DİFERANSİYEL DENKLEMLER DERS TANITIM VE UYGULAMA BİLGİLERİ

Kodu	Dersin Adı	Yarıyıl	Süresi(T+U)	Kredisi	AKTS Kredisi
MAT203	DİFERANSİYEL DENKLEMLER	3	4	3	5

DERS BİLGİLERİ
Dersin Öğretim Dili :	Türkçe
Dersin Düzeyi	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Dersin Türü	Zorunlu
Dersin Veriliş Şekli	-
Dersin Koordinatörü	Prof. TARIK ÇAKAR
Dersi Veren Öğretim Üyesi/Öğretim Görevlisi	Dr.Öğr.Üyesi FERHAT KÜRÜZ
Ders Ön Koşulu	Yok

AMAÇ VE İÇERİK
Amaç:	This is one of the basic calculus course of the sequence which serves as the foundation of all advanced subjects in applied and theoretical mathematics.
İçerik:	First order equations: separable, linear, homogeneous exact equations, orthogonal and oblique trajectories, applications. Higher order linear differential equations: Reduction of order, method of undetermine coefficients, method of variation of parameters, Cauchy-Euler equations, operator methods, applications. Power series solutions: ordinary points, regular singular points. The Laplace Transform: basic properties, solution of initial value problems, convolution integral, solution of various equations. Systems of linear differential epuations: Brief discussion of theory of linear systems, solving linear systems; by operator method, by Laplace transform. Introduction to Partial Differential equations: Separation of variables.

DERSİN ÖĞRENME ÇIKTILARI (Öğrenciler, bu dersi başarı ile tamamladıklarında aşağıda belirtilen bilgi, beceri ve/veya yetkinlikleri gösterirler.)

HAFTALIK DERS KONULARI VE ÖNGÖRÜLEN HAZIRLIK ÇALIŞMALARI
Hafta	Ön Hazırlık	Konular	Yöntem
1	-	Preliminaries. Solutions. Existence-Uniqueness Theorem. Separable Equations. Linear Equations. Homogeneous Equations.	-
2	-	Exact Equations and Integrating Factors.Substitutions. Approximate solutions (2.6.1 and 2.6.2). Application	-
3	-	Basic Theory of Higher Order Linear Equations.	-
4	-	Reduction of Order. Homogeneous Constant Coefficient Equations.	-
5	-	Undetermined Coefficients. Variation of Parameters.	-
6	-	The Cauchy-Euler equation. Operator Method.	-
7	-	Power Series Solutions (ordinary points).	-
8	-	MID-TERM EXAM	-
9	-	Power Series Solutions (regular singular points)	-
10	-	The Laplace Transform. Basic Properties. Convolution.	-
11	-	Solution of Differential Equations by the Laplace Transform.	-
12	-	Solutions of Systems of Linear Differential Equations by the Laplace Transform.	-
13	-	Solutions of Systems of Linear Differential Equations by Elimination: simple elimination and operator method.	-
14	-	Introduction to Partial Differential Equations	-
15	-	Introduction to Partial Differential Equations	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

KAYNAKLAR

ÖLÇME VE DEĞERLENDİRME
Yarıyıl İçi Yapılan Çalışmaların Ölçme ve Değerlendirmesi	Etkinlik Sayısı	Katkı Yüzdesi	Açıklama

(0) Etkisiz	(1) En Düşük	(2) Düşük	(3) Orta	(4) İyi	(5) Çok İyi
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Gain sufficient knowledge in Mathematics, Science and Industrial Engineering.						5

KNOWLEDGE
Factual
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Analyzes and evaluates existing application areas in the field of Industrial Engineering and develops applications for their solutions.				3

SKILLS
Cognitive
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Analyzes a system, the components of that system, the process of that system, and designs the system by examining it in line with realistic constraints and goals.				3
2	Gains the ability to model and solve engineering problems.			2

SKILLS
Practical
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Identifies the problems that may be encountered in the field of industrial engineering and acquires the ability to choose and apply the appropriate method to be used in problem solving.				3
2	Selects and uses technical tools necessary for industrial engineering applications; uses information technologies effectively.					4
3	Designs experiments, conducts experiments, collects data, analyzes and interprets the results to examine problems in the field of industrial engineering.			2

OCCUPATIONAL
Autonomy & Responsibility
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Gains the ability to work effectively within a team.					4
2	Works effectively individually and takes responsibility.				3

OCCUPATIONAL
Learning to Learn
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Accesses the necessary information for a determined problem and searches for resources for this purpose.					4
2	Has the ability to follow all developments in the field of industrial engineering and constantly renew itself.						5

OCCUPATIONAL
Communication & Social
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Gains oral and written communication skills and speaks at least one foreign language.		1

OCCUPATIONAL
Occupational and/or Vocational
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Has awareness of professional and ethical responsibility.				3
2	Has knowledge about the universal and social effects of industrial engineering applications and reaches solutions by being aware of the importance of an innovative approach in solving engineering problems.			2

DERSİN İŞ YÜKÜ VE AKTS KREDİSİ
Öğrenme-Öğretme Etkinlikleri İş Yükü
Öğrenme-Öğretme Etkinlikleri	Etkinlik(hafta sayısı)	Süresi(saat sayısı)	Toplam İş Yükü
Lecture & In-Class Activities	14	3	42
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	3	4	12
Assignment (Homework)	6	5	30
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	0	0	0
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	39	0	128