FACULTY OF ENGINEERING
METALLURGICAL AND MATERIALS ENGINEERING
Course Name   DIFFERENTIAL EQUATIONS
Semester Course Code Theoretical / Practice time ECTS
3 1219304 4,00 / 0,00 5,00
Course Degree Bachelor's degree
Course Language Turkish
Format of Delivery: Face to Face
Course Coordinator Assoc. Prof. Dr. Hasan AKYILDIZ
Coordinator e-mail akhasan selcuk.edu.tr
Instructors
Öğr. Gör. Dr. Ferhat YILDIRIM
Asistant Instructors
Course Objectives This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to develop the basics of modeling of real life problems.
Basic Sciences Engineering Scinces Social Sciences Educational Sciences Artistic sciences Medical Science Agricultural sciences
100 0 0 0 0 0 0
Course Learning Methods and Techniquies
1-Lecture, 2-Question-Answer, 3-Discussion
Week Course Content Resource
1 Classification of differential equations: Explicit solution, ,implicit solution, Initial Value Problem, Existence of Solution. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
2 First Order Ordinary Differential Equations: Exact Differential Equations, NonExact Differential Equations. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
3 Separable Differential Equations, Homogeneous Differential Equations. First Order Linear Differential Equations. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
4 Bernoulli Differential Equations. Substitutions and Transformations. Equations with Linear Coefficients. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
5 Theory of Higher Order Linear Differential Equations, Existence and Uniqueness, Linear Dependence and Independence, Representation of Solutions for Homogeneous and Nonhomogeneous Case. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
6 Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
7 Solution of Nonhomogeneous Differential Equations: Method of Undetermined Coefficients, Method of Variation of Parameters. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
8 Mid-Term Exam
9 Cauchy Euler Differential Equations, Laplace Transforms: Definition of the Laplace Transform, Properties of the Laplace Transform. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
10 Inverse Laplace Transforms. Solving Initial Value Problems by Laplace Transforms. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
11 Series Solutions of Differential Equations. Power Series Solutions: Series Solutions around an Ordinary Point. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
12 Series Solutions around a Singular Point. Method of Frobenius. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
13 Systems of Linear Differential Equations: Differential Operators and an Operator Method. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
14 Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown Functions. Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
15 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two Unknown Functions, n Equations in n Unknown Functions. Paul DuChateau,David W. Zachmann, Nobel Yayın Dağıtım, Kısmi Diferansiyel Denklemler
Assesment Criteria   Mid-term exam Final exam
  Quantity Percentage Quantity Percentage  
Term Studies : - - - -
Attendance / Participation : - - - -
Practical Exam : - - - -
Special Course Exam : - - - -
Quiz : - - - -
Homework : - - - -
Presentations and Seminars : - - - -
Projects : - - - -
Workshop / Laboratory Applications : - - - -
Case studies : - - - -
Field Studies : - - - -
Clinical Studies : - - - -
Other Studies : - - - -
Mid-term exam   1 40 - -
Final exam   - - 1 60
ECTS WORK LOAD TABLE   Number Duration
Course Duration : 14 4
Classroom Work Time : 14 4
Presentations and Seminars : - -
Course Internship : - -
Workshop / Laboratory Applications : - -
Field Studies : - -
Case studies : - -
Projects : - -
Homework : - -
Quiz : - -
Mid-term exam : 1 20
Final Exam : 1 30
ECTS 5
No COURSE LEARNING OUTCOMES CONTRIBUTION
D.Ö.Ç. 1 will be able to classify the differential equations. 4
D.Ö.Ç. 2 will be able to use solution methods of first order ordinary differential equations. 4
D.Ö.Ç. 3 will be able to understand explicit methods of solving higherorder linear differential equations. 4
D.Ö.Ç. 4 will be able to analyze series solutions of linear differential equations. 4
D.Ö.Ç. 5 will be able to solve systems of linear differential equations. 4
D.Ö.Ç. 6 will be able to analyze approximate methods of solving firstorder equations by using the method of succesive approximations and the Euler method. 4
D.Ö.Ç. 7 will be able to understand solution methods of solving systems of linear differential equations. 4
D.Ö.Ç. 8 will be able to understand the Laplace transform method of linear differential equations. 4
* 1: Zayıf - 2: Orta - 3: İyi - 4: Çok İyi
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