Course Name Code Semester T+U Hours Credit ECTS
Mathematics I MAT 111 1 4 + 0 4 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Course Coordinator Doç.Dr. SELMA ALTUNDAĞ
Course Lecturers 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, Prof.Dr. METİN YAMAN, Prof.Dr. MEHMET ÖZEN, Prof.Dr. REFİK KESKİN, Dr.Öğr.Üyesi MEHMET GÜNER, Prof.Dr. MEHMET ALİ GÜNGÖR, Dr.Öğr.Üyesi EMRE KİŞİ, Dr.Öğr.Üyesi AYNUR ŞAHİN, Arş.Gör.Dr. TUĞBA PETİK, İBRAHİM ÖZGÜR,
Course Assistants

Research Assistants in mathematics department

Course Category Available Basic Education in the Field
Course Objective

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

Course Content

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

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. , , , , , , , ,
2 He/she recognizes functions and its properties. , , , , ,
3 He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) , , , , ,
4 He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. , , , , ,
5 He/she defines right and left approached limit. Knows the undetermined conditions. , , , , ,
6 He/she defines the concept of continuity and discontinuity. , , , , , ,
7 He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. , , , , ,
8 Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. , , , , ,
9 He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. , , , , , ,
10 Defines the increasing and decreasing functions with the help of tangent and normal equations. , , , , , , ,
11 Can calculate the limit of undetermined conditions with the help of derivatives. , , , , ,
12 Can define the maximum, minimum and asymptote of functions. , , , , , , ,
13 Expresses the curve plot. , , , , ,
14 Solves the engineering problems with the help of derivative and approximates with differential approach. , , , , , ,
Week Course Topics Preliminary Preparation
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.
Resources
Course Notes <p>Lecture Notes</p>
Course Resources

[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.

Order Program Outcomes Level of Contribution
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.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
1. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6