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 Engineering graduates with sufficient knowledge background on science and engineering subjects of their related area, and who are skillful in implementing theoretical and practical knowledge for modelling and solving engineering problems. X
2 Engineering graduates with skills in identifying, describing, formulating and solving complex engineering problems, and thus,deciding and implementing appropriate methods for analyzing and modelling. X
3 Engineering graduates with skills in designing a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; for this purpose, skills in implementing modern design methods.
4 Engineering graduates with skills in developing, selecting and implementing modern techniques and tools required for engineering applications as well as with skills in using information technologies effectively.
5 Engineering graduates with skills in designing and conducting experiments, collecting data, analyzing and interpreting the results in order to evaluate engineering problems.
6 Engineering graduates who are able to work within a one discipline or multi-discipline team,as well as who are able to work individually
7 Engineering graduates who are able to effectively communicate orally and officially in Turkish Language as well as who knows at least one foreign language
8 Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology
9 Engineering graduates with well-structured responsibilities in profession and ethics
10 Engineering graduates having knowledge about practices in professional life such as project management, risk management and change management, and who are aware of innovation and sustainable development.
11 Engineering graduates having knowledge about universal and social effects of engineering applications on health, environment and safety, as well as having awareness for juridical 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
Assignment 1 15 15
Performance Task (Laboratory) 1 25 25
Toplam İş Yükü 162
Toplam İş Yükü /25(s) 6.48
Dersin AKTS Kredisi 6.48
; ;