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Information
| Code | BMM103 |
| Name | Calculus I |
| Term | 2024-2025 Academic Year |
| 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 Instructor |
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
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 | 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. | 3 |
| 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 | Introduction to functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 2 | Limit concept, limit definition | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 3 | Limit at infinity, infinity as a limit, continuity | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 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, Gösterip Yaptırma |
| 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, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 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, Alıştırma ve Uygulama |
| 10 | Fundamental Theorem of Calculus, indefinite integral, substitution rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Gösterip Yaptırma |
| 11 | Exponential and logarithmic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 12 | Inverse trigonometric functions, indeterminate limits and LHospital rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 13 | Integration by parts, trigonometric integrals, trigonometric substitution | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Gösterip Yaptırma |
| 14 | Integration of rational functions, rationalizing substitutions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 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 | ||