Lesson plan / MATHEMATICS-I

Lesson Information

Course Credit 4.0
Course ECTS Credit 7.0
Teaching Language of Instruction Türkçe
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
Instructor (s)
Course Assistant

Purpose and Content

The aim of the course Give fundamental conceptions of mathematical analysis and the functions limit,continuity, derivative and applications of derivative. To learn limits, continuity and differentiation in single-valued functions.Do the applications of differentiation.Give an ability to apply knowledge of mathematics on engineering problems.
Course Content Fundamental conceptions 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 ve logarithmic functions, limit of single-valued functions, properties of limit, 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 implicit differentiation, 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 basic properties.
4Trigonometric and inverse trigonometric functions, trigonometric equalities,trigonometric equations.
5Exponential ,logarithmic functions and fundamental properties, exponential ve logarithmic equations, exponential ve 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.
9Midterm Exam.
10Derivatives of trigonometric and inverse trigonometric, exponential , logarithmic and special defined functions functions, implicit differentiation. Higher 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 est,asymptotes, curve sketching.
14Applied optimization problems, conic sections and quadratic equations, polar coordinates.

Resources

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

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

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

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.