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Information
| Code | BMM201 |
| Name | Advanced Engineering Mathematics 1 |
| 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 Goal
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 | Scientific problems encountered in the field of medicine and medical technologies; the ability to solve problems by applying the technical approaches of mathematics, science and engineering sciences. | 5 |
| PLO02 | Yetkinlikler - Öğrenme Yetkinliği | To be able to improve oneself by embracing the importance of lifelong learning and by following the developments in science-technology and contemporary issues. | |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Assess the contributions of engineering solutions on medicine, medical technologies and healthcare. | |
| PLO04 | Yetkinlikler - Öğrenme Yetkinliği | Identifying problems related to biomedical engineering. | 5 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Modeling problems related to biomedical engineering. | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Analyzing data and interpreting the results. | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | To be able to use modern techniques and computational tools required for engineering applications. | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Ability to analyze and design a process in line with a defined goal. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To be able to understand the problems and wishes of the medical doctor in their scientific studies from an engineering point of view. | 2 |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Expressing ideas verbally and in writing, clearly and concisely. | |
| PLO11 | Yetkinlikler - Alana Özgü Yetkinlik | To be conscious of calibration and quality assurance systems in Biomedical Engineering. | |
| PLO12 | Beceriler - Bilişsel, Uygulamalı | Design and Implement Experiments. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to act independently, set priorities and creativity. | |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Being aware of national and international contemporary issues in the field of Biomedical Engineering. | |
| PLO15 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Ability to work in interdisciplinary teams. | |
| PLO16 | Yetkinlikler - Alana Özgü Yetkinlik | To have a sense of professional and ethical responsibility. |
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 | ||