TÜRKÇE
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Information
| Code | BBZ107 |
| Name | Mathematics I |
| Semester | 1. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GÜZİN YÜKSEL |
Course Goal
The main objective of the course is to make the students form a mathematical background by instructing required information about relation,function, limit, continuity, derivative.
Course Content
Limit and continuity. Derivatives. Using derivatives to find extrema. Sketching graphs, taking limits with derivatives. Single variable integration. Integration techniques and applications of integration. Geometry in R^3. Vector-valued functions.
Course Precondition
None
Resources
1.Lecture notes. 2. 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 | Learn some basic mathematical concepts and see examples of applications of these concepts. |
| LO02 | Learn methods of computation and develop their skills of computation. |
| LO03 | Get substantial experience to set up mathematical models for real- world problems from their area of interest and solve such problems. |
| LO04 | Students who believe that mathematics is a scary subject change this attitude after they complete this course and they gain self-confidence. |
| LO05 | Learn the preliminaries and build up their background for mathematical subjects that they will study in the following years. |
| LO06 | Students are convinced by examples of real-world applications that mathematics is really useful. |
| LO07 | Applies differentiation techniques and uses them in applied problems such as extreme value finding, curve drawing. |
| LO08 | Comprehends and applies basic integral techniques. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Gain comprehensive knowledge of fundamental concepts, algorithms, and data structures in Computer Science. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Learn essential computer topics such as software development, programming languages, and database management | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Understand advanced computer fields like data science, artificial intelligence, and machine learning. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Acquire knowledge of topics like computer networks, cybersecurity, and database design. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develop skills in designing, implementing, and analyzing algorithms | 5 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Gain proficiency in using various programming languages effectively | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Learn skills in data analysis, database management, and processing large datasets. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Acquire practical experience through working on software development projects. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Strengthen teamwork and communication skills. | 4 |
| PLO10 | Yetkinlikler - Alana Özgü Yetkinlik | Foster a mindset open to technological innovations. | 3 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Encourage the capacity for continuous learning and self-improvement. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Enhance the ability to solve complex problems | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Preliminaries, Special functions (summary). Limit and continuity. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Derivatives | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | Chain Rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 4 | Derivatives of inverse functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 5 | Applications of derivative: Related rates, maxima /minima | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Applications of derivative: Maxima/minima (continued), sketching graphs | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Applications of derivative: L'Hopital's Rule. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Introduction to integrals, Proper integrals, the Fundamental Theorem of Calculus | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 10 | Integration techniques: Substitution, trigonometric substitution | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Integration techniques: Integration by parts, partial fractions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Improper integrals, areas and volumes | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Vectors in R^3, dot and cross products | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Derivatives and integrals of vector-valued functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Gösterip Yaptırma, Anlatım, Alıştırma ve Uygulama |
| 15 | General problem solving | Review and problem solving | Öğretim Yöntemleri: Problem Çözme, Soru-Cevap, Tartışma |
| 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 | 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 | ||