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Information
| Code | BMM103 |
| Name | Calculus I |
| Semester | 1. 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 Goal
To teach the student the topics of limit, derivative and integral, which are the main topics of engineering mathematics, in a functional integrity.
Course Content
Introduction to the types of functions and drawing of graphics. Limit. Derivative, definition of the derivative, geometric and physical interpretation of the derivative. Definition of integral, indefinite and definite integral calculation.
Course Precondition
Yok
Resources
Calculus and Analytic Geometry, Sherman K. Stein, Anthony Barcellos.
Notes
Analize Giriş Cilt I, Doğan Dönmez, Yusuf Ünlü, Fikri Akdeniz
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Identifies every function, draw their graphics. |
| LO02 | Comprehends the limit concept and evaluates limits. |
| LO03 | Grasps the geometical and physical meaning of derivative, writes the derivative definition, defines the derivative rules based on this definition, evaluates the derivative of any function. |
| LO04 | Defines definite integral, evaluates indefinite integrals using appropriate methods. |
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. | 5 |
| 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. | 3 |
| 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. | 5 |
| 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 | Introduction to functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Limit concept, limit definition | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Limit at infinity, infinity as a limit, continuity | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Tangent problem, derivative definition | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Derivative rules, derivatives of trigonometric functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Chain rule, higher order derivatives, implicit differentiation | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Curve sketching, applied optimization problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 9 | Area problem, definite integral and its properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Fundamental Theorem of Calculus, indefinite integral, substitution rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Exponential and logarithmic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Inverse trigonometric functions, indeterminate limits and LHospital rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Integration by parts, trigonometric integrals, trigonometric substitution | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Integration of rational functions, rationalizing substitutions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, 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 | ||