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Syllabus ( MATH 551 )


   Basic information
Course title: Theory Of Differential Equations I
Course code: MATH 551
Lecturer: Prof. Dr. Coşkun YAKAR
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: English
Mode of delivery: Face to face
Pre- and co-requisites: Diff. Eqs. I, Diff. Eqs. II, Real Analysis and Functional Analysis
Professional practice: No
Purpose of the course: To Study Basic Theorem and Definition for Dynamical Systems , Qualitative and Quantitative Techniques, Behavior of the Solutions.
   Learning outcomes Up

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

  1. Explain the basic concepts of Theory of Differential Equations.

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Acquire scientific knowledge and work independently
    3. Develop mathematical, communicative, problem-solving, brainstorming skills.
    4. Effectively express his/her research ideas and findings both orally and in writing
    5. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
  2. Generilaze, Empasize and Apply the concept of Theory of Ordinary Differential Equations

    Contribution to Program Outcomes

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

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Interpret the Stability results and Applications of Dynamical Systems

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
    3. Acquire scientific knowledge and work independently
    4. Develop mathematical, communicative, problem-solving, brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Picard’s and Peano’s Existence Theorems;
Week 2: Lipschitz Uniqueness Theorems;
Week 3: Differential Inequalities;
Week 4: Gronwall, Bihari and Bellman-types Inequalities;
Week 5: Continuation of Solution, Dependence on Initial Conditions; Contraction Mapping Principle;
Week 6: Midterm exam I
Week 7: Extremal Solutions, Upper and Lower Solutions, Comparison Theorems;
Week 8: Monotone Iterative Technique;
Week 9: Method of Quasilinearization;
Week 10: Nonlinear Variation of Parameters Technique and Alekseev’s Formulae;
Week 11: Basic Comparison Results;
Week 12: Midterm exam II
Week 13: Stability Theory;
Week 14: Lyapunov’s Second Method;
Week 15*: Stability of Quasi-linear systems.
Week 16*: Final exam
Textbooks and materials:
Recommended readings: Method of Variation of Parameters for Dynamical Systwems.(V. Lakshmikantham and S.G, Deo)
Stability Analysis of Nonlinear Systems.
(V. Lakshmikantham and A.S. Vatsala)
Uniqueness and Nonuniqueness Criteria for ODEs
(R.P. Agarval and V. Lakshmikantham)
Monotone Iterative Techniques for Nonlinear Differential Equations.
(G.S. Ladde, V. Lakshmikantham and A.S. Vatsala)
Ordinary Differential Equations
( S.G, Deo, V. Lakshmikantham and V.Raghavendra)
Diferansiyel Denklemler Teorisi( E.Hasanov,G.Uzgören, İ. A. Büyükaksoy)

  * 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: 6,12 40
Other in-term studies: 0
Project: 0
Homework: 2, 3, 4, 5, 8, 9,10, 11 5
Quiz: 5, 11 5
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 15
Own studies outside class: 4 15
Practice, Recitation: 0 0
Homework: 6 6
Term project: 0 0
Term project presentation: 0 0
Quiz: 1 2
Own study for mid-term exam: 15 1
Mid-term: 1 1
Personal studies for final exam: 20 1
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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