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 Comprehend science and advanced mathematics subjects fundamental to engineering; An ability to apply knowledge of mathematics, science, and engineering to solve civil engineering problems X
2 An ability to analyze and model civil engineering systems specific problems, identify and define the appropriate requirements for their solutions. X
3 An ability to design, implement and evaluate a civil engineering systems, component, process or program that meets specified requirements.
4 Use the techniques, skills, and modern tools of engineering effectively and correctly in engineering practice
5 An ability to gather/acquire, analyze, interpret data and make decisions to understand civil engineering problems
6 An ability to work effectively in inter- and in-disciplinary teams or individually.
7 An ability to communicate effectively in Turkish and English.
8 Recognition of the need for, and the ability to access information, to follow recent developments in science and technology and to engage in life-long learning.
9 An understanding of professional, legal, ethical and social issues and responsibilities related to computer engineering.
10 Skills in project and risk management, awareness about importance of entrepreneurship, innovation and long-term development, and recognition of international standards and methodologies.
11 An understanding about the impact of Civil  Engineering solutions in a global, environmental, societal and legal context while making decisions.

#### 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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