Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT572 - MATHEMATICS

Code: MAT572 Course Title: APPLICATIONS OF DIFFERENTIAL EQUATIONS II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring Semester
Level of Course 2nd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr)
Name of Lecturer(s) SEYDİ BATTAL GAZİ KARAKOÇ,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
The aim of the course is to understand the different solution methods for differential equations.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Knows the Solutions of Differential Equations with Variable Coefficients. Knows Laplace Transform and Applies it to Differential Equations. Solves Higher Order Nonlinear Differential Equations. Knows Numerical Solutions of Differential Equations. Solves Sturm Liouville Problems. Knows Green's Function Method. PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems.
PO-3 Mathematics, natural sciences and their branches in these areas and related issues has sufficient infrastructure solutions for the problems of theoretical and practical uses of mathematics.
 		Examination
Performance Project
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
The Laplace Transformation, Systems of First Order Linear Equation, Numerical Methods, Nonlinear Differantial Equations and Stability
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Indeterminate Coefficients Method Reverse Image Method Oral representation, Qestioning-Answering, Problem Solving
2 Linear Differential Equations With Variable Coefficients Operator Factorization Oral representation, Qestioning-Answering, Problem Solving
3 Decreasing Order Oral representation, Qestioning-Answering, Problem Solving
4 Method of Change of Parameters Cauch-Euler Equation Oral representation, Qestioning-Answering, Problem Solving
5 Power Series Ordinary Point Series Solutions Around the Ordinary Point Oral representation, Qestioning-Answering, Problem Solving
6 Smooth Outlier Serial Solutions Around the Uniform Outlier Oral representation, Qestioning-Answering, Problem Solving
7 Legendre's Equation Bessel Equation Oral representation, Qestioning-Answering, Problem Solving
8 mid-term exam
9 Laplace Transform Existence of the Laplace Transform Properties of Laplace Transform Oral representation, Qestioning-Answering, Problem Solving
10 Inverse Laplace Transform Application of Laplace Transform to Ordinary Differential Equations Oral representation, Qestioning-Answering, Problem Solving
11 Numerical Solutions of Differential Equations Euler's Method Regulated Euler's Method Oral representation, Qestioning-Answering, Problem Solving
12 Runge-Kutta Method Oral representation, Qestioning-Answering, Problem Solving
13 2nd Order Linear Boundary Value Problems Regular Sturm-Liouville Problems Oral representation, Qestioning-Answering, Problem Solving
14 Periodic Sturm-Liouville Problems Oral representation, Qestioning-Answering, Problem Solving
15 Green's Function Method Oral representation, Qestioning-Answering, Problem Solving
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 Diferensiyel Denklemler ve Sınır Değer Problemleri, Ö. Akın, Palme yayınları
2 Adi Diferensiyel Denklemler, Mehmet Çağlıyan, Nisa Çelik, Setenay Doğan
Required Course instruments and materials
Lecture Notes

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 3 14 42
       b) Search in internet/Library 2 7 14
       c) Performance Project 2 8 16
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 8 24
mid-term exam 2 1 2
Own study for final exam 3 15 45
final exam 2 1 2
0
0
Total work load; 187