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Information
| Code | MAT131 |
| Name | Mathematics - I |
| Term | 2024-2025 Academic Year |
| Semester | 1. Semester |
| Duration (T+A) | 4-2 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 5 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ |
| Course Instructor |
Doç. Dr. NAZAR ŞAHİN ÖĞÜŞLÜ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Defining the concepts of limit, continuity and derivative using properties of real numbers and solve maximum and minimum problems using these concepts.
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. LHospitals Rule and Taylors Theorem with remainder.
Course Precondition
No
Resources
Calculus and Analytic Geometry, Sherman K. Stein, Anthony Barcellos.
Notes
Analize Giriş Cilt I, Doğan Dönmez, Yusuf Ünlü, Fikri Akdeniz.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes number sets |
| LO02 | Recognizes functions |
| LO03 | Can calculate limit of functions |
| LO04 | Can calculate derivatives of functions |
| LO05 | Can draw graphs of functions |
| LO06 | Rocognizes properties of functions |
| LO07 | Recognizes special functions |
| LO08 | Calculate Taylor formula |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the essence fundamentals and concepts in the field of Statistics | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Emphasize the importance of Statistics in life | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Define basic principles and concepts in the field of Law and Economics | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Produce numeric and statistical solutions in order to overcome the problems | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use proper methods and techniques to gather and/or to arrange the data | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Utilize computer programs and builds models, solves problems, does analyses and comments about problems concerning randomization | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Apply the statistical analyze methods | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Make statistical inference (estimation, hypothesis tests etc.) | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Generate solutions for the problems in other disciplines by using statistical techniques and gain insight | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Discover the visual, database and web programming techniques and posses the ability of writing programs | |
| PLO11 | Beceriler - Bilişsel, Uygulamalı | Distinguish the difference between the statistical methods | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Make oral and visual presentation for the results of statistical methods | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have capability on effective and productive work in a group and individually | 4 |
| PLO14 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Professional development in accordance with their interests and abilities, as well as the scientific, cultural, artistic and social fields, constantly improve themselves by identifying training needs | 4 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Develop scientific and ethical values in the fields of statistics-and scientific data collection |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Sets, operation on sets, sets of number. | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Inequalities, absolute value | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 3 | Relations, functions and special functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Limit | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Gösterip Yaptırma, Alıştırma ve Uygulama |
| 5 | Continuity | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 6 | Definition of derivation and rule of derivations | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 7 | Rolle Theorem, The Mean Value Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review and problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Drawing graph of a function | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Gösterip Yaptırma |
| 10 | Exponential and logarithmic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 11 | Trigonometri ve hyperbolic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 12 | Properties of inverse trigonometric functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Properties of inverse hyperbolic functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Lhospital rule | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 15 | Taylor Formula | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, 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 | 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 | 18 | 18 |
| Final Exam | 1 | 36 | 36 |
| Total Workload (Hour) | 166 | ||
| Total Workload / 25 (h) | 6,64 | ||
| ECTS | 7 ECTS | ||