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Syllabus ( MATH 302 )


   Basic information
Course title: Complex Analysis II
Course code: MATH 302
Lecturer: Assoc. Prof. Dr. Hülya ÖZTÜRK
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 3, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Departmental Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Math 111
Professional practice: No
Purpose of the course: To study advanced studies and applications in the theory of functions of a complex variable.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Grap residue theorem and its applications in evaluation of reel integrals

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
  2. Explain general principles of theory of conformal mappings.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  3. Grab Laplace and Fourier Transforms.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Concept of Residue, Residue Theorem.
Week 2: Applications of Residue Theorem to Real Integrals.
Week 3: Argument Principle, Rouche and Hurwitz Theorems.
Week 4: Infınıte Products, Weierstrass Formula.
Week 5: Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula.
Week 6: Concept of Analytic Continuity, Analytic Continuity of an Analytic Function.
Week 7: Weierstrass Method of Analytic Continuity.
Week 8: General Principle of Conformal Mappings.
Midterm exam
Week 9: Riemann Mapping Theorem.
Week 10: Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula.
Week 11: Functions Denoted by Cauchy Kernel.
Week 12: Regularity of an Integral Depending on a Parameter.
Week 13: Laplace Transform.
Week 14: Fourier Transform.
Week 15*: -
Week 16*: Final exam.
Textbooks and materials:
Recommended readings: A.I. Markushevich “Theory of Functions of a Complex Variable”
Ruel V. Churchill, James Ward Brown, “Complex variables and applications”
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 6 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 10 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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