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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| PHYSICS PR. | |
| Code | FZK203 |
| Name | Differential Equations |
| Term | 2021-2022 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. AYSUN AKYÜZ |
| Course Instructor |
Prof. Dr. AYSUN AKYÜZ
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Teaching of basic theories of differential equations, solutions and applications
Course Content
Classification of diferential equations, Existence of solutions, First-order differential equations, Applications of first-order differential equations, Solutions of Second and Higher-order linear differential equations, Applications of Second-order linear diferential equations, Series solutions of differential equations, Frobenius method, Approximate methods of solving first-order equations, Laplace transform, Laplace transform solution of linear differential equations with constant coefficients
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Describes the differential equation, explains its formation and solution. |
| LO02 | Comprehends the solution methods of first order differential equations |
| LO03 | Understands, applications of first -order equations in mechanics |
| LO04 | Understands, solution methods of higher-order linear differential equations |
| LO05 | Understands applications of second- order linear differential equations |
| LO06 | Express the fundamental theorem of higher order linear differential equations. |
| LO07 | Determine the type of linear equation system |
| LO08 | Solve homogeneous linear systems with constant coefficients |
| LO09 | Understand the series solutions of linear equation systems |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and principles in the field of physics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Follows the developments in the field of Physics and uses scientific methods and techniques. | 1 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Combine the knowledge gained in the field of Physics with the knowledge in other scientific fields and explains the method of producing scientific knowledge. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identify problems in the field of physics and for the solutions apply the analytical and simulative methods. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use the advanced theoretical and practical knowledge he has acquired in the field of Physics and designs experiments related to his field. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Take responsibility as a team or alone to overcome the problems encountered in the field of physics . | 2 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Classify, use and critically evaluate the knowledg taken by his/her efforts. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Improves himself by knowing that the learning process is lifelong. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Knowing the importance of individual development, she/he implements what is necessary. | 1 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Evaluates the developments in the field of physics in terms of social ethics by watching and learning them. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Classification of differential equations, definitions, existence of solutions | no preparation | |
| 2 | Exact differential equations and Integral factors, separable equations | Study the relevant chapter in the book | |
| 3 | Linear equations and Bernoulli equations, Special integrating factors | Study the relevant chapter in the book | |
| 4 | Applications of first-order differential equations, applications in mechanics | Study the relevant chapter in the book | |
| 5 | Second-order differential equations, Homogeneous linear equation with constant coefficient | Study the relevant chapter in the book | |
| 6 | The method of Undetermined coefficients | Study the relevant chapter in the book | |
| 7 | Variation of parameters method | Study the relevant chapter in the book | |
| 8 | Mid-Term Exam | review the topics | |
| 9 | Applications of the second-order linear differential equations with constant coefficient | Study the relevant chapter in the book | |
| 10 | Series solutions, Series solutions about an ordinary point | Study the relevant chapter in the book | |
| 11 | Solutions about singular points, The Method of Frobenius | Study the relevant chapter in the book | |
| 12 | Successive approximation method | Study the relevant chapter in the book | |
| 13 | The Laplace transform, basic properties | Study the relevant chapter in the book | |
| 14 | Laplace transform solution of linear differential equations with constant coefficients | Study the relevant chapter in the book | |
| 15 | The inverse Laplace transforms | Study the relevant chapter in the book | |
| 16 | Term Exams | review the topics | |
| 17 | Term Exams | an overview |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Homework | 10 | 4 |
| 1. Midterm Exam | 90 | 36 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 122 | ||
| Total Workload / 25 (h) | 4,88 | ||
| ECTS | 5 ECTS | ||