Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MATHEMATICS I MAT 111 1 4 + 0 4 6
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü ZORUNLU Dersin Koordinatörü Doç.Dr. MURAT GÜZELTEPE Dersi Verenler Dr.Öğr.Üyesi İBRAHİM ÖZGÜR Prof.Dr. SOLEY ERSOY Doç.Dr. MURAT SARDUVAN Doç.Dr. MUSTAFA ERÖZ Doç.Dr. MAHPEYKER ÖZTÜRK Doç.Dr. İSMET ALTINTAŞ Doç.Dr. MURAT GÜZELTEPE Doç.Dr. MAHMUT AKYİĞİT Doç.Dr. YALÇIN YILMAZ Doç.Dr. METİN YAMAN Prof.Dr. MEHMET ÖZEN Prof.Dr. REFİK KESKİN Dr.Öğr.Üyesi MEHMET GÜNER Prof.Dr. MEHMET ALİ GÜNGÖR Doç.Dr. HÜSEYİN ALTUNDAĞ Arş.Gör.Dr. EMRE KİŞİ Doç.Dr. NESRİN GÜLER Dr.Öğr.Üyesi AYNUR ŞAHİN Arş.Gör. TUĞBA PETİK İBRAHİM ÖZGÜR Dersin Yardımcıları Research Assistants in mathematics department Dersin Kategorisi Genel Eğitim 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
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. 1 - 2 - 3 - 4 - 15 - A - B - C - 2 - He/she recognizes functions and its properties. 1 - 4 - 15 - A - C - 3 - He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) 1 - 4 - 15 - A - C - 4 - He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. 1 - 4 - 15 - A - C - 5 - He/she defines right and left approached limit. Knows the undetermined conditions. 1 - 4 - 15 - A - C - 6 - He/she defines the concept of continuity and discontinuity. 1 - 4 - 15 - A - B - C - 7 - He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. 1 - 4 - 15 - A - C - 8 - Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. 1 - 4 - 15 - A - C - 9 - He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. 1 - 4 - 15 - A - B - C - 10 - Defines the increasing and decreasing functions with the help of tangent and normal equations. 1 - 2 - 4 - 5 - 6 - A - B - 11 - Can calculate the limit of undetermined conditions with the help of derivatives. 1 - 2 - 15 - A - B - 12 - Can define the maximum, minimum and asymptote of functions. 1 - 2 - 4 - 15 - A - B - C - 13 - Expresses the curve plot. 1 - 2 - 15 - A - B - 14 - Solves the engineering problems with the help of derivative and approximates with differential approach. 1 - 2 - 15 - A - B - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 15:Problem Solving 5:Demonstration 6:Motivations to Show Ölçme Yöntemleri: A:Testing B:Oral Exam C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
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

Lecture Notes

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.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
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, X
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 X
3 An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently, X
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, X
5 An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research, X
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, X
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, X
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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

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