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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
DIFFERENTIAL EQUATIONS II	801500715380		3 + 0	3.0	8.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery	Expression, Ouestion-Answer, Discussion, Solving problem
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Assistants
Goals	To introduce the stability and boundness properties of solutions of differential equations, to prove basic Lyapunov theorems, to be compesed Lyapunov function for autonomous systems(Krasovskii Method), to invetigate linearization method, to introduce the concept of orbital stability, to investigate nonlinear boundary value problems and to be composed Green functions, to be made qualitative examination of some important equations encountered physics and engineering problems.
Course Content	Classification and discussing of singular points, singular points of linear and nonlinear differential equations, fixed and movable singularities, binomial equations, elliptic integrals and elliptic functions, Briot-Bouquet equation, method of majorants, Cauchy’s majorant, Lindelöf majorant, Painleve property, analysis of singular points, Thomas-Fermi equation, global solutions, second Painleve transcendent, Euler-Painleve equations.
Learning Outcomes	1) Examines to stabilties of autonomous systems with Lyapunov method 2) Gets Lyapunov function with Krasovskii method. 3) Understand the linearization method. 4) Examines two-dimensional autonomous systems. 5) Finds equilavant points and calculates stability cases. 6) To recognize the concept of orbital stability. 7) To comment the results of related to the limitations of second order differential equations . 8) Investigate the existence and uniqueness of solutions of nonlinear boundary value problem and find the solution with the help of Green's function.