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- 25TH YEAR
MATH 601 | Course Introduction and Application Information
| Course Name |
Differential Equations
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
MATH 601
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
|||||
| Course Language |
English
|
|||||
| Course Type |
Elective
|
|||||
| Course Level |
Third Cycle
|
|||||
| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | Problem SolvingCase StudyQ&A | |||||
| National Occupation Classification | - | |||||
| 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;
|
| 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 |
|
|
|
Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 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 | Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition |
| 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 |
1
|
20
|
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
1
|
30
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
2
|
50
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
50
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
6
|
90
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
1
|
10
|
10
|
| Presentation / Jury |
0
|
||
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
1
|
30
|
30
|
| Final Exam |
1
|
47
|
47
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
|||||||
|
1
|
2
|
3
|
4
|
5
|
|||||
| 1 |
|
-
|
-
|
-
|
X
|
-
|
|||
| 2 |
|
-
|
-
|
-
|
-
|
X
|
|||
| 3 |
|
-
|
-
|
-
|
-
|
X
|
|||
| 4 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 5 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 6 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 7 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 8 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 9 |
|
-
|
-
|
-
|
-
|
-
|
|||
| 10 |
|
-
|
-
|
-
|
-
|
X
|
|||
| 11 |
|
-
|
-
|
-
|
-
|
-
|
|||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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