# GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
DIFFERENTIAL EQUATIONS/MM 215 E
 Course Title: DIFFERENTIAL EQUATIONS Credits 3 ECTS 5 Semester 3 Compulsory/Elective Compulsory
COURSE INFO
-- LANGUAGE OF INSTRUCTION
English
-- NAME OF LECTURER(S)
Asst.Prof.Dr.Cevdet AYGÜN, Asst.Prof.Dr. Muhittin BİLGİLİ, Dr.Tunç APATAY
-- WEB SITE(S) OF LECTURER(S)
websitem.gazi.edu.tr/site/caygun, websitem.gazi.edu.tr/site/bilgili, websitem.gazi.edu.tr/site/tapatay
-- EMAIL(S) OF LECTURER(S)
caygun@gazi.edu.tr, bilgili@gazi.edu.tr, tapatay@gazi.edu.tr
-- LEARNING OUTCOMES OF THE COURSE UNIT
Understand the differential equation concept.
Learning the types of differential equation.
Be able to formulate mathematical models for engineering problems
Be able to determine the particular and general solutions of the first and second-order differential equations.
Be able to solve the differential equations with Laplace transform.

-- MODE OF DELIVERY
The mode of delivery of this course is Face to face
-- PREREQUISITES AND CO-REQUISITES
There is no prerequisite or co-requisite for this course.
-- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
MAT 101 Mathematics I
 --COURSE CONTENT 1. Week Mathematical models. Definition of linear and nonlinear differential equations . Separable equations. 2. Week Solution of for various linear and nonlinear forms in y of f(x,y). 3. Week Exact differential equations. Integrating factors. Linear first-order equation. Existence and uniqueness of solutions. Picard’s iteration. 4. Week Second-order constant-coefficient linear differential equations. Higher-order differential equations. 5. Week Characteristic equation and case of real repeated and complex roots.Euler’s formula for complex exponential function. Cauchy-Euler. 6. Week The nonhomogeneous equation and applications of second order differential equations 7. Week 2.vize 8. Week Laplace transform method. First and second shifting theorems 9. Week Transformation of initial-value problems with various discontinuous loading functions 10. Week Convolution. Unit impulses and the dirac delta function. 11. Week Laplace Transfom solution of Systems. 12. Week Midterm 2 13. Week Differential equations with polynomial coefficients 14. Week Power series solutions of initial value problems . 15. Week Singular points and the method of Frobenius. 16. Week Final