TÜRKÇE
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Information
| Code | G152 |
| Name | Mathematics II |
| Term | 2024-2025 Academic Year |
| Semester | 2. Semester |
| Duration (T+A) | 3-0 (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 | Arş.Gör.Dr. AYŞE ÇOBANKAYA |
| Course Instructor |
1 2 |
Course Goal / Objective
Calculation of Mathematical and physical quantities through 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
Petrucci, R. H. xx Mathematics
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Can calculate limits of sequences. |
| LO02 | Can decide if the infinite series are convergent. |
| LO03 | Can express functions in infinite series. |
| LO04 | Identify and draw different curves. |
| LO05 | Calculate the indefinite integral. |
| LO06 | Calculate the definite integral. |
| LO07 | Can calculate area, volume, arc length, surface area and the center of gravity using the Definite Integral . |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Have sufficient knowledge in the fields of basic sciences (mathematics / science) and food engineering and the ability to use theoretical and applied knowledge in these areas in complex engineering problems. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Identifies, defines and solves complex engineering problems in applications in the fields of food engineering and technology. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Gains the ability to apply a complex system or process related to food products and production components using modern design methods under certain constraints and conditions. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Choosing and using modern technical tools necessary for analysis and solution of complex problems encountered in food engineering and technology applications; For this purpose, he/she uses information technologies. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Gaining laboratory skills for the analysis and solution of complex problems in the field of food engineering, designing an experiment, conducting an experiment, collecting data, analyzing and interpreting the results. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Takes responsibility individually and as a team member to solve problems encountered in food engineering applications. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Gains the ability to communicate verbally and in writing in Turkish / English related to the field of food engineering, to write reports, to prepare design and production reports, to present effectively and to use communication technologies. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Recognizing the necessity of lifelong learning and constantly improving himself/herself in the field of food engineering. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Gains the awareness of food legislation and management systems and professional ethics. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Using the knowledge of project design and management, he/she attempts to develop and realize new ideas about food engineering applications; have information about sustainability. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Has awareness about the effects and legal consequences of engineering practices related to food safety and quality on consumer health and environmental safety within the framework of national and international legal regulations. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sequences, Limits. Limit theorems, infinite limits. Monotone convergence theorem. Subsequences. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Convergence of the series, the n-th term test, geometric series, p-series, Comparison, Limit Comparison, Ratio and Root Tests. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Power series, radius of convergence, power series term term Differentiation theorem, Taylor and McLaurin series, Binomial theorem. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Polar Coordinates. Some of the important curves. Curve drawings. The slope of the tangent formula. Parameterized curves. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | The Indefinite Integral definition, properties. Variable change and partial Integration. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Integration of some trigonometric functions. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Integration of some algebraic functions with variable change and reduction formulas. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Integration of Rational Functions. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Special trigonometric and algebraic integrals. Definition and properties of the definite integral. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Fundamental theorems of differential calculus. Change of variables formula. Improper integrals. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Convergence of improper integrals. Integral test. Cartesian and polar coordinates and area calculation. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Calculate the volume with Disk and cylindrical layers method. Arc length. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Surface area of revolution. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Finding the center of gravity. Pappus formula. | Lecture Question-Answer | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Evaluation | Ölçme Yöntemleri: Performans Değerlendirmesi |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||