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Information
| Code | BMM104 |
| Name | Calculus II |
| Term | 2024-2025 Academic Year |
| Semester | 2. 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 |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
1 2 |
Course Goal / Objective
To teach the student the topics of infinite series, functions of several variables, multiple integrals and integral theorems, which are the main topics of engineering mathematics, in a functional integrity.
Course Content
Integral applications, volumes and areas of surfaces of revolution, arc length. Parametric equations and curves, polar coordinates. Infinite sequences and series, convergence tests, power series, Taylor and Maclaurin series, approximation with Taylor polynomials. Functions of several variables, partial derivatives. Double and triple integrals, change of variables, integrals over polar coordinates. Surface area, line integrals, Green theorem, surface integrals, divergence theorem, Stokes theorem.
Course Precondition
No
Resources
Calculus and Analytic Geometry, Sherman K. Stein, Anthony Barcellos.
Notes
Analize Giriş Cilt II, Doğan Dönmez, Yusuf Ünlü, Fikri Akdeniz
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Analyzes infinite series in conjuction with convergence and divergence concepts |
| LO02 | Derives the Taylor-Maclaurin expansion of a given function. |
| LO03 | Calculates and comments on the partial derivatives of multivariable functions. |
| LO04 | Calculates multiple integrals, line and surface integrals |
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. | 4 |
| 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. | |
| 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. | 4 |
| 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. | 4 |
| 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. | 4 |
| 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 | Integral applications, arc length, volume and surface area calculation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Parametric curves | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Polar coordinates, polar curves | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Infinite series, convergence tests | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Convergence tests (continued) | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 6 | Taylor and Maclaurin expansions, Taylor approximation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Gösterip Yaptırma |
| 7 | Introduction to multivariable functions, partial derivatives and the chain rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Double integrals over general regions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 10 | Triple integrals, change of variables in multiple integrals | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Double and triple integrals in polar coordinates | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Surface area calculation, line integrals | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Surface integrals, Greens theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 14 | Stokes and Divergence theorems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | FINAL | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
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 | ||