Computer Engineering (English)

Lesson plan / CALCULUS-I

Lesson Information

Course Credit 4.0
Course ECTS Credit 7.0
Teaching Language of Instruction İngilizce
Level of Course Bachelor's Degree, TYYÇ: Level 6, EQF-LLL: Level 6, QF-EHEA: First Cycle
Type of Course Compulsory
Mode of Delivery Face-to-face
Does the course require compulsory or optional work experience? Z
Course Coordinator Prof. Dr. RAFET AKDENİZ
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course Discuss the basic notions of mathematical analysis, sets, number sets, properties of single-valued functions and limits, continuity and derivative in single-valued functions, and the applications of derivative. Help students apply mathematics in solving problems in the field of engineering.
Course Content Basic notions of mathematical analysis, sets and number sets, induction, rectangular coordinate system, relation, inverse relation, functions, types of functions, special defined functions, trigonometric and inverse trigonometric, exponential and logarithmic functions, limits of single-valued functions, properties of limits, continuity of single-valued functions, properties of continuous functions, limits at infinity, derivative of single-valued functions, geometric and physical meaning of the derivative, theorems on derivatives, rules of derivative, chain rule, derivatives of trigonometric and inverse trigonometric, exponential, logarithmic and special defined functions, higher order derivatives, Rolle’s Theorem, Mean Value Theorem, Cauchy’s Theorem, L’Hospital ‘s Rule, indeterminate forms, Newton’s Method, applications of derivative, the first derivative test, extreme values, concavity, the second derivative test, asymptotes, curve sketching, applied optimization problems, conic sections and quadratic equations, polar coordinates

Weekly Course Subjects

1Sets, set operations, number sets, intervales, absulute value, induction
2Cartesian product of sets, rectangular coordinate system, relation, inverse relation, functions and its properties
3Types of functions, operations with functions, inverse function, composite function, special defined functions and their basic properties
4Trigonometric and inverse trigonometric functions, trigonometric equalities, trigonometric equations
5Exponential, logarithmic functions and fundamental properties, exponential and logarithmic equations, exponential and logarithmic inequalities
6Rate of change, concept of limit, limit of single-valued functions and basic properties, theorems of limit
7Concept of continuity, continuity of single-valued functions and basic properties, properties of continuous functions, limits at infinity
8Newton quotient, concept of derivative, derivative of single-valued functions, geometric and physical meaning of the derivative, theorems on derivatives, rules of derivative, chain rule
9Derivatives of trigonometric and inverse trigonometric, exponential, logarithmic and special defined functions, implicit differentiation. Midterm Exam.
10Higher order derivatives, Rolle’s Theorem, Mean Value Theorem, Cauchy’s Theorem
11L’Hospital ‘s Rule, indeterminate forms, Newton’s Method
12Applications of derivative, the first derivative test, extreme values
13Concavity, the second derivative test, asymptotes, curve sketching
14Applied optimization problems, conic sections and quadratic equations, polar coordinates

Resources

1- G.B Thomas, M.D.Weir, J.Hass and F.R.Giordano,Thomas’ Calculus, 11th Edition, Addison-Wesley, 2005.

2- Mustafa Balcı,Genel Matematik I,Balcı Yayınları,Ankara,2008.

3- Mustafa Bayraktar, Analize Giriş I(2.Baskı) , Grafiker Yayınları,Ankara,2007.

4- Speigel, M. R., Çeviri Editörü: H. H. Hacısalioğlu, İleri Matematik, 6. Baskı, McGraw-HILL, Schaum’s Outline Series, NY., Ankara Üniversitesi,1997.

5- Ahmet Dernek, Genel Mat ematik, 3. Baskı, Nobel Yayın Dağıtım Tic. Ltd. Şti. Ankara,2009.