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. 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 Arş.Gör.Dr. EMRE KİŞİ 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 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. X
2 Ability to identify formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. X
3 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues, according to the nature of the design.)
4 Ability to devise, select, and use modem techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5 Ability to design and conduct experiments, gather data analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11 Knowledge about the global and social effects of engineering practice on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

#### 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

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(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
Quiz 2 12 24
Assignment 1 15 15
Performance Task (Laboratory) 0 0 0
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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