TÜRKÇE
ENGLISH
Information
| Code | TMT123 |
| Name | Mathemetics 1 |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 3-1 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NERGİZ POYRAZ |
| Course Instructor |
Emrah KORKMAZ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The objective of this course is to enable students to acquire competency in doing calculus computations. In the field of calculus, the primary methodologies employed for the examination and characterization of functions are limits, derivatives, and integrals. These tools will be utilized by students to address application problems across a wide range of disciplines, including physics, biology, business, and economics.
Course Content
Equations and inequalities, Functions and graphs, Limits and continuity, Derivatives, Applications of derivatives, Anti-derivatives and integrals
Course Precondition
There is no prerequisite for this course.
Resources
Calculus 1, Professor George Brinton Thomas Jr.
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Solve algebraic equations and inequalities. |
| LO02 | Recognize and graph polynomial, rational and trigonometric functions. |
| LO03 | Calculate limits of functions and indefinite forms (using the L'Hopital rule). |
| LO04 | Use the rules for computing derivatives and be familiar with the definition of derivatives and tangent line. |
| LO05 | Find the maximum and minimum of a function using derivatives. |
| LO06 | Apply derivatives to determine monotinicity and concavity and graph functions. |
| LO07 | Apply derivatives to real world problems. |
| LO08 | Understand the concept of indefinite integral as antiderivative. |
| LO09 | Comprehend standard indefinite integrals and basic rules of indefinite integral. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Beceriler - Bilişsel, Uygulamalı | Adequate ability to use of mathematics, science and Agricultural Machinery and Technologies engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields in complex engineering problems | 3 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Gains ability of defining, formulating and solving problems in the fields of Agricultural Machinery and Technologies Engineering, choosing and applying appropriate analysis and modeling methods for this purpose. | 3 |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | Gains ability of how to design a complex system, process, device or product related to the engineering field, under realistic constraints and conditions, in other words, by considering the available possibilities and the current state of the field, and to apply modern design methods for this purpose. | 1 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Gains ability of developing, selecting and using modern tools necessary for the analysis and solution of complex problems encountered in Agricultural Machinery and Technologies Engineering applications and to use information technologies effectively. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Gains ability to design experiments, conduct experiments, field studies, collect data, analyze and interpret results in order to examine the complex problems or discipline-specific research issues encountered in the field of Agricultural Machinery and Technologies Engineering. | |
| PLO06 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It carries out studies related to its field independently, and acts as a consultant, audit and expert. | |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to work effectively in disciplinary and multi-disciplinary teams; gains the ability to work individually. | |
| PLO08 | Yetkinlikler - Öğrenme Yetkinliği | Gains ability to write effective reports in the field, to understand written reports, to prepare design and production reports, to make effective presentations, to take and give clear and understandable instructions. | |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Awareness of the necessity of lifelong learning; gains a positive attitude towards accessing information, following developments in science and technology, and continuous innovation. | |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | It is sensitive to the events/developments on the agenda of the society and the world and monitors these developments, prepares projects, produces and shares solution suggestions. | |
| PLO11 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Follows the information in the field and communicates with colleagues by using a foreign language at least at the beginner level. | |
| PLO12 | Yetkinlikler - Alana Özgü Yetkinlik | Knowledge of business practices related to engineering, such as project management, risk management and change management; awareness of entrepreneurship, innovation; gains knowledge about sustainable development. | |
| PLO13 | Yetkinlikler - Alana Özgü Yetkinlik | Knowledge of the effects of engineering practices on health, environment and safety in universal and social dimensions and the problems reflected in the field of engineering; gain awareness of the legal consequences of engineering solutions. | |
| PLO14 | Yetkinlikler - Alana Özgü Yetkinlik | Acts in accordance with ethical principles, professional and ethical responsibility, and standards used in engineering practices |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Inequalities and Absolute Values | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Functions; Domain and Range Sets | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Types of Functions: Linear, Polynomial and Rational Functions | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Types of Functions: Trigonometric, Increasing-Decreasing and Odd-Even Functions | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Limits: Limit of a Function and Precise Definition of Limit | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Limits: Calculating Limits Using the Limit Laws. One-sided Limits. Infinite Limits and Limits at Infinity | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Continuity: Continuity of a Function at a Point. Continuous Functions. Types of Discontinuous | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Derivative: Introducing the Derivative. The Derivative as a Function. Rules of Differentiation | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Derivative: Derivatives of Trigonometric Functions. Derivatives as Rates of Change | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Derivative: The Chain Rule, Implicit Differentiation | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Applications of Derivatives: Maxima and Minima. Mean Value Theorem | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Applications of Derivatives: Graphing Functions. Optimization Problems | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Applications of Derivatives: L’Hôpital’s Rule | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Anti-Derivatives and Indefinite Integral | Studying from source books and lecture notes. | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Term Exams | 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 | 1 | 1 | 1 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 123 | ||
| Total Workload / 25 (h) | 4,92 | ||
| ECTS | 5 ECTS | ||