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Information
| Code | TMT132 |
| Name | Mathematics II |
| Term | 2024-2025 Academic Year |
| Semester | 2. 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 |
1 2 |
Course Goal / Objective
Calculation of mathematical and physical quantities by integral or series sum
Course Content
Array and series, convergent, divergent series, definite and indefinite integral, Area, volume and arc length in orthogonal and polar coordinates.
Course Precondition
There is no prerequisite for this course.
Resources
Lecture presentations
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Calculates Array Limits. |
| LO02 | Decides whether infinite series are convergent. |
| LO03 | Expresses functions as an infinite series. |
| LO04 | Defines and draws different curves. |
| LO05 | Calculates the indefinite integral. |
| LO06 | Calculates definite integrals. |
| LO07 | Finds Area, Volume, Arc Length Surface area and center of gravity using definite 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 | 4 |
| 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. | 1 |
| 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 | Arrays, Limit. Limit theorems, infinite limits. Sub Arrays | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Convergence of series, Geometric series, Comparison, Limit Comparison, Ratio and Root Tests | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Power series, Convergence radius, Taylor and MacLaurin series, Binomial Theorem | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Polar Coordinates. Some important Curves. Curve drawings. The slope of the tangent formula | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Indefinite Integral definition and properties. Variable Substitution and Partial Integration | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Integrating trigonometric functions | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Integration of algebraic functions with substitution and reduction formulas | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Mid-term Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Integrating Rational Functions | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Trigonometric and Algebraic integrals. Definite integral definition and properties | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Fundamental theorems of Differential-Integral calculus. Variable replacement formula | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Finding area in perpendicular and polar coordinates | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Volume finding. Arc-length of a curve | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Rotational surface area | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Finding the center of gravity | Reviewing literature | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Term Exam | 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 | ||