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Syllabus ( MATH 553 )


   Basic information
Course title: Linear Differential Equations
Course code: MATH 553
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: Ordinary Differential Equations
Professional practice: No
Purpose of the course: To Discuss Numerical and Analytical Solution Methods of Linear Differential Equations, Characteristic of Solution.
   Learning outcomes Up

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

  1. Explain the basic concepts of Linear Differential Equations

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Work effectively in multi-disciplinary research teams
    4. Design and conduct research projects independently
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Effectively express his/her research ideas and findings both orally and in writing
    7. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
    3. Seminar/presentation
  2. Obtain and Explain the Fundamental Definitions, Concepts, Theorems , Stability and Applications of Linear Differential Equations

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Work effectively in multi-disciplinary research teams
    4. Design and conduct research projects independently
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Effectively express his/her research ideas and findings both orally and in writing

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Gain Experience on Linear Differential Equations

    Contribution to Program Outcomes

    1. Define and manipulate advanced concepts of Mathematics
    2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
    3. Acquire scientific knowledge and work independently
    4. Work effectively in multi-disciplinary research teams
    5. Develop mathematical, communicative, problem-solving, brainstorming skills.
    6. Effectively express his/her research ideas and findings both orally and in writing
    7. Demonstrating professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
    2. Term paper
   Contents Up
Week 1: Basic Definition and Theorems on Linear Differential Equations;
Week 2: Basic Definition and Theorems of Linear Differential Equations;
Week 3: First Order Linear Differential Equations;
Week 4: Second Order Linear Homogeneous/Nonhomogeneous Differential Equations;
Week 5: nth-Order Linear Homogeneous/Nonhomogeneous Differential Equations;
Week 6: Midterm exam I
Week 7: Method of Variation of Parameters; Series Solutions Methods of Linear Differential Equations;
Week 8: Special Functions on the Solution of Linear Differential Equations;
Week 9: Numerical Approximation Solutions of Linear Differential Equations;
Week 10: N-Linear Differential Systems of Equations;
Week 11: Method of Variation of Parameters;
Week 12: Midterm exam II
Week 13: Unperturbed Matrix Differential Systems of Equations;
Week 14: Perturbed Matrix Differential Systems of Equations;
Week 15*: Qualitative Methods of Matrix Differential Systems of Equations;
Week 16*: Final exam
Textbooks and materials:
Recommended readings: Ordinary Differential Equations
( S.G, Deo, V. Lakshmikantham and V.Raghavendra)
Nonlinear Variation of Parameters Formula 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: 7,13 5
Project: 14 5
Homework: 1,2,3, 4, 5, 8, 9, 10, 11,13 5
Quiz: 5,11 5
Final exam: 16 40
  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: 6 10
Term project: 4 1
Term project presentation: 1 1
Quiz: 1 2
Own study for mid-term exam: 10 2
Mid-term: 3 2
Personal studies for final exam: 10 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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