ECTS - Differential Equations
Differential Equations (MATH276) Course Detail
Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
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Differential Equations | MATH276 | 4. Semester | 4 | 0 | 0 | 4 | 6 |
Pre-requisite Course(s) |
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MATH158 ve MATH152 |
Course Language | English |
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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) |
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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;
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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 |
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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 |
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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 |
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Percentage of Final Work | 40 |
Total | 100 |
Course Category
Core Courses | X |
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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 | Gains adequate knowledge of mathematics, physical sciences and the subjects specific to engineering disciplines; gains the ability to apply theoretical and practical knowledge of these areas in the solution of complex engineering problems. | X | ||||
2 | Gains the ability to define, formulate, and solve complex engineering problems; gains the ability to select and apply proper analysis and modeling methods for this purpose. | |||||
3 | Gains the ability to design a complex system, process, device or product under realistic constraints and conditions in such a way as to meet the specific requirements; gains the ability to apply modern design methods for this purpose. | |||||
4 | Gains the ability to select, and use modern techniques and tools needed to analyze and solve complex problems encountered in engineering practices; gains the ability to use information technologies effectively. | |||||
5 | Gains the ability to design experiments, conduct experiments, gather data, and analyze and interpret results for investigating complex engineering problems or research areas specific to engineering disciplines. | |||||
6 | Gains the ability to work efficiently in inter-, intra-, and multi-disciplinary teams; gains the ability to work individually. | |||||
7 | (a) Gains effective oral and written communication skills; gains the ability to write a report properly, understand previously written reports, prepare design and manufacturing reports, deliver influential presentations, give unequivocal instructions, and carry out the instructions properly. (b) Gains the knowledge of, at least, one foreign language; gains the ability to write a report properly, understand previously written reports, prepare design and manufacturing reports, deliver influential presentations, give unequivocal instructions, and carry out the instructions properly in this foreign language. | |||||
8 | Gains awareness of the need for lifelong learning; gains the ability to access information, follow developments in science and technology, and adapt and excel oneself continuously. | |||||
9 | Gains knowledge about acting in conformity with the ethical principles, professional and ethical responsibility and knowledge of the standards employed in engineering applications. | |||||
10 | Gains knowledge of business practices such as project management, risk management, and change management; gains awareness of entrepreneurship and innovation; knowledge of sustainable development. | |||||
11 | Gains knowledge of the global and social effects of engineering practices on health, environment, and safety issues, and knowledge of the contemporary issues in engineering areas; gains awareness of the possible legal consequences of engineering practices. | |||||
12 | (a) Gains knowledge of (i) fluid mechanics, (ii) heat transfer, (iii) manufacturing process, (iv) electronics and control, (v) vehicle components design, (vi) vehicle dynamics, (vii) vehicle propulsion/drive and power systems, (viii) technical laws and regulations in automotive engineering field, and (ix) vehicle verification tests. (b) Gains the ability to merge and apply these knowledge in solving multi-disciplinary automotive problems. | |||||
13 | Gains the ability to make use of theoretical, experimental, and simulation methods, and computer aided design techniques in automotive engineering field. | |||||
14 | Gains he ability to work in the field of vehicle design and manufacturing. |
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 |