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 | Bachelor’s Degree (First Cycle) |
| 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 | Adequate knowledge in mathematics, science and subjects specific to the energy systems engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems. | X | ||||
| 2 | The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. | |||||
| 3 | The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. | |||||
| 4 | The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in energy systems engineering applications; the ability to utilize information technologies effectively. | |||||
| 5 | The ability to design experiments, conduct experiments, gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the energy systems engineering discipline. | |||||
| 6 | The ability to work effectively in inter/inner disciplinary teams, the ability to work individually. | |||||
| 7 | a)Effective oral and writen communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions. b)The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions. | |||||
| 8 | Recognition of the need for lifelong learning; the ability to access information, to follow recent developments in science and technology. | |||||
| 9 | a)The ability to behave according to ethical principles, awareness of professional and ethical responsibility; b)knowledge of the standards utilized in energy systems engineering applications. | |||||
| 10 | Knowledge on business practices such as project management, risk management and change management; awareness about entrepreneurship, innovation; knowledge on sustainable development. | |||||
| 11 | a) Knowledge on the effects of energy systems engineering applications on the universal and social dimensions of health, environment and safety; b) and awareness of the legal consequences of engineering solutions. | |||||
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 | ||