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Information
| Code | MK108 |
| Name | General Mathematics |
| 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 | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
| Course Instructor |
1 2 |
Course Goal / Objective
Mathematical and physical quantities are calculated with integral or series.
Course Content
Sequences and series, convergent, divergent series, definite and indefinite integral, area, volume and arc length with rectangular and polar coordinates.
Course Precondition
None
Resources
Analize Giriş Cilt II , Authors: Fikri Akdeniz, Yusuf Ünlü, Doğan Dönmez
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Students who successfully complete this course, Calculate limits of sequences. |
| LO02 | Decide whether or not an infinite series convergent. |
| LO03 | Express functions as infinite series. |
| LO04 | Identify different curves. |
| LO05 | Draw different curves. |
| LO06 | Compute indefinite integrals. |
| LO07 | Calculate definite integrals. |
| LO08 | Calculate 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 | Bilgi - Kuramsal, Olgusal | Relates his/her knowledge in the field of chemistry to life and industry by relying on his/her knowledge | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Evaluates the developments in the world by following and perceiving the orientations in the industry. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Gains awareness of lifelong learning and renews his/her knowledge. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Access to information and associate their knowledge with other fields of science. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the need to combine information in the application of information and perceives the total quality awareness. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | S/he has knowledge in the use of resources, in the creation of technology depending on the country's resources. | 4 |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | S/he conveys what s/he knows to people close or distant to the subject by concretising. | 4 |
| PLO08 | Yetkinlikler - Öğrenme Yetkinliği | Gains the ability to access new information and technology. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Learns to think creatively and produce solutions to problems in the field. | 5 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | To be able to associate information by having the ability of reasoning and transfer what they know to practice. | 5 |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Sets up laboratory equipment and makes decisions alone. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | To be able to follow the current technology in the field of chemistry and gain added value. | |
| PLO13 | Bilgi - Kuramsal, Olgusal | Follows the developments, gains the ability to follow the directions in the field. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Knowing information sharing and participating in teamwork and directing the team. | 5 |
| PLO15 | Beceriler - Bilişsel, Uygulamalı | Gains universal thinking and critical perspective. | 5 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Starts to have a say in the field. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sequences, Limits. Limit theorems, infinite limits. Monotone convergence theorem. Subsequences. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Convergence of the series, the n-th term test, geometric series, p-series, Comparison, Limit Comparison, Ratio and Root Tests. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Power series, radius of convergence, power series term term Differentiation theorem, Taylor and McLaurin series, Binomial theorem. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Polar Coordinates. Some of the important curves. Curve drawings. The slope of the tangent formula. Parameterized curves. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | The Indefinite Integral definition, properties. Variable change and partial Integration. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Integration of some trigonometric functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Integration of some algebraic functions with variable change and reduction formulas. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Integration of Rational Functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Special trigonometric and algebraic integrals. Definition and properties of the definite integral. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Fundamental theorems of differential calculus. Change of variables formula. Improper integrals. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Convergence of improper integrals. Integral test. Cartesian and polar coordinates and area calculation. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Calculate the volume with Disk and cylindrical layers method. Arc length. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Surface area of revolution. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Finding the center of gravity. Pappus formula. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and Problem Solving | 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 | ||