BMM104 Calculus II

5 ECTS - 4-0 Duration (T+A)- 2. Semester- 4 National Credit

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
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ (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

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

Update Time: 14.06.2024 03:39