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 | Acquires sufficient knowledge in mathematics, natural sciences, and related engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. | X | ||||
| 2 | Gains the ability to identify, define, formulate, and solve complex engineering problems; acquires the skill to select and apply appropriate analysis and modeling methods for this purpose. | X | ||||
| 3 | Gains the ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions, and applies modern design methods for this purpose. | |||||
| 4 | Develops the skills to develop, select, and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in industrial engineering applications; gains the ability to effectively use information technologies. | |||||
| 5 | Gains the ability to design experiments, conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics. | X | ||||
| 6 | Acquires the ability to work effectively in intra-disciplinary and multidisciplinary teams, as well as individual work skills. | X | ||||
| 7 | Acquires effective oral and written communication skills in Turkish; at least one foreign language proficiency; gains the ability to write effective reports, understand written reports, prepare design and production reports, make effective presentations, and give and receive clear instructions. | |||||
| 8 | Develops awareness of the necessity of lifelong learning; gains the ability to access information, follow developments in science and technology, and continuously renew oneself. | |||||
| 9 | Acquires the consciousness of adhering to ethical principles, and gains professional and ethical responsibility awareness. Gains knowledge about the standards used in industrial engineering applications. | |||||
| 10 | Gains knowledge about practices in the business life such as project management, risk management, and change management. Develops awareness about entrepreneurship and innovation. Gains knowledge about sustainable development. | |||||
| 11 | Gains knowledge about the universal and social dimensions of the impacts of industrial engineering applications on health, environment, and safety, as well as the problems reflected in the engineering field of the era. Gains awareness of the legal consequences of engineering solutions. | |||||
| 12 | Gains skills in the design, development, implementation, and improvement of integrated systems involving human, material, information, equipment, and energy. | |||||
| 13 | Gains knowledge about appropriate analytical and experimental methods, as well as computational methods, for ensuring system integration. | |||||
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 | ||