Ders Adı Kodu Yarıyıl T+U Saat Kredi AKTS
Mathematıcs I MAT 111 1 4 + 0 4 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili İngilizce
Dersin Seviyesi Lisans
Dersin Türü Zorunlu
Dersin Koordinatörü Doç.Dr. YALÇIN YILMAZ
Dersi Verenler Doç.Dr. SELMA ALTUNDAĞ, Prof.Dr. SOLEY ERSOY, Doç.Dr. MURAT SARDUVAN, Doç.Dr. MAHPEYKER ÖZTÜRK, Prof.Dr. MURAT GÜZELTEPE, Doç.Dr. MAHMUT AKYİĞİT, Doç.Dr. YALÇIN YILMAZ, Prof.Dr. HALİM ÖZDEMİR, Prof.Dr. REFİK KESKİN, Dr.Öğr.Üyesi MEHMET GÜNER, Prof.Dr. MEHMET ALİ GÜNGÖR, Doç.Dr. AYNUR ŞAHİN, Dr.Öğr.Üyesi HİDAYET HÜDA KÖSAL, Öğr.Gör.Dr. EMİNE ÇELİK,
Dersin Yardımcıları

Research Assistants in mathematics department

Dersin Kategorisi Alanına Uygun Temel Öğretim
Dersin Amacı

To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions

Dersin İçeriği

Foreknowledge, functions, Limit and continuity, Derivate, Application of derivative 

# Ders Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
2 He/she recognizes functions and its properties. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she defines right and left approached limit. Knows the undetermined conditions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 He/she defines the concept of continuity and discontinuity. Lecture, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
7 He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
8 Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
9 He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. Lecture, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
10 Defines the increasing and decreasing functions with the help of tangent and normal equations. Lecture, Question-Answer, Drilland Practice, Demonstration, Motivations to Show, Testing, Oral Exam,
11 Can calculate the limit of undetermined conditions with the help of derivatives. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam,
12 Can define the maximum, minimum and asymptote of functions. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
13 Expresses the curve plot. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam,
14 Solves the engineering problems with the help of derivative and approximates with differential approach. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam, Homework,
Hafta Ders Konuları Ön Hazırlık
1 Sets. Number sets. Equations. Equality and inequality.
2 Concept of function. Types of functions (Polynomial sets, rational function, exponential and logarithmic functions and the definition set of these functions)
3 Function types (Trigonometric, reverse trigonometric and hyperbolic functions, Partial functions , special defined functions (Absolute value, exact value, sign functions) .
4 Concept of limit and limit calculation with the definition of limit. Proof of the rules used for limit rule. Sandwich theorem. Limit of trigonometric functions.
5 Right and left limit. Undetermined conditions (0/0,infinity/infinity, 0.infinity, infinity-infinity,1^infinity)
6 Continuity concept in functions. Types of discontinuity and characteristics of continuous functions (Mid value theorem, absolute maximum and minimum, concept of local maximum and minimum.. )
7 Concept of derivative, and calculation with derivative rule. Proof of derivate with derivative rule. Derivative of reverse function.
8 Derivative of trigonometric and reverse trigonometric functions. Derivative of exponential and logarithmic functions. Derivative of hyperbolic and reverse hyperbolic functions
9 High order derivatives. Derivatives of functions with parametric equations. Derivative of implicit functions.
10 Equation of tangent and normal. Increasing and decreasing functions.
11 Undetermined conditions ( Analyses of 8 condition with L’hopital Rule )
12 Maximum, minimum and asymptote of functions.
13 Curve plotting.
14 Engineering problems. Approximation with differential.
Kaynaklar
Ders Notu <p>Lecture Notes</p>
Ders Kaynakları

[1] Thomas, G.B., Thomas Calculus, 11.baskı, çeviri:Recep Korkmaz, Beta Basım, 2010.

[2] Kadıoğlu, E., Kamali, M., Genel Matematik, Kültür Eğitim Vakfı, 2009.

[3] Can, M., Yüksek Matematik 1, Literatür, 2009.

[4] Balcı, M., Genel Matematik 1, Sürat Yayınları, 2012.

Hafta Dokümanlar Açıklama Boyut
2 Matematik I 2. Hafta 1. Ders 99,52 MB
0 Matematik I 2. Hafta 2. Ders 78,89 MB
0 Matematik I 1. Hafta 1. Ders 84,22 MB
0 Matematik I 1. Hafta 2. Ders 0 MB
0 Matematik I ve Matematik II Tüm videolar (youtube üzerinden) videoları sisteme yüklediğimde sistem içeriği göstermemektedir. Bu sebeple link paylaşıyorum 0 MB
3 Matematik I 3. Hafta 1. Ders 473,58 MB
7 Matematik I 7. Hafta 1. Ders 486,02 MB
Sıra Program Çıktıları Katkı Düzeyi
1 2 3 4 5
1 To have sufficient foundations on engineering subjects such as science and discrete mathematics, probability/statistics; an ability to use theoretical and applied knowledge of these subjects together for engineering solutions.
2 An ability to determine, describe, formulate and solve engineering problems; for this purpose, an ability to select and apply proper analytic and modeling methods,al background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations.
3 An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently.
4 An ability to analyze a system, a component or a process and design a system under real limits to meet desired needs; in this direction, an ability to apply modern design methods.
5 An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research.
6 Understanding, awareness of administration, control, development and security/reliability issues about information technologies.
7 An ability to work efficiently in multidisciplinary teams, self confidence to take responsibility.
8 An ability to present himself/herself or a problem with oral/written techniques and have efficient communication skills; know at least one extra language.
9 An awareness about importance of lifelong learning; an ability to update his/her knowledge continuously by means of following advances in science and technology.
10 Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society.
11 An understanding of project management, workplace applications, health issues of laborers, environment and job safety; an awareness about legal consequences of engineering applications.
12 An understanding universal and local effects of engineering solutions; awareness of entrepreneurial and innovation and to have knowledge about contemporary problems.
Değerlendirme Sistemi
Yarıyıl Çalışmaları Katkı Oranı
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
Toplam 100
1. Yıl İçinin Başarıya 50
1. Final 50
Toplam 100
AKTS - İş Yükü Etkinlik Sayı Süre (Saat) Toplam İş Yükü (Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Assignment 1 15 15
Quiz 2 12 24
Toplam İş Yükü 161
Toplam İş Yükü / 25 (Saat) 6,44
Dersin AKTS Kredisi 6