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Information
| Unit | FACULTY OF ENGINEERING |
| ENVIRONMENTAL ENGINEERING PR. | |
| Code | CMZ123 |
| Name | Mathematics I |
| Term | 2020-2021 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 |
| Label | C Compulsory |
| Mode of study | Uzaktan Öğretim |
| Catalog Information Coordinator | Prof. Dr. ZERRİN GÜL ESMERLİGİL |
| Course Instructor |
Prof. Dr. ZERRİN GÜL ESMERLİGİL
(Güz)
(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
Resources
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 | |
| 2 | Functions, Graph of Functions, Odd and Even Functions, Composite Functions, Partial Functions | Lecture notes | |
| 3 | Trigonometric Functions, Addition Formulas, Sine and Cosinus Rule | Lecture notes | |
| 4 | Limit, Limit of a Function, Limiting with Limit Rules, One Way Limits | Lecture notes | |
| 5 | Limit of Polynomial and Rational Functions, Infinite Limit, Infinite Limit | Lecture notes | |
| 6 | Continuity in One Point, Continuity from Right and Left, Continuity in One Range, Continuous Functions | Lecture notes | |
| 7 | Derivative, Tangent Line and Instantaneous Velocity Problem, Rate of Change of a Function | Lecture notes | |
| 8 | Mid-Term Exam | - | |
| 9 | Force Rule, Other Derivative Rules, Derivative of Compound Functions, Chain Rule | Lecture notes | |
| 10 | Derivative of Implicit Functions, Higher Order Derivatives, Higher Order Derivatives in Implicit Functions | Lecture notes | |
| 11 | One-to-One Functions, Inverse Functions, Inverse Functions, Inverse Trigonometric Functions | Lecture notes | |
| 12 | Exponential Function, Exponential Function Rules, Logarithm Function, Logarithm Rules, Derivatives of Exponential and Logarithm Functions, Logarithmic Derivative | Lecture notes | |
| 13 | Hyperbolic Functions, Inverse Hyperbolic Functions, Increasing and Decreasing Functions, Extreme Values of a Function | Lecture notes | |
| 14 | First Derivative Test, Second Derivative Test, Convexity of a Function, Bend Points, Oblique Asymptote, Graph Drawing | Lecture notes | |
| 15 | Maximum and Minimum Problems, Undetermined Shapes, Hospital Rule | Lecture notes | |
| 16 | Term Exams | - | |
| 17 | Term Exams | - |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | ||