
0
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
2
28
 Weekly Tutorial Hours
0
 Reading Tasks
10
4
40
 Searching in Internet and Library
0
 Material Design and Implementation
0
 Report Preparing
5
3
15
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
4
4
 Final Exam and Preperation for Final Exam
2
4
8
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
95
 TOTAL WORKLOAD / 25: 
3.8
 Course Credit (ECTS): 
4
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1Acquisition of scientific thinking skillsX
2Making research and investigation independentlyX
3Acquisition of carefully observing and analytically thinking skillsX
4Acquisition of learning and teaching mathematics problemsX
5Comprehending, applying and explaining the importance of mathematical conceptsX
6Developing the thinking, producing, argumenting and probing abilitiesX
7Having the algorithm and sotftware writing abilities for solving computer supported problems
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technologyX
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.
 -- NAME OF LECTURER(S)
   (Related Instructor)
 -- WEB SITE(S) OF LECTURER(S)
   (..)
 -- EMAIL(S) OF LECTURER(S)
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