TÜRKÇE
ENGLISH
Information
| Code | IMZ101 |
| Name | Mathematics 1 |
| Semester | 1. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ HAMZA TANRIKULU |
Course Goal
Teaching the concepts of limit and derivative and their applications in engineering
Course Content
Calculus and Engineering Applications
Course Precondition
Yok
Resources
1. STEWART, J., Kalkülüs Diferansiyel ve İntegral Hesap Kavram ve Kapsam. Türkiye Bilimler Akademisi, Ankara, 990 s.
Notes
Calculus books
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Students will learn using the concepts of limit, continuity and differetation of one variable functions. |
| LO02 | Students will learn sketching the graph of a function using asymptotes, critical points and the derivative test for increasing/decreasing and concavity properties. |
| LO03 | Students will learn setting up and solving max/min problems. |
| LO04 | Students will learn evaluating definite integrals by using the Fundamental Theorem of Calculus and evaluating areas, volumes and arc lenghts by mean of definit integral. |
| LO05 | Students will learn applying techniques of integration and working with transcendental functions. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has the basic knowledge of math, science and civil engineering | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has a good commman of basic concepts, theories and principles in civil engineering. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Independently reviews and learns the applications, makes a critical assessment of the problems faced with, selects the proper technique to formulate problems and propose solutions | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Designs a system, a component or a process in order to meet the needs of various engineering problems within technical, economic, environmental, manufacturability, sustainability limitations. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Selects and uses the modern techniques and tools necessary for engineering practice | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Designs and carries out experiments in the fields of civil engineering, and interprets the results and the data obtained from the experiments | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Gains the abiltiy to work effectively as a member in interdisciplinary teams | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Identifies proper sources of information and databases, reaches them and uses them efficiently. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Follows the advancements in science and technology being aware of the necessity of lifelong learning and continuously improves her/himself. | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Uses the computers and information technologies related with civil engineering actively. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Gains the ability to communicate effectively both orally and in writing. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Communicates using technical drawing | |
| PLO13 | Bilgi - Kuramsal, Olgusal | Constantly improves her/himself by identifying the training needs in scientific, cultural, artistic and social fields. | |
| PLO14 | Bilgi - Kuramsal, Olgusal | Continuously improves her/himself by defining necessities in learning in scientific, social, cultural and artistic areas besides the occupational requirements. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Has an understanding of entrepreneurship and innovation subjects, and is knowledgeable of contemporary issues. | 2 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Has an awareness of professional and ethical responsibility | |
| PLO17 | Bilgi - Kuramsal, Olgusal | Has the required knowledge in project management, workplace practices, employee health, environmental and occupational safety; and the legal implications of engineering applications. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Real Numbers, Real Axis, inequalities, absolute value, Cartesian coordinates, graph an equation or inequality | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 2 | Functions, Functions Chart, Single and Dual Functions, Composite Functions, Partial Functions | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 3 | Trigonometric functions, Addition Formulas, Sine and Cosine Rule | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 4 | Informal definition of Limit, Limit of a Function, Limit Rules, One-Sided Limits | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 5 | Limit of polynomial and rational functions, Infinity Limit, Limit at infinity | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 6 | Continuity at a point, right and left continuity, Continuity at an interval, Continuous Functions | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 7 | Derivatives, Tangent Line and Instant Speed Problem, Rate of Change of a Function | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Power Rule, Other Derivative Rules, Derivatives of composite functions, Chain rule | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 10 | Implicit Differentiation, Higher Order Derivatives, Higher Order Derivatives of Implicit Functions | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 11 | One-to-One Functions, Inverse Functions, Inverse Functions Properties, Inverse trigonometric functions | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 12 | Exponential Function, Exponential Function Rules, Logarithm function, Logarithm rules, Exponential and Logarithm Functions Derivatives, 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, Concavity of a function, Inflection Points, Oblique asymptote, Graph Drawing | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 15 | Maximum and Minimum Problems, Indeterminate Forms, Hospital Rule | Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Exam | Ölçme Yöntemleri: Performans Değerlendirmesi |
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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||