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 | Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering | X | ||||
| 2 | Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions | X | ||||
| 3 | Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering | X | ||||
| 4 | Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design | X | ||||
| 5 | Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology | X | ||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | X | ||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | X | ||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | X | ||||
| 9 | Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management | X | ||||
| 10 | Awareness of professional and ethical responsibility | X | ||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | X | ||||
| 12 | Knowledge on entrepreneurship, innovation and sustainability | X | ||||
| 13 | Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety. | 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 | ||