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Information
| Code | BMM201 |
| Name | Advanced Engineering Mathematics 1 |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. MUSTAFA KEREM ÜN |
| Course Instructor |
Doç. Dr. MUSTAFA KEREM ÜN
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To teach the student differential equations which is among the fundamental topics of applied mathematics
Course Content
First order ordinary differential equations, separation of variables, exact differentials, integrating factors, higher order equations, methods of undetermined coefficients and variation of parameters, power series solution of differential equations, differential equation systems, Laplace transform
Course Precondition
None.
Resources
Elementer Diferansiyal Denklemler ve Sınır Değer Problemleri - W. Boyce, R. DiPrima
Notes
Differential Equation - H. Phillips
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Categorizes a given ordinary differential equation and proposes a method for its solution |
| LO02 | Solves a first order equation |
| LO03 | Solves a constant-coefficient, linear, higher order equation and a system of constant-coefficient linear equations |
| LO04 | Finds the power series solution to a given linear, non-constant-coefficient equation. |
| LO05 | Solves a linear equation using Laplace transform. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have sufficient knowledge in mathematics, natural sciences, and biomedical engineering, along with the ability to use theoretical and applied knowledge in these areas to solve complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquire the ability to identify, formulate, and solve complex Biomedical Engineering problems; for this purpose, will have the ability to choose and apply appropriate analysis and modeling methods. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | The ability to design a complex system, process, device, or product in Biomedical Engineering under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | The ability to select and use modern techniques and tools necessary for analyzing and solving complex problems encountered in Biomedical Engineering applications; the ability to use information technologies effectively. | 5 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics in Biomedical Engineering. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | The ability to work effectively in intra-disciplinary (Biomedical Engineering) and multi-disciplinary teams; ability to work individually. | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | The ability to communicate effectively verbally and in writing; knowledge of at least one foreign language; ability to write effective reports in Biomedical Engineering and understand written reports, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Get awareness of the necessity of lifelong learning; the ability to access information in the field of Biomedical Engineering, to follow developments in science and technology, and the ability to constantly self-renewal. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Acting following ethical principles, professional and ethical responsibility in the field of Biomedical Engineering, and knowledge of the standards used in engineering practice. | 2 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Knowledge of project management and practices in the field of Biomedical Engineering, such as risk management and change management; awareness about entrepreneurship, innovation, and sustainable development. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understanding the universal and societal impacts of Biomedical Engineering applications on health, environment, and safety; awareness of the legal implications of Biomedical Engineering solutions. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Understanding of biology and physiology. | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Ability to make measurements on living systems and interpret data collected from these measurements. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Ability to solve problems related to the interactions between living and nonliving materials and systems. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to ordinary differential equations (ODE) | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | First order ODEs, seperation of variables, physical applications. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | First order ODEs, exact differentials | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | First order ODEs, integrating factors | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | General first order linear ODEs | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Second order ODEs, solution of constant coefficient, homogeneous equations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Methods of undetermined coefficients and variation of parameters | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Higher order ODEs | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Solution of systems of ODEs | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Solution of systems of ODEs (continued) | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Solution with power series. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Laplace transform | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Laplace transform - 2 | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Review | Review of the topics discussed in the lecture notes and sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Review of the entire course material, solving exercise questions | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the entire course material, solving exercise questions | Ölçme Yöntemleri: Yazılı Sınav |
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 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 10 | 10 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 96 | ||
| Total Workload / 25 (h) | 3,84 | ||
| ECTS | 4 ECTS | ||