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Syllabus ( MATH 203 )


   Basic information
Course title: Differential Equations I
Course code: MATH 203
Lecturer: Prof. Dr. Coşkun YAKAR
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 2, 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 teach the methods of solutions of Ordinary Differential Equations
   Learning outcomes Up

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

  1. Perceive the basic solution methods of differential equations

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Ability to work in interdisciplinary research teams effectively.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. Gain the mathematical experience to engineering and other applied sciences

    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. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Ability to work in interdisciplinary research teams effectively.
    4. Using technology as an efficient tool to understand mathematics and apply it.
    5. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
  3. Gain the capability of mathematical modeling

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Being fluent in English to review the literature, present technical projects, and write journal papers.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Some geometrical and physical problems reducing to ordinary differential equations (ODE), basic concepts and definations, isoclines
Week 2: Equations with separated variables, homogeneous equations
Week 3: Linear, Bernoulli and Riccati equations
Week 4: Exact equations, integrating factors
Week 5: Euler lines, Arzela’s lemma, Peano’s existence theorem
Week 6: Osgood’s uniqueness theorem, Lipschitz condition, Gronwall’s integral inequality
Week 7: Cauchy-Picard existence and uniqueness theorem, method of successive approximations
Week 8: Midterm exam I. First order ODE not solved by derivative , existence and uniqueness theorem for Cauchy problem
Week 9: Method adding parameter, Lagrange and Clairaut equations
Week 10: Singular solutions and methods to find them
Week 11: Linear systems of ODE, properties of solutions of homogeneous linear systems
Week 12: Midterm exam II. Fundamental system of solutions, Wronskian, Liouville-Ostrogradski-Jakoby formula
Week 13: General solution of homogenous linear systems with constant coefficients
Week 14: Method of variation of constants, general solution of homogenous high order linear equations with constant coefficients.
Week 15*: -
Week 16*: Final exam.
Textbooks and materials:
Recommended readings: Ordinary Differential Equations (I. G. Petrovski),
An Introduction to Ordinary Differential Equations (Earl A. Coddington)
Differential Equations (S. L. Ross)
  * 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, 12 50
Other in-term studies: 0
Project: 0
Homework: 1, 2, 3, 4, 5, 6, 9, 10, 13, 14 10
Quiz: 0
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: 3 10
Term project: 0 0
Term project presentation: 0 0
Quiz: 1 2
Own study for mid-term exam: 8 2
Mid-term: 4 2
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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