TÜRKÇE
ENGLISH
Information
| Code | TLZ201 |
| Name | Math III |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. LEYLA BUGAY |
| Course Instructor |
Doç. Dr. DİLEK KAHYALAR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Diferansiyel denklemlere giriş, Diferansiyel denklemlerin tanımı ve sınıflandırılması
Course Content
Diferansiyel denklemlere giriş, Diferansiyel denklemlerin tanımı ve sınıflandırılması
Course Precondition
Basic knowledge of derivatives and integrals is required.
Resources
Differentiel Equuations, L.Shipley Ross Differentiel Equuations, Frank Ayres Differential Equations, Lester R. Ford
Notes
Diferansiyel Denklemler ve Uygulamaları, mehmet Aydın, Gönül Gündüz,Beno Kuryel
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes some differential equations. |
| LO02 | Recognizes first order differantial equations. |
| LO03 | Recognizes exact differantial equations. |
| LO04 | Recognizes linear differantial equations. |
| LO05 | Recognizes and solves Cauchy - Euler equations. |
| LO06 | Recognizes to find the solution of certain differantial equations by using Laplace transformations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has sufficient background in the fields of Mathematics, Science and Textile Engineering | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Uses the knowledge obtained from the basic sciences and engineering in the field of textile engineering | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Does process analysis, Identifies problems, interprets and evaluates data in the field of textile engineering | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Selects and uses modern techniques and tools for engineering applications | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Has the skills of designing experiments, data collection, cognitive analysis and interpretation of the results | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Works effectively both individually and as a team member and takes responsibility | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Searches literature, has access to information, uses databases and other sources of information | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Recognizes the need of lifelong learning; follows developments in science and technology and renews self continuosly | 3 |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has effective oral and written communication skills. | 4 |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Follows developments in the field in a foreign language, has good communication skills with colleagues. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and softwares at a required level | 1 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Defines learning requirements in scientific, social, cultural and artistic areas and improves himself/herself accordingly. | 2 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Has the professional and ethical responsibility. | 2 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the necessary awareness on the fields of occupational health and safety, legal side of engineering applications and environmental health. | 2 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Has required competence in project management, entrepreneurship and innovation. | 1 |
| PLO16 | Bilgi - Kuramsal, Olgusal | An ability to identify, formulate, and solve complex engineering problems by selecting appropriate analysis and modeling methods. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Differential equations and their solutions | Required readings | |
| 2 | Classification of differential equations | Required readings | |
| 3 | Initial value problemsand existence of their solutions | Required readings | |
| 4 | Exact differential equations and integrating factor | Required readings | |
| 5 | Seperable equations and equations reducible to this form | Required readings | |
| 6 | Linear equations and Bernoulli equations | Required readings | |
| 7 | To find the solution of the linear differantial equations with higher order | Required readings | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | |
| 9 | The homogeneous linear equations with constant coefficients | Required readings | |
| 10 | The method of undetermined coefficients | Required readings | |
| 11 | Variations of parameters | Required readings | |
| 12 | Cauchy - Euler equations | Required readings | |
| 13 | System of linear differantial equations | Required readings | |
| 14 | Laplace transformations | Required readings | |
| 15 | Basic properties of Laplace transformations | Required readings | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||