| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Dıfferentıal Equatıons | MAT 211 | 3 | 4 + 0 | 4 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | İngilizce |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Dr.Öğr.Üyesi EMİNE ÇELİK |
| Dersi Verenler | Dr.Öğr.Üyesi EMİNE ÇELİK, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | The general purpose of this course is to provide an understanding of ordinary differential equations (ODEs), and to give methods for solving them. Because differential equations express relationships between changing quantities, this material is applicable to many fields, and is essential for students of engineering and physical sciences. |
| Dersin İçeriği | This course covers topics in ordinary differential equations: First-order differential equations; Modeling with first-order differential equations; Higher-order differential equations; Modeling with higher-order differential equations; Laplace transform; Series solutions of Linear Equations. |
| Kalkınma Amaçları |
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| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | Students will obtain a thorough knowledge of solution techniques for first- order and for second- and higher-order constant coefficient linear homogenous and nonhomogeneous initial value problems using standard methods of undetermined coefficients and variation of parameters. | Anlatım, Soru-Cevap, Beyin Fırtınası, Tartışma, Gezi / Gözlem, | |
| 2 | In addition, the students will acquire a general understanding of how to apply the Laplace transform in solving initial value problems and convolution integral equations. | Anlatım, Soru-Cevap, Tartışma, Gezi / Gözlem, | |
| 3 | Students will gain an appreciation for some of the applications of ordinary differential equations in biology and engineering. | Anlatım, Soru-Cevap, Tartışma, Gezi / Gözlem, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Definitions and Terminology. Basic Concepts and Classifying Differential Equations. Obtaining differential equations. Initial-Value Problems. | |
| 2 | Separable differential equations. Linear Equations. Differential Equations as Mathematical Models. | |
| 3 | Homogeneous functions, homogenous differential equations. Engineering Applications. | |
| 4 | Homogeneous functions, homogenous differential equations. Engineering Applications. | |
| 5 | Higher-Order Differential Equations. Preliminary Theory. | |
| 6 | Homogeneous Equations. Nonhomogeneous Equations. Reduction of Order. | |
| 7 | Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients. | |
| 8 | Variation of Parameters. Cauchy-Euler Equations. Modeling with Higher-Order Differential Equations. | |
| 9 | Midterm Exam. | |
| 10 | Series Solutions of Linear Equations. Solutions about ordinary points. Solutions about singular points. Special Functions. | |
| 11 | The Laplace transform. Inverse Transforms and Transforms of Derivatives. Operational Properties. | |
| 12 | Operational Properties. The Dirac Delta Function. Engineering Applications. | |
| 13 | Systems of Linear First-Order Differential Equations. Preliminary Theory. Homogeneous Linear Systems. | |
| 14 | Solutions of Homogeneous Linear Systems. Undetermined Coefficients and Laplaca Transform Methods. Engineering Applications. |
| Kaynaklar | |
|---|---|
| Ders Notu | Lecture Notes. |
| Ders Kaynakları | [1] Differential Equations with Boundary-Value Problems, 9th edition, by D.G. Zill and M.R. Cullen, published by Cengage. [2] Çözümlü Problemlerle Diferansiyel Denklemler, E. S. Türker, ve M. Başarır, 2003, Değişim Kitabevi, Sakarya. [3] Adi Diferansiyel Denklemler, 7. baski, M. Cagliyan, N. Celik, S. Dogan, Dora Yayinevi, Bursa 2018. |
| # | Ders Öğrenme Çıktılarının Program Çıktılarına Katkısı |
|---|---|
| 1 | Students will obtain a thorough knowledge of solution techniques for first- order and for second- and higher-order constant coefficient linear homogenous and nonhomogeneous initial value problems using standard methods of undetermined coefficients and variation of parameters. |
| 2 | In addition, the students will acquire a general understanding of how to apply the Laplace transform in solving initial value problems and convolution integral equations. |
| 3 | Students will gain an appreciation for some of the applications of ordinary differential equations in biology and engineering. |
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Kısa Sınav | 10 |
| 2. Kısa Sınav | 10 |
| 3. Kısa Sınav | 10 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Ders Süresi (Sınav haftası dahildir: 16x toplam ders saati) | 16 | 4 | 64 |
| Sınıf Dışı Ders Çalışma Süresi(Ön çalışma, pekiştirme) | 16 | 3 | 48 |
| Ara Sınav | 1 | 6 | 6 |
| Kısa Sınav | 3 | 6 | 18 |
| Final | 1 | 10 | 10 |
| Toplam İş Yükü | 146 | ||
| Toplam İş Yükü / 25 (Saat) | 5,84 | ||
| Dersin AKTS Kredisi | 6 | ||