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 corequisites: 
none 
Professional practice: 
No 
Purpose of the course: 
To teach the methods of solutions of Ordinary Differential Equations 



Learning outcomes


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

Perceive the basic solution methods of differential equations
Contribution to Program Outcomes

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

Ability to work in interdisciplinary research teams effectively.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

Homework assignment

Gain the mathematical experience to engineering and other applied sciences
Contribution to Program Outcomes

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.

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

Ability to work in interdisciplinary research teams effectively.

Using technology as an efficient tool to understand mathematics and apply it.

Exhibiting professional and ethical responsibility.
Method of assessment

Homework assignment

Gain the capability of mathematical modeling
Contribution to Program Outcomes

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

Being fluent in English to review the literature, present technical projects, and write journal papers.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

Homework assignment


Contents


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: 
CauchyPicard 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, LiouvilleOstrogradskiJakoby 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



Method of assessment 
Week number 
Weight (%) 

Midterms: 
8, 12 
50 
Other interm 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



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: 
3 
10 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
1 
2 

Own study for midterm exam: 
8 
2 

Midterm: 
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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