TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING PR. (ENGLISH) | |
| Code | YZZ101 |
| Name | Mathematics I |
| Term | 2025-2026 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Label | BS Basic Science Courses C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. Ayşe Gül KAPLAN |
| Course Instructor |
Prof. Dr. YILMAZ DURĞUN
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to provide students with a mathematical background by teaching them the necessary information about relations, functions, limits, continuity and derivatives.
Course Content
In this course, real numbers, their properties, functions, limits, continuity, basic properties of continuous functions, derivatives and their applications, graphing, maximum and minimum calculations, logarithms, exponential functions, inverse trigonometric functions, and L'Hospital's Rule are covered.
Course Precondition
None
Resources
Ayşe Peker Dobie, Matematik I Çözümlü Problemleri
Notes
Kenneth A. Ross, Elementary Analysis:The Theory of Calculus, Springer –Verlag(1980) . Calculus and Analytic Geometry, Sherman K. Stein, Anthony Barcellos.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes number sets. |
| LO02 | Recognizes functions. |
| LO03 | Calculates the limit of functions. |
| LO04 | Calculates the derivative of functions. |
| LO05 | Draws graphs of functions. |
| LO06 | Recognize the properties of functions. |
| LO07 | Recognizes special functions. |
| LO08 | Calculates the Taylor formula. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | It provides a broad range of knowledge about fundamental Computer Science concepts, algorithms and data structures. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learns basic computer topics such as software development, programming languages, and database management. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understands advanced computing fields such as data science, artificial intelligence, and machine learning. | |
| PLO04 | Belirsiz | Learn about topics such as computer networks, cyber security, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops skills in designing, implementing and analyzing algorithms. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gains the ability to use different programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learns data analysis, database management and big data processing skills. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Gains practical experience by working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthens collaboration and communication skills within the team. | 4 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | It provides a mindset open to technological innovations. | 3 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourages continuous learning and self-improvement competence. | 3 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Develops the ability to solve complex problems. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sets and operations on sets, sets of numbers. | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Inequalities, absolute value. | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Relations, functions, special functions. | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Limit | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 5 | Continuity | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Definition of derivative, derivative rules | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Rolle's Theorem, Mean Value Theorem | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 8 | Mid-Term Exam | Repetition and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Graphing functions | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 10 | Properties of exponential and logarithmic functions and drawing their graphs. | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Properties of trigonometric and hyperbolic functions | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Properties of inverse trigonometric functions | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Properties of inverse hyperbolic functions | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | L'Hospital rule | Review of relevant pages in resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 15 | Taylor formula. | Repetition and Problem Solving | Öğretim Yöntemleri: Problem Çözme, Soru-Cevap, Tartışma |
| 16 | Term Exams | Repetition and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Repetition 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 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 26 | 26 |
| Total Workload (Hour) | 136 | ||
| Total Workload / 25 (h) | 5,44 | ||
| ECTS | 5 ECTS | ||