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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
DIFFERENTIAL EQUATIONS I	MAT3315		0 + 0	3.0	3.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery
Course Coordinator
Instructors
Assistants
Goals	The goal of this course is to introduce differential equations, to teach solving methods, to study existence and uniqueness of the solutions of initial value problems, to find exact solutions and to examine these solutions.
Course Content	Differential equation, Order, Degree, Solutions and obtaining differential equations, initial and boundary value problems, mathematical models, Direction fields and isoclines, differential equations by solving derivative: separable equations , Homogeneous equations, Exact differential equations, Integrating factor, Linear, Substitution(Bernoulli and Riccati differential equations, et al.), Existence and uniqueness theorems, Numerical solutions(Euler, Runge-Kutta, Taylor expansion method), Clairaut and Lagrange equations, Theory of linear differential equations, Second order linear homogeneous equations with constant coefficiens , The method of undetermined coefficients.
Learning Outcomes	1) Classifies the differential equations. 2) Solves homogeneous differential equations and exact differential equations. 3) Finds the solutions of Linear equations, Bernoulli and Riccati equations. 4) Recognizes the initial and boundary value problems. 5) Examines the existence and uniqueness of solutions of initial value problems. 6) Solves some of the problems of physics, chemistry and biology with the help of differential equations. 7) Groups the differential equations which can not be solved accordint to derivative. 8) Investigates the theory of higher order linear equations. 9) Finds the general solution of high-order linear homogeneous equations with constant coefficients 10) Calculates the particular solutions using the method of undetermined coefficients.