|
Week
|
Topics
|
Study Metarials
|
|
1
|
Definition of differential equation and classification of differential equations, make up of solutions and differential equations
|
R1) Lecture notes
|
|
2
|
Initial and boundary value problems, Mathematical models
|
R1) Lecture notes
|
|
3
|
First order differential equations, linear equations, separable equations
|
R1) Lecture notes
|
|
4
|
Homogeneous equations, reducible to homogeneous differential equation, exact differential equations
|
R1) Lecture notes
|
|
5
|
Exact differential equations
|
R1) Lecture notes
|
|
6
|
Linear, Bernoulli and Riccati differential equations
|
R1) Lecture notes
|
|
7
|
Substitution, Existence and uniqueness theorems
|
R1) Lecture notes
|
|
8
|
Differential equations that are not solvable by derivative, Clairaut and Lagrange equations
|
R1) Lecture notes
|
|
9
|
Theory of linear differential equations, characteristic equation, fundamental solutions, linear independence and Wronskian
|
R1) Lecture notes
|
|
10
|
Complex roots and repeated roots, reduction of order
|
R1) Lecture notes
|
|
11
|
Solutions of higher order linear homogeneous equations with constant coefficiens
|
R1) Lecture notes
|
|
12
|
Higher order nonhomogeneous equations, method of undetermined coefficients
|
R1) Lecture notes
|
|
13
|
The method of variation of parameters
|
R1) Lecture notes
|
|
14
|
Cauchy-Euler equation
|
R1) Lecture notes
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Prof. Dr. Ahmet Yaşar ÖZBAN
|
|
Instructors
|
-
|
|
Assistants
|
Assist. Prof. Dr. Şerifenur CEBESOY ERDAL
|
|
Resources
|
[1] Lecture notes [2] Mustafa BAYRAM, Diferensiyel Denklemler, Birsen Yayınevi, 2002. [3] Shepley L. ROSS, Differential Equations, Fourth Edition, John Wiley and Sons, New York, 1989.
|
|
Supplementary Book
|
[1] Ravi P. AGARWAL, Donal O` REGAN, An Introduction to Ordinary Differential Equations, Springer, 2008. [2] Mehmet Aydın, Gönül Gündüz, Beno Kuryel, Galip Oturanç, Diferensiyel Denklemler ve Uygulamaları, Fakülteler Barış Yayınları, 2007.
|
|
Goals
|
The goal of this course is to introduce differential equations, to teach solving methods, to study existence and uniqueness of solutions of initial value problems, to find exact solutions and to examine these solutions.
|
|
Content
|
Differential equation, order, degree, solutions and obtaining differential equations, initial and boundary value problems, mathematical models, differential equations by solving derivative: separable equations , homogeneous equations and equations reducible to this form, exact differential equations, integrating factor, linear, Bernoulli and Riccati differential equations, substitution, existence and uniqueness theorems, Clairaut and Lagrange equations, theory of linear differential equations, second order linear homogeneous equations with constant coefficiens, the method of undetermined coefficients, the method of variation of parameters, Cauchy-Euler equation
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
To have a grasp of theoretical and applied knowledge in main fields of mathematics
|
4
|
|
2
|
To have the ability of abstract thinking
|
-
|
|
3
|
To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps
|
-
|
|
4
|
To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life
|
5
|
|
5
|
To have the qualification of studying independently in a problem or a project requiring mathematical knowledge
|
-
|
|
6
|
To be able to work compatibly and effectively in national and international groups and take responsibility
|
-
|
|
7
|
To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge
|
-
|
|
8
|
To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge
|
4
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally
|
-
|
|
11
|
To be able to produce projects and arrange activities with awareness of social responsibility
|
-
|
|
12
|
To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level
|
-
|
|
13
|
To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results
|
-
|
|
14
|
To have the awareness of acting compatible with social, scientific, cultural and ethical values
|
-
|