ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE ECTS @ IUE

Syllabus ( MATH 446 )


   Basic information
Course title: Quasilinearization Methods
Course code: MATH 446
Lecturer: Prof. Dr. Coşkun YAKAR
ECTS credits: 5
GTU credits: 3 (3+0+0)
Year, Semester: 4, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Departmental Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Math 203
Professional practice: No
Purpose of the course: Analytical Solution Methods for Nonlinear Differential Equations.
   Learning outcomes Up

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

  1. Explain the basic concepts of Initial Value Problems.

    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.

    Method of assessment

    1. Written exam
  2. Obtain and Explain the Fundamental Definitions, Theorems and Applications of Initial Value Problems

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Generalize, Empasize and Apply the concept of Theory of Ordinary 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. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
    2. Term paper
   Contents Up
Week 1: First Order Differential Equations: Introduction; Method of Upper and Lower Solutions;
Week 2: Method of Quasilinearization;
Week 3: Periodic Boundary Value Problems;
Week 4: Anti-Periodic Boundary Value Problems; Interval Analysis and Quasilinearization;
Week 5: Higher Order Convergence; Extension to System of Differential Equation;
Week 6: MIDTERM I and solutions
Week 7: Second Order Differential Equations: Introduction; Method of Upper and Lower Solutions;
Week 8: Extension of Quasilinearization; Generalized Quasilinearization;
Week 9: General Second Order Boundary Value Problems; Higher Order Convergence.
Week 10: Extension of Method of Quasilinearization: Introduction; Integro-Differential Equations;
Week 11: Functional Differential Equations;
Week 12: MIDTERM II and solutions
Week 13: Stochastic Differential Equations;
Week 14: Differential Equations in a Banach Spaces.
Week 15*: -
Week 16*: Final
Textbooks and materials:
Recommended readings: Lakshmikantham, V. and Vatsala, A.S., Generalized
Quasilinearization for Nonlinear Problems, Kluwer
Academic Publisher, The Netherlands 1998.
Lakshmikantham, V. and Vatsala, A.S., Theory of
differential and integral inequalities with initial time
difference and applications.
Köksal, S. and Yakar, C., Generalized quasilin-
earization method with initial time difference, Sim-
ulation, an International Journal of Electrical,
Electronic and other Physical Systems, 24(5), 2002.
  * 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: 9,15 5
Project: 7, 13 5
Homework: 1,2,3,4,7,8,9,10,13,14 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: 2 14
Practice, Recitation: 0 0
Homework: 1 10
Term project: 3 2
Term project presentation: 2 2
Quiz: 1 2
Own study for mid-term exam: 4 2
Mid-term: 6 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)
-->