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Syllabus ( MATH 301 )


   Basic information
Course title: Complex Analysis I
Course code: MATH 301
Lecturer: Assoc. Prof. Dr. Hülya ÖZTÜRK
ECTS credits: 7
GTU credits: 3 (3+0+0)
Year, Semester: 3, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: To study the essential principles of the Theory of Functions of a Complex Variable
   Learning outcomes Up

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

  1. Explain analytic function of a single complex variable.

    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
  2. Gain basic knowledge about linear fractional transformations.

    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
  3. Obtain basic knowledge about contour integrals of complex functions.

    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: Complex Numbers, Riemann Sphere, Sequences and Series.
Week 2: Functions of Complex Variables, Limit, Continuity.
Week 3: Derivative of Functions of Complex Variables, Cauchy-Riemann Conditions, Analytic Functions.
Week 4: Modules of derivative and Geometric meaning of Argument,Concept of Conformal Mapping.
Week 5: Linear Fractional Function and its Properties.
Week 6: Mapping Properties of Some Fundamental Functions.
Week 7: Integral of the Functions of Complex Variable and its Relation with Curve Integrals, Newton-Leibnitz Formula,Cauchy Integral Theorem.
Week 8: Cauchys İntegral Formula, Cauchys İntegral Formula for Derivatives, Cauchy Type Integral.
Midterm exam I
Week 9: Sequences and Series of Analytic Functions, Weierstrass Theorem. Morera’s Theorem.
Week 10: Power Series, Abel Theorem, Cauchy-Hadamard Formula, Cauchys Inequality, Liouville Theorem.
Week 11: Uniqueness Theorem, Maximum Module Principle and Schwarz Lemma.
Week 12: Laurent Series, Cauchy Formula for Coefficients.
Week 13: Zeros of Analytic Functions and Orders of Zeros.
Week 14: Disjoint Singular Points, Poles and Essential Singular Points, Riemann, Casoratti-Weierstrass and Picard Theorms.
Week 15*: -
Week 16*: Final exam
Textbooks and materials:
Recommended readings: A.I. Markushevich “Theory of Functions of a Complex Variable”, “Complex variables and applications” Ruel V. Churchill, James Ward Brown, Edward B. Saff and Arthur David Snider "Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics".
  * 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: 14 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: 5 14
Practice, Recitation: 0 0
Homework: 3 12
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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