TÜRKÇE
ENGLISH
Information
| Code | CKZ117 |
| Name | Mathematics 1 |
| Term | 2024-2025 Academic Year |
| 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Öğr. Gör. NECLA ÖZTELLI |
| Course Instructor |
Dr. Öğr. Üyesi İhsan ULUOCAK
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this lecture is to equip students with the knowledge of basic engineering mathematics and applications of this information to teach the Mechanical Engineering
Course Content
Introduction to the concepts of function, limit, continuity, derivatives, definition of differentials and their geometrical understanding and applications (increasing and decreasing functions, and searching the turning points, maximum and minimum points). Introduction to exponential, logarithmic, hyperbolic and inverse trigonometric functions and their derivatives, definite integrals and their uses compose the context of this lecture.
Course Precondition
None
Resources
BALCI, M., 1999. General Mathematic
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understand the relationship between engineering and mathematics. |
| LO02 | Recognize all kinds of functions and draws their graphs. |
| LO03 | Define the limit concept and makes the limit calculations. |
| LO04 | Understand and define the geometric and physical meaning of the derivative and define the derivative rules based on this definition. |
| LO05 | Calculates the derivative of all functions. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Student become equipped with the basic knowledge of math, science and engineering | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Students gain a command of basic concepts, theories and principles in chemical engineering | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Students are able to design and carry out experiments in the basic fields of chemical engineering, and interpret the results and the data obtained from the experiments | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Students become equipped with a variety of skills and knowledge regarding engineering techniques | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Students are able to design a system, component or process in order to meet the needs of various engineering problems within technical, economic, environmental, manufacturability, and sustainability limits. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Students independently review and learn the applications in an enterprise, make a critical assessment of the problems faced with, formulate problems and propose solutions by selecting the proper technique | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Students take initiative in identification, design, development and use of a product or production process | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Students become aware of the necessity of lifelong learning and continuously self-renew | 3 |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students use Turkish effectively for technical or non-technical topics orally or in wirtten form, and at least one foreign language | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students become effective in using computer, computer-aided drafting, design, analysis, and presentation | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Students have good communicatino skills with a tendency to work in teams, and are able to work effectively as a member of an interdisciplinary team | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | Students become aware of the technical and ethical responsibilities, as well as being inquisitive and innovative |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Real Numbers | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 2 | Real Numbers Axis, Inequalities, Absolute Value, Cartesian Coordinates, Graph of Equation or Inequality | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 3 | Trigonometric Functions, Collection Formulas, Sine and Cosinus Rule | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Limit, Limit of a function, Limit rules and limitation, One-Way Limits | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 5 | Limit of Polynomial and Rational Functions, Infinite Limit, Infinite Limit | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 6 | Continuity at a Point, Continuity at a Range, Continuity, Continuous Functions | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 7 | Derivative, Tangent Accurate and Instantaneous Speed Problem, The Ratio of Variation of a Function | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 8 | Mid-Term Exam | Exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Force Rule, Other Derivative Rules, Derivative of Compound Functions, Chain Rule | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 10 | Derivatives of Closed Functions, Higher Order Derivatives, Higher Order Derivatives in Closed Functions | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 11 | One to One Functions, Inverse Functions, Properties of Inverse Functions, Inverse Trigonometric Functions | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Exponential Function, Exponential Function Rules, Logarithm Function, Logarithm Rules, Derivatives of Exponential and Logarithm Functions, Logarithmic Derivative | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Hyperbolic Functions, Inverse Hyperbolic Functions, Increasing and Descending Functions, Extreme Values of a Function | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | First Derivative Test, Second Derivative Test, Twist Point of a Function, Twist Points, Oblique Asymptot, Graphical Drawing | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 15 | Maximum and Minimum Problems, Uncertain Shapes, L' Hospital Rule | Read the related topics in the lecture notes and reference books | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 16 | Term Exams | Exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Exam preparation | 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 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 3 | 3 |
| Final Exam | 1 | 3 | 3 |
| Total Workload (Hour) | 118 | ||
| Total Workload / 25 (h) | 4,72 | ||
| ECTS | 5 ECTS | ||