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Information
| Code | G101 |
| Name | Mathematics I |
| Semester | 1. 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 Goal
Understands basic properties of limit, continuity and derivation, and use them in drawing the graphs of functions, making approximate calculation and problem solving.
Course Content
Sets and number sets, Functions, Limits, derivation and rule of derivation, Drawing graphs of functions.
Course Precondition
none
Resources
Analize Giriş , Doğan Dönmez
Notes
Analize Giriş , Doğan Dönmez
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines the limit and expresses the properties of the limit. |
| LO02 | Defines the continuity and refers to some of the theorems |
| LO03 | Solves the problem by using some of the properties of continuous functions. |
| LO04 | Defines and calculates derivation. |
| LO05 | Makes approximate calculations of some numbers through derivation. |
| LO06 | Finds minimums and maximums of univariant functions and draws graphs. |
| LO07 | Solves practical problems. |
| LO08 | Finds the limits through LHospital rule. |
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 | Numbers. Rational and real numbers. Ranking. Absolute value. Number axis. Spacing. Inequalities. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Functions. Finding Definition and Value Sets. Transactions related to the functions and function types. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Ascending, descending functions. Reverse function. Graphics. Off functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Trigonometric functions. Problem-solving. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Limit of functions of one variable. Properties of limits. One-sided limits. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Limits are endless. Limits at infinity. Continuity. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Continuous functions from their properties. Problem-solving. Derivatives, slope of the tangent. Rules of differentiation. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The chain rule. Higher-order derivatives. Derivative of inverse functions. Physical meaning of the derivative. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | The inverse trigonometric functions and their derivatives. Problem-solving. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Rolles Theorem, Mean Value Theorem. Maximum, minimum detection. 1. and 2. Derivative test . | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | The second derivative and convexity. Asymptotes. Graphic design. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Maximum and minimum problems. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Exponential and logarithmic functions. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Uncertainties and LHopitals rule. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, 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 | 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 | ||