TÜRKÇE
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Information
| Code | MMB101 |
| Name | Mathematics for Engineers 1 |
| 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 | Öğr. Gör. NECLA ÖZTELLI |
Course Goal
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
Yok
Resources
Lecture Notes
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 | Beceriler - Bilişsel, Uygulamalı | Understanding the fundamentals of Mechanical Engineering | 4 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Being well equipped with knowledge of Mathematics, Science and Basic Engineering | 4 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Having capability of designing and executing experiments; examining the results and data | 3 |
| PLO04 | Yetkinlikler - Öğrenme Yetkinliği | Being well equipped with various engineering techniques and skills | 1 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Being able to design a system ,a component or a process with taking into consideration the technical, economic, enviromental, sustainability limitations | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Ability to analyze the applications on a factory without any help, investigate the problems, formulizing and finding a proper solution for the problems | 2 |
| PLO07 | Yetkinlikler - Öğrenme Yetkinliği | Ability to design , developing getting ready for use of a product or manufacturing process | 1 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understanding the importance of life-time learning and being updated | 2 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Having advanced speaking and writing English skills | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Using Computer effectively; for computed aided design, analysis and illustrating | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Being prone to teamwork, well communication with others, adaptability to interdisciplinary teams | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Being aware of the technical and ethical responsibility, being curious and innovative | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Real Numbers, 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 |
| 2 | Functions, Graph of Functions, Single and Dual Functions, Compound Functions, Partial Functions | 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 | 3 | 42 |
| 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 128 | ||
| Total Workload / 25 (h) | 5,12 | ||
| ECTS | 5 ECTS | ||