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Syllabus ( MATH 549 )


   Basic information
Course title: Theory Of Univalent Functions
Course code: MATH 549
Lecturer: Prof. Dr. Tahir AZEROĞLU
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 1/2, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: Turkish
Mode of delivery: Face to face
Pre- and co-requisites: MATH 501, MATH 502
Professional practice: No
Purpose of the course: In this course the basic results of the univalent functions theory, such as: the area theorem, Koebes one-quarter theorem and the growth and distortion theorems and proof of the famous Bieberbach conjecture by dBranges , will be learned.
   Learning outcomes Up

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

  1. Explain the area theorem and Koebe one-quarter theorem.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Develop mathematical, communicative, problem-solving, brainstorming skills.
    3. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
  2. Explain growth and distortion theorems about univalent functions.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Develop mathematical, communicative, problem-solving, brainstorming skills.
    3. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
  3. Explain the proof of the famous Bieberbach Conjecture given by deDranges.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Develop mathematical, communicative, problem-solving, brainstorming skills.
    3. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
   Contents Up
Week 1: Fundamental Distortion Theorems for Univalent Functions
Week 2: Fundamental Inequalities of Coefficient for Univalent Functions.
Week 3: Some Special Classes of Univalent Functions.
Week 4: Some Special Classes of Univalent Functions.
Week 5: Parametric Representation of Loewner.
Week 6: Faber Polynomials and Generalization of Area Principle.
Week 7: Faber Transform.
Week 8: Subordination.
Week 9: Integral Means.
Week 10: Variational Tecniques.
Week 11: Extreme points of Some Special Class of Functions.
Week 12: Extreme points of Some Special Class of Functions.
Week 13: Proof of Bieberbach Conjecture.
Week 14: Proof of Bieberbach Conjecture.
Week 15*: General review.
Week 16*: Final exam.
Textbooks and materials:
Recommended readings: Peter L. Duren, "Univalent Functions", Springer-Verlag, 1983.
Pommerenke, Ch.,"Univalent Functions", Vandenhoeck und Ruprecht, GÄottingen, 1975.
  * 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: 0
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 100
  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: 3 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: 0 0
Mid-term: 0 0
Personal studies for final exam: 20 5
Final exam: 3 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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