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 corequisites: 
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


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

Explain the basic concepts of Linear Differential Equations
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Work effectively in multidisciplinary research teams

Design and conduct research projects independently

Develop mathematical, communicative, problemsolving, brainstorming skills.

Effectively express his/her research ideas and findings both orally and in writing

Demonstrating professional and ethical responsibility.
Method of assessment

Written exam

Homework assignment

Seminar/presentation

Obtain and Explain the Fundamental Definitions, Concepts, Theorems , Stability and Applications of Linear Differential Equations
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Work effectively in multidisciplinary research teams

Design and conduct research projects independently

Develop mathematical, communicative, problemsolving, brainstorming skills.

Effectively express his/her research ideas and findings both orally and in writing
Method of assessment

Written exam

Homework assignment

Gain Experience on Linear Differential Equations
Contribution to Program Outcomes

Define and manipulate advanced concepts of Mathematics

Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems

Acquire scientific knowledge and work independently

Work effectively in multidisciplinary research teams

Develop mathematical, communicative, problemsolving, brainstorming skills.

Effectively express his/her research ideas and findings both orally and in writing

Demonstrating professional and ethical responsibility.
Method of assessment

Homework assignment

Term paper


Contents


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: 
nthOrder 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: 
NLinear 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



Method of assessment 
Week number 
Weight (%) 

Midterms: 
6,12 
40 
Other interm 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



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface 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 midterm exam: 
10 
2 

Midterm: 
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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