COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Differential Equations
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 601
Fall
3
0
3
7.5
Prerequisites
None
Course Language
English
Course Type
Required
Course Level
Third Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Case Study
Q&A
Course Coordinator
Course Lecturer(s)
Assistant(s)
Course Objectives This course aims to give the analysis of linear and nonlinear systems, existence and uniqueness of solutions and stability theory.
Learning Outcomes The students who succeeded in this course;
  • will be able to analyze, transform, use in the models and solve the second order differential equations
  • will be able to solve Systems of Linear differential equations.
  • will be able to analyze the methods of nonlinear differential equations.
  • will be able to solve Hamiltonian Systems.
  • will be able to determine Stability of linear and nonlinear systems.
Course Description This course contains the results of linear equations and systems, perturbations of linear systems, the existence and uniqueness of nonlinear initial value problems and the stability theory of linear and nonlinear equations. It also includes the boundary value problems.
Related Sustainable Development Goals

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Initial-value problems, Picard existence theorem. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 1.2, 1.3
2 Peano existence theorem. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section: 1.4
3 Continiuity of solutions. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.1, 2.3, 2.4
4 Continuous dependance of solutions on initial conditions, Continuity of solutions wrt Parameter John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.3, 2.4
5 Linear systems of differential equations John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 5.1
6 Stability Theory: First order systems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 7.1
7 Stability Theory: Lyapunov’s method R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 12.5
8 Stability Theory: Higher order systems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 12.7
9 Perturbated Linear Systems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 8.1
10 Comparison theorems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
11 Diffrential inequalities John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
12 Diffrential inequalities: Applications John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
13 Boundary value problems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.3
14 Boundary value problems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.4,11.7
15 Semester Review
16 Final Exam
Course Notes/Textbooks

John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), ISBN: 9811221359,9789811221354,9813236450,9789813236455.

Suggested Readings/Materials

Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN-13: 978-0321747747.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
2
60
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
6
90
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
2
25
Final Exams
1
37
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest