ECTS - Numerical Solution of Differential Equations

Numerical Solution of Differential Equations (MDES620) Course Detail

Course Name	Course Code	Season	Lecture Hours	Application Hours	Lab Hours	Credit	ECTS
Numerical Solution of Differential Equations	MDES620	Area Elective	3	0	0	3	5

Pre-requisite Course(s)
N/A

Course Language	English
Course Type	Elective Courses
Course Level	Ph.D.
Mode of Delivery	Face To Face
Learning and Teaching Strategies	Lecture, Discussion, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives	This course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of differential equations problems that arise in many different fields of science.
Course Learning Outcomes	The students who succeeded in this course; At the end of the course the students are expected to: 1-Choose an efficient method to solve the differential equation(s) coming from a certain application field, 2- Investigate the stability and convergence properties of the methods, 3- Recognize some of the numerical difficulties that can occur when solving problems arising in scientific applications.
Course Content	Numerical solution of initial value problems; Euler, multistep and Runge-Kutta methods; numerical solution of boundary value problems; shooting and finite difference methods; stability, convergence and accuracy; numerical solution of partial differential equations; finite difference methods for parabolic, hyperbolic and elliptic equations; explic

Weekly Subjects and Releated Preparation Studies

Week	Subjects	Preparation
1	1. Week Review to differential equations 2. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 3. Week Numerical solutions of initial value problems; Euler, multistep and Runge-Kutta methods 4. Week Numerical solutions of boundary value problems; finite difference methods 5. Week Numerical solutions of boundary value problems; finite difference methods 6. Week Stability, convergence and accuracy of the numerical techniques given 7. Week Stability, convergence and accuracy of the numerical techniques given 8. Week Midterm Exam 9. Week Partial differential equations and their solutions 10. Week Numerical solution of partial differential equations; finite difference methods 11. Week Numerical solution of partial differential equations; finite difference methods 12. Week Numerical solution of parabolic, hyperbolic and elliptic equations by finite difference methods 13. Week Explicit and implicit methods, Crank-Nicolson method 14. Week Explicit and implicit methods, Crank-Nicolson method. System of ordinary differential equations 15. Week Convergence, stability and consistency analysis of the methods 16. Week Final Exam

Sources

Course Book	1. 1. Numerical Solution of Partial Differential Equations by K.W. Morton and D.F. Mayers, Cambridge University Press, 1994. 2.Numerical Analysis of Differential Equations by A. Iserles, Cambridge University Press, 1996.
Other Sources	2. 1.Computer Methods for ODEs and Differential-Algebraic Equations by U.M. Ascher & L.R. Petzold, SIAM, 1998. 2.Numerical Solution of Partial Differential Equations: Finite Difference Methods by G.D. Smith, Clarendon Press, Oxford, 1985.

Evaluation System

Requirements	Number	Percentage of Grade
Attendance/Participation	-	-
Laboratory	-	-
Application	-	-
Field Work	-	-
Special Course Internship	-	-
Quizzes/Studio Critics	-	-
Homework Assignments	5	30
Presentation	-	-
Project	-	-
Report	-	-
Seminar	-	-
Midterms Exams/Midterms Jury	1	30
Final Exam/Final Jury	1	40
Toplam	7	100

Percentage of Semester Work
Percentage of Final Work	100
Total	100

Course Category

Core Courses	X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

#	Program Qualifications / Competencies	Level of Contribution
#	Program Qualifications / Competencies	1	2	3	4	5
1	Alanında, bağımsız olarak, bir problem kurgulayabilir, çözüm yöntemi geliştirerek problemi çözebilir ve sonuçları değerlendirebilir				X
2	Matematiğin temel alanlarında ve kendi uzmanlığı olarak seçtiği alanda gerekli alt yapıyı oluşturur.				X
3	Matematik literatürünü ve özel olarak kendi araştırma konusu ile ilgili ulusal ve uluslararası güncel yayınları takip edebilir ve bunlardan kendi araştırma konusu ile ilgili olanları çalışmalarında kullanabilir					X
4	Bilimsel etik değerleri ve kuralları dikkate alır ve mesleki ve toplumsal yaşamda kullanabilir				X
5	Kendi çalışmalarının sonuçlarını veya belli bir konudaki güncel çalışmaları ve bulguları, çeşitli bilimsel toplantılarda topluluk önünde Türkçe ve İngilizce olarak sunabilir ve tartışmalara katılabilir.				X
6	Gerek bireysel, gerek bir çalışma grubunun üyesi olarak çalışabilme becerisini geliştirir			X
7	Yaratıcı ve eleştirel düşünme, problem çözme, özgün bir çalışma üretme becerisini geliştirir. Bilimsel gelişmeleri takip eder, özümsediği bilgilerin analiz, sentez ve değerlendirmesini yapabilir.					X
8	Kazandığı bilgi, beceri ve yetkinlikleri yaşam boyu geliştirmeye açık olur.				X
9	Alanında özümsediği bilgiyi ve problem çözme yeteneğini disiplinler arası çalışmalarda uygulayabilir; karşılaşılan problemleri matematiksel modellerle ifade ederek, matematiksel bakış açısı ile farklı çözüm yöntemleri önerir.				X
10	Matematik temelli yazılımları, bilişim ve iletişim teknolojilerini bilimsel amaçlı kullanabilir.	X

ECTS/Workload Table

Activities	Number	Duration (Hours)	Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)	16	3	48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class	16	2	32
Presentation/Seminar Prepration
Project
Report
Homework Assignments	5	5	25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury	2	8	16
Prepration of Final Exams/Final Jury	1	10	10
Total Workload			131