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Information
| Code | CMZ123 |
| Name | Mathematics I |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 6 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 |
Doç. Dr. ZİYAFER GİZEM PORTAKAL
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Teaching limit and derivative concepts and their applications in engineering
Course Content
Higher Mathematics and their Engineering Applications
Course Precondition
None
Resources
Analize Giriş Cilt II Prof. Dr. Fikri AKDENİZ Prof.Dr. Yusuf ÜNLÜ
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Students will learn to use the concepts of limit, continuity and derivative in one variable functions. |
| LO02 | Students will learn to draw graphs of functions, asymptotes, critical points, decreasing / increasing properties and concave. |
| LO03 | Students will learn to set up maximum minimum problems and solve them by using derivatives. |
| LO04 | Students will learn to calculate the area, volume and length by using the Basic Theorem of the integral Calculator and calculating the specific integral and using the specific integral. |
| LO05 | Students will learn to apply transcendent functions and integral techniques. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Becomes equipped with adequate knowledge in mathematics, science, environment and engineering sciences | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Becomes able to apply theoretical knowledge in mathematics, science, environment and engineering sciences | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Determines, describes, formulates and gains capabilities in solving engineering problems | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Analyzes a system, components of the system or process, gains the designing capabilities of the system under the real restrictive conditions. | 5 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Chooses ans uses the ability to apply modern tools and design technics, suitable analytical methods, modeling technics for the engineering applications | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Designs and performs experiments, data collection, has the ability of analyzing results | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Works individually and in inter-disciplinary teams effectively | 5 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Becomes able to reach knowledge and for this purpose does literature research and to uses data base and other information sources | |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Becomes aware of the necessity of lifelong learning and continuously self renewal | |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Capable of effective oral and written skills in at least one foreign language for technical or non-technical use | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Effective use of Information and communication technologies | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Defines necessities in learning in scientific, social, cultural and artistic areas and improves himself/herself accordingly. | 1 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Professional and ethical responsibility | 4 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Project management, workplace practices, environmental and occupational safety; awareness about the legal implications of engineering applications | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes aware of universal and social effects of engineering solutions and applications, entrepreneurship and innovation and to have idea of contemporary issues |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Real Numbers, Real Numbers Axis, Inequalities, Absolute Value, Cartesian Coordinates, An Equation or Graph of Inequality | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 2 | Functions, Graph of Functions, Odd and Even Functions, Composite Functions, Partial Functions | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 3 | Trigonometric Functions, Addition Formulas, Sine and Cosinus Rule | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 4 | Limit, Limit of a Function, Limiting with Limit Rules, One Way Limits | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 5 | Limit of Polynomial and Rational Functions, Infinite Limit, Infinite Limit | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 6 | Continuity in One Point, Continuity from Right and Left, Continuity in One Range, Continuous Functions | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 7 | Derivative, Tangent Line and Instantaneous Velocity Problem, Rate of Change of a Function | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Force Rule, Other Derivative Rules, Derivative of Compound Functions, Chain Rule | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 10 | Derivative of Implicit Functions, Higher Order Derivatives, Higher Order Derivatives in Implicit Functions | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 11 | One-to-One Functions, Inverse Functions, Inverse Functions, Inverse Trigonometric Functions | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 12 | Exponential Function, Exponential Function Rules, Logarithm Function, Logarithm Rules, Derivatives of Exponential and Logarithm Functions, Logarithmic Derivative | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 13 | Hyperbolic Functions, Inverse Hyperbolic Functions, Increasing and Decreasing Functions, Extreme Values of a Function | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 14 | First Derivative Test, Second Derivative Test, Convexity of a Function, Bend Points, Oblique Asymptote, Graph Drawing | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 15 | Maximum and Minimum Problems, Undetermined Shapes, Hospital Rule | Lecture notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture notes | 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 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 152 | ||
| Total Workload / 25 (h) | 6,08 | ||
| ECTS | 6 ECTS | ||