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. ABDULSAMET HAŞILOĞLU |
Dersi Veren Öğretim Üyesi/Öğretim Görevlisi |
Dr.Öğr.Üyesi MELTEM UZUN-Dr.Öğr.Üyesi SEDA YAMAÇ AKBIYIK |
Ders Ön Koşulu |
MAT105 - MATHEMATICS I |
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 |
- |
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 |
DERSİN PROGRAM ÖĞRENME ÇIKTILARINA KATKISI
KNOWLEDGE |
Theoretical |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Explains the fundamental engineering concepts of computer science and relates them to the groundwork of computer science.
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KNOWLEDGE |
Factual |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Uses theoretical and practical knowledge coming from mathematics, probability, statistics and various other branches of life sciences, to find solutions to engineering problems.
|
|
|
|
|
|
|
SKILLS |
Cognitive |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Determines the components and the underlying process of a system and designs an appropriate computational model under reasonable constraints.
|
|
|
|
|
|
|
2 |
Designs a computer-aided conceptual model with modern techniques.
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|
|
|
|
|
|
SKILLS |
Practical |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Determines, detects and analyzes the areas of computer science applications and develops appropriate solutions.
|
|
|
|
|
|
|
2 |
Identifies, models and solves computer engineering problems by applying appropriate analytical methods.
|
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|
|
|
|
|
3 |
Determines and uses the necessary information technologies in an efficient way for engineering applications.
|
|
|
|
|
|
|
OCCUPATIONAL |
Autonomy & Responsibility |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.
|
|
|
|
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2 |
Possess the ability to conduct effective individual study.
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|
3 |
Takes responsibility as a team work and contributes in an effective way.
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|
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|
|
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OCCUPATIONAL |
Learning to Learn |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Monitors the developments in the field of information technologies by means of internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.
|
|
|
|
|
|
|
2 |
Develops positive attitude towards lifelong learning.
|
|
|
|
|
|
|
OCCUPATIONAL |
Communication & Social |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Communicates effectively by oral and/or written form and uses at least one foreign language.
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|
|
|
|
|
|
2 |
Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.
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|
|
|
|
|
|
OCCUPATIONAL |
Occupational and/or Vocational |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Possess professional and ethical responsibility and willingness to share it.
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|
|
|
|
|
|
2 |
Possess sufficient consciousness about the universality of engineering solutions and applications and be well aware of the importance of innovation.
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|
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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 |
|
Genel Toplam |
128 |
|
|
Toplam İş Yükü / 25.5 |
5 |
|
|
Dersin AKTS(ECTS) Kredisi |
5,0 |
|