ECTS - Differential Equations
Differential Equations (MATH276) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Differential Equations | MATH276 | 4. Semester | 4 | 0 | 0 | 4 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH158 ve MATH152 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Natural & Applied Sciences Master's Degree |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | The course is specifically designed for engineering students as this material is applicable to many fields. The purpose of this course is to provide an understanding of ordinary differential equations (ODE's), systems of ODE’s and to give methods for solving them. This course provides also a preliminary information about partial differential equations (PDE's). |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | First-order, higher-order linear ordinary differential equations, series solutions of differential equations, Laplace transforms, linear systems of ordinary differential equations, Fourier analysis and partial differential equations. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | First Order Ordinary Differential Equations: Preliminaries, pp. 1-5 | pp. 1-5 |
| 2 | Solutions, Existence-Uniqueness Theorem, Separable Equations, Linear Equations. | pp. 5-27 |
| 3 | Bernoulli Equations, Homogeneous Equations, Exact Equations and Integrating Factors. | pp. 27-49 |
| 4 | Substitutions, Higher Order Linear Ordinary Differential Equations: Basic Theory of Higher Order Linear Equations | pp. 49-98 |
| 5 | Reduction of Order Method, Homogeneous Constant Coefficient Equations | pp. 98-113 |
| 6 | Undetermined Coefficients Method, Variation of Parameters Method | pp. 113-125 |
| 7 | Midterm | |
| 8 | Cauchy-Euler Equations, Series Solutions of Ordinary Differential Equations: Power Series Solutions (Ordinary Point) | pp. 125-191 |
| 9 | Power Series Solutions (Ordinary Point) (continued), Power Series Solutions (Regular-Singular Point) | pp. 191-221 |
| 10 | Laplace Transforms: Basic Properties of the Laplace Transforms, Convolution | pp. 223-244 |
| 11 | Solution of Differential Equations by the Laplace Transforms | pp. 244-255 |
| 12 | Systems of Linear Ordinary Differential Equations: Solution of Systems of Linear ODE Using Elimination | pp. 257-291 |
| 13 | Solution of Systems of Linear ODE Using Laplace Transforms | pp. 292-306 |
| 14 | Fourier Analysis: Odd and Even Functions, Periodic Functions, Trigonometric Series, Fourier Series and Fourier Sine and Fourier Cosine Series for Functions of Any Period | pp. 319-333 |
| 15 | Partial Differential Equations: Separation of Variables, Solution of Heat, Wave and Laplace Equations | pp. 307-319 and pp. 333-335 |
| 16 | Final Exam |
Sources
| Course Book | 1. Lectures on Differential Equations, E. Akyıldız, Y. Akyıldız, Ş.Alpay, A. Erkip and A.Yazıcı,, Matematik Vakfı Yayın No:1 |
|---|---|
| Other Sources | 2. Differential Equations, 2nd Edition, Shepley L. Ross, John Wiley and Sons, 1984. |
| 3. Advanced Engineering Mathematics, 8th Edition, Erwin Kreyszig, John Wiley and Sons, 1998. | |
| 4. Ordinary Differential Equations Problem Book with Solutions, Rajeh Eid, Atılım University Publications 16, Ankara, Atılım University, 2005. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | - | - |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 60 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 3 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | An ability to apply advanced knowledge of computing and/or informatics to solve software engineering problems. | |||||
| 2 | Develop solutions using different technologies, software architectures and life-cycle approaches. | |||||
| 3 | An ability to design, implement and evaluate a software system, component, process or program by using modern techniques and engineering tools required for software engineering practices. | |||||
| 4 | An ability to gather/acquire, analyze, interpret data and make decisions to understand software requirements. | |||||
| 5 | Skills of effective oral and written communication and critical thinking about a wide range of issues arising in the context of working constructively on software projects. | |||||
| 6 | An ability to access information in order to follow recent developments in science and technology and to perform scientific research or implement a project in the software engineering domain. | |||||
| 7 | An understanding of professional, legal, ethical and social issues and responsibilities related to Software Engineering. | |||||
| 8 | Skills in project and risk management, awareness about importance of entrepreneurship, innovation and long-term development, and recognition of international standards of excellence for software engineering practices standards and methodologies. | |||||
| 9 | An understanding about the impact of Software Engineering solutions in a global, environmental, societal and legal context while making decisions. | |||||
| 10 | Promote the development, adoption and sustained use of standards of excellence for software engineering practices. | |||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 4 | 56 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 10 | 20 |
| Prepration of Final Exams/Final Jury | 1 | 10 | 10 |
| Total Workload | 86 | ||