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Information
| Unit | FACULTY OF ENGINEERING |
| BIOMEDICAL ENGINEERING PR. | |
| Code | BMM104 |
| Name | Calculus II |
| Term | 2021-2022 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
(Bahar)
(A Group)
(Ins. in Charge)
|
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
Resources
Notes
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. | 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. | 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. | 3 |
| 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. | 3 |
| 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. | 3 |
| 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 | Integral applications, arc length, volume and surface area calculation | Review of the relevant pages from sources | |
| 2 | Parametric curves | Review of the relevant pages from sources | |
| 3 | Polar coordinates, polar curves | Review of the relevant pages from sources | |
| 4 | Infinite series, convergence tests | Review of the relevant pages from sources | |
| 5 | Convergence tests (continued) | Review of the relevant pages from sources | |
| 6 | Taylor and Maclaurin expansions, Taylor approximation | Review of the relevant pages from sources | |
| 7 | Introduction to multivariable functions, partial derivatives and the chain rule | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | |
| 9 | Double integrals over general regions | Review of the relevant pages from sources | |
| 10 | Triple integrals, change of variables in multiple integrals | Review of the relevant pages from sources | |
| 11 | Double and triple integrals in polar coordinates | Review of the relevant pages from sources | |
| 12 | Surface area calculation, line integrals | Review of the relevant pages from sources | |
| 13 | Surface integrals, Greens theorem | Review of the relevant pages from sources | |
| 14 | Stokes and Divergence theorems | Review of the relevant pages from sources | |
| 15 | FINAL | Review of the topics discussed in the lecture notes and sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||