TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF ENGINEERING |
| BIOMEDICAL ENGINEERING PR. | |
| Code | BMM301 |
| Name | Advanced Engineering Mathematics 3 |
| Term | 2026-2027 Academic Year |
| Semester | 5. 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 | Prof. Dr. MUTLU AVCI |
| Course Instructor |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
The aim of this course is to teach advanced mathematical methods used in biomedical engineering applications. Students are expected to apply topics such as Fourier analysis, complex analysis, numerical methods, optimization, and stochastic processes to biomedical signal processing, imaging, and modeling problems.
Course Content
Fourier series and transforms, complex numbers and complex analysis, integral transforms, numerical solution methods, matrix decompositions, optimization techniques, stochastic processes, and mathematical modeling in biomedical signal and image processing applications.
Course Precondition
None
Resources
• Kreyszig, E. – Advanced Engineering Mathematics. • Boyce & DiPrima – Elementary Differential Equations and Boundary Value Problems. • Bracewell, R. – The Fourier Transform and Its Applications. • Bronzino, J. – Biomedical Engineering Handbook. • Strang, G. – Linear Algebra and Its Applications.
Notes
Short Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Apply Fourier transforms to biomedical signals. |
| LO02 | Use complex analysis methods in engineering problems. |
| LO03 | Apply numerical methods to differential equations. |
| LO04 | Use optimization techniques in biomedical engineering problems. |
| LO05 | Perform biomedical system analysis using mathematical modeling. |
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. | 4 |
| 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. | 3 |
| 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. | 3 |
| 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. | |
| 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. | |
| 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 | Sufficient knowledge in the disciplines of anatomy and physiology | |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | Ability to perform measurements on living systems and to interpret the data collected from these measurements. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Solving problems related to the interaction of living organisms with materials and systems, and interpreting the outcomes. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to engineering mathematics and biomedical applications. | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Fourier series | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Fourier transform and biomedical signal processing | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Advanced applications of the Laplace transform | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Complex numbers and analytic functions | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Complex integrals and the residue theorem | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Numerical linear algebra and matrix decompositions | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Reading lecture materials | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Interpolation and regression methods | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Numerical differential equation solutions | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Fundamental concepts of optimization | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Linear and nonlinear optimization | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Probability distributions and stochastic processes | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Markov chains and biological systems | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Mathematical methods for biomedical image processing. | Reading lecture materials | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Reading lecture materials | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Reading lecture materials | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 5 | 5 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 24 | 24 |
| Total Workload (Hour) | 125 | ||
| Total Workload / 25 (h) | 5,00 | ||
| ECTS | 5 ECTS | ||