TÜRKÇE
ENGLISH
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 | 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. | 4 |
| 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. | |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Modeling problems related to biomedical engineering. | |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Analyzing data and interpreting the results. | 4 |
| 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. | 4 |
| 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. | |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Expressing ideas verbally and in writing, clearly and concisely. | 4 |
| 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 | 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 | ||