Differential Equations(ING208)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| ING208 | Differential Equations | 4 | 2 | 1 | 0 | 2.5 | 4 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | DAMİEN LOUS BERTHET berthet.damien@gmail.com (Email) |
| Assistant | |
| Objective |
-Following the discovery of infinitesimal calculus by Newton and Leibniz in the 17th century, and its subsequent application in physics and mechanics, mathematicians and physicists began studying the solutions of differential equations. Today, nearly all scientific disciplines, from economics to modeling, make use of differential equations. In this context, the objectives of the course are as follows: • To show students that some equations, even simple ones, cannot be solved explicitly, and that in certain cases, even the very definition of a solution may be delicate. • To teach and demonstrate the affine structure of the set of solutions of a linear differential equation. • To train students in methods for solving linear differential equations and systems of linear differential equations. • To teach students how to carry out a qualitative analysis of certain differential equations. |
| Content |
- • First-order linear differential equations: structure of the solution set; solution using the method of variation of constants; Cauchy problem and matching of solutions. • Solution of second-order homogeneous linear differential equations with constant coefficients. • Solution of second-order linear differential equations with constant coefficients: use of the variation of constants method and matching problems. • Solution of second-order linear differential equations with variable coefficients, including an adapted use of the variation of constants method. • Study of examples of nonlinear first-order differential equations. • Solution of linear differential systems with constant coefficients: variation of constants method and applications. • Analysis of equilibrium points of two-dimensional differential systems. |
| Course Learning Outcomes |
Upon successful completion of this course, the student will have acquired the following competencies: 1. Ability to solve first- and second-order linear differential equations, whether homogeneous or non-homogeneous, with constant or variable coefficients. 2. Ability to use the method of variation of constants to solve differential equations. 3. Ability to determine maximal solutions for first-order linear differential equations. 4. Ability to sketch phase portraits or integral curves associated with differential equations. 5. Ability to distinguish between different types of equilibrium points. |
| Teaching and Learning Methods | Lectures and practical sessions |
| References |
Equations différentielles, Cours et Exercices, Jean-Luc Raimbault, 2007 http://www.lpp.fr/IMG/pdf_EquaDiffS4.pdf |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | First-order linear differential equations: structure of the solution set and solution methods. |
| 2 | Solution of first-order linear differential equations using the method of variation of constants. |
| 3 | First-order linear differential equations: study of matching (patching) problems. |
| 4 | Solution of second-order homogeneous linear differential equations with constant coefficients. |
| 5 | Solution of second-order linear differential equations with constant coefficients using the method of variation of constants. |
| 6 | Second-order linear differential equations with constant coefficients: study of matching problems. |
| 7 | Solution of second-order linear differential equations with variable coefficients, including an adapted use of the variation of constants method. |
| 8 | Midterm examination. |
| 9 | Study of examples of nonlinear first-order differential equations. |
| 10 | Solution of homogeneous linear differential systems with constant coefficients, with applications. |
| 11 | Solution of linear differential systems using the method of variation of constants. |
| 12 | Analysis of equilibrium points of two-equation differential systems. |
| 13 | Continued study of equilibrium points of two-equation differential systems. |
| 14 | Final examination |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 1 | 40 |
| Contribution of final exam to overall grade | 1 | 60 |
| Toplam | 2 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 40 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Toplam | 1 | 40 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Matematik, fizik ve mühendislik bilimlerine özgü konularda yeterli bilgi birikimi; bu alanlardaki kuramsal ve uygulamalı bilgileri, mühendislik problemlerinin modellenmesi ve çözümünde kullanabilme becerisi. | X | ||||
| 2 | Karmaşık bilgisayar mühendisliği problemlerini saptama, tanımlama, formüle etme ve çözme becerisi; bu amaçla uygun analiz ve modelleme yöntemlerini seçme ve uygulama becerisi. | X | ||||
| 3 | Yazılımsal veya donanımsal karmaşık bir sistemi, süreci veya donanımı gerçekçi kısıtlar ve koşullar altında, belirli gereksinimleri karşılayacak şekilde tasarlama becerisi; bu amaçla modern tasarım yöntemlerini uygulama becerisi. | X | ||||
| 4 | Mühendislik uygulamalarında karşılaşılan karmaşık problemlerin analizi ve çözümü için gerekli olan modern teknik ve araçları geliştirme, seçme ve kullanma becerisi; bilişim teknolojilerini etkin bir şekilde kullanma becerisi. | X | ||||
| 5 | Analitik düşünce ile bir sistemi, sistem bileşenini ya da süreci analiz etme, modelleme, deney tasarlama ve yapma, veri toplama, çözüm algoritmaları üretebilme, uygulamaya alma ve geliştirme becerileri. | X | ||||
| 6 | Disiplin içi ve çok disiplinli takımlarda etkin biçimde çalışabilme becerisi; bireysel çalışma becerisi. | X | ||||
| 7 | Türkçe sözlü ve yazılı etkin iletişim kurma becerisi; en az iki yabancı dil bilgisi; etkin rapor yazma ve yazılı raporları anlama, yazılım ve donanım tasarımını, gerekirse teknik resim metotları kullanarak raporlayabilme, etkin sunum yapabilme becerisi. | X | ||||
| 8 | Bilgiye erişebilme ve bu amaçla kaynak araştırması yapabilme, veri tabanları ve diğer bilgi kaynaklarını kullanabilme becerisi | X | ||||
| 9 | Yaşam boyu öğrenmenin gerekliliği bilinci; kendini sürekli yenileme becerisi. | X | ||||
| 10 | Mesleki etik ilkelerine uygun davranma, mesleki sorumluluk bilinci; mühendislik uygulamalarında kullanılan standartlar hakkında bilgi. | X | ||||
| 11 | Proje yönetimi, risk yönetimi ve değişiklik yönetimi gibi, iş hayatındaki uygulamalar hakkında bilgi; girişimcilik, yenilikçilik hakkında farkındalık; sürdürülebilir kalkınma hakkında bilgi. | X | ||||
| 12 | Mühendislik uygulamalarının evrensel ve toplumsal boyutlarda sağlık, çevre ve güvenlik üzerindeki etkileri ve çağın mühendislik alanına yansıyan sorunları hakkında bilgi. | X | ||||
| 13 | Bilgisayar mühendisliği uygulamalarının hukuki ve etik boyutları konusunda farkındalık. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 13 | 3 | 39 |
| Working Hours out of Class | 13 | 3 | 39 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 10 | 10 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Make-up | 0 | 0 | 0 |
| Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Yıl Sonu | 0 | 0 | 0 |
| Hazırlık Bütünleme | 0 | 0 | 0 |
| Total Workload | 98 | ||
| Total Workload / 25 | 3.92 | ||
| Credits ECTS | 4 | ||