TÜRKÇE
ENGLISH
Information
| Code | MT131 |
| Name | Calculus I |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 4-2 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 5 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ ARSLAN ÖZKURT |
| Course Instructor |
Prof. Dr. ALİ ARSLAN ÖZKURT
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course to define the concepts of limit, continuity and derivative using properties of real numbers and solve maximum and minimum problems using these concepts. Approximate computation with a prescribed error.
Course Content
Real Numbers and their properties. Functions. Limit, continuity. Properties of continuous functions. Derivative and its applications. Sketching graphs. Finding Maxima and minima. Logarithm, exponential functions, hyperbolic functions. Inverse trigonometric and inverse hyperbolic functions. L Hospital s Rule and Taylor s Theorem with remainder.
Course Precondition
Pre-requisites None
Resources
http://math.cu.edu.tr/Dersler/MT131/MT131.htm
Notes
Analize Giriş Cilt I ; Fikri Akdeniz, Yusuf Ünlü, Doğan Dönmez
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Expresses theorems related to limits. |
| LO02 | Defines continuity and expresses related theorems |
| LO03 | Solves problems using some of the properties of continuous functions. |
| LO04 | Defines and computes derivatives. |
| LO05 | Computes some irrational numbers approximately. |
| LO06 | Finds the maximum and minimum of functions of one variable and sketches their graphs. |
| LO07 | Knows logarithmic, exponential, trigonometric and Arc-trigonometric functions. |
| LO08 | Solves applied maximum and minimum problems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 2 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 3 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Numbers, rational and real numbers. Order. Absolute Value, number line, Intervals, inequalities. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 2 | Functions, Finding the domain and range. Composition, inverse function, graphs. trigononmetric functions. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 3 | Limit of a function of one variable, Limit theorems, One sided limits | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 4 | Infinite limits, Indefinite forms, limits at infinity, Continuity | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 5 | Limit criterion, Intermediate Value and Maximum-Minimum Theorems. Types of discontinuity. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 6 | Derivative, slope of the tangent. Rules of differentiation. Chain Rule | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 7 | Higher order derivatives, Implicit differentiation. Differential and approximation using differential. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Rolle s Theorem, Mean Value Theorem. Finding maxima and minima. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 10 | First derivative Test, Second derivative and convexity. Second derivative test. Asymptotes. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 11 | Graphing. Solving applied maxima and minima problems. Derivative of the inverse function. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 12 | Logarithm function, properties of the logarithm | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 13 | Exponential function. Properties of the exponential function. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 14 | Trigonometric and inverse trigonometric functions. Hyperbolic functions, inverse hyperbolic functions. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 15 | L Hospital s rule and Taylor s Theorem with remainder. Applications. | Studying the relevant parts of the textbook and problem solving | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 16 | Term Exams | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 6 | 84 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 192 | ||
| Total Workload / 25 (h) | 7,68 | ||
| ECTS | 8 ECTS | ||