COURSE SYLLABUS

ANALYSIS I

1	Course Title:	ANALYSIS I
2	Course Code:	İMT1007
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	10
8	Theoretical (hour/week):	4
9	Practice (hour/week) :	2
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Dr. Ögr. Üyesi BAHTİYAR BAYRAKTAR
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	E-mail: bbayraktar@uludag.edu.tr, İş Tel: +90(224) 294 22 98. Adres: UÜ, Eğitim Fakültesi, İlköğretim Bölümü, Matematik Eğitimi Anabilim Dalı, 16059 Görükle / BURSA
18	Website:
19	Objective of the Course:	The purpose of the course is to be able to examine development of limit, differential and integral calculus of theoretical structure in univariate functions and to gain skills in its interpreting.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Ability to define concept of progressions, concept of approach, concept of convergent and divergent sequences, concept of zillion and infinitesimal;
2	Ability to explain limit, continuity and differentiation concepts of univariate functions.;
3	Ability to explain limit, continuity, discontinuity and differentiation concepts of univariate functions.;
4	Ability to do examination of limit calculations and determination of continuity of function;
5	According to elementary functions, their reverses, definitions of closed and parametric function derivatives ability to calculate with formulas.;
6	Ability to solve derivative tasks( problem solving, analysis and graph drawing of function);
7	Ability to interpret concept of differential of a function. Ability to use concept of differential in tasks related with approach calculations.;
8	Ability to use rule of L'Hospital in limit calculations. Ability to make Taylor extension of functions.;

22	Course Content:

Week	Theoretical	Practical
1	Progressions. Basic definitions and examples. Monotone progressions. Examples. Convergent, divergent progressions and their geometric meanings. Limited sequences. Zillion and Infinitesimal progressions. General theorems about sequences and practice tasks.	Determination of characters of progressions. Examination of convergence of sequences. Practice of theorems.
2	Limit conception of univariate functions and its practice. Perfect limits. Limit calculation techniques.	Limit calculation
3	Types of continuity and discontinuity. Properties of continuous functions	Examination of continuity of functions.
4	Concept of derivative in univariate functions. Geometrical and physical interpretation of derivative. Rules of derivation. Features of derivation.	Derivative calculations according to the definition of derivative. Derivative calculations.
5	Derivate of functions given in the form of closed and parametric ones. Derivative of inverse and compound functions.	Derivative calculations.
6	Differential of function and its practice.	Differential of the function and its practice
7	Midterm exam	Midterm exam
8	High-ordered derivatives. Finite theorem of Taylor	Practice of Taylor's formula.
9	Theorem of Role and Average Value Theorem. L'Hospital rule and limit calculations according to this rule.	L'Hospital rule and limit calculations according to this rule.
10	Practice for derivative: Ascending and descending intervals of function. Concavity direction of a curve. Bending points. Asymptotes. Extreme points of function.	Extreme points of function and absolute extrema points. Maximum and minimum problems.
11	Practice for derivative: Ascending and descending intervals of function. Concavity direction of a curve. Bending points. Asymptotes. Extreme points of function.	Extreme points of function and absolute extrema points. Maximum and minimum problems.
12	Absolute extreme points of a function. Maximum and minimum problems.	Maximum and minimum problems.
13	Analyse of function and graphic drawing. Examples	Analyse of function and graphic drawing
14	Analyse of function and graphic drawing. Examples	Analyse of function and graphic drawing

23	Textbooks, References and/or Other Materials:	1. Prof. Dr. Ahmet A. KARADENIZ High Mathematics. Volume 1, 2nd, 4th Edition, 1985. 2. Professor. Mustafa BAYRAKTAR Introduction analysis I, II. 2nd Edition, 2008. 3. Prof. Dr. Mustafa BALCI, Analysis 1.2. 7.Edition, 2008. 4. Assoc. Dr. Ahmet TEKCAN, Advanced Analysis. DORA 2010.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	4	56
Practicals/Labs	14	2	28
Self Study and Preparation	13	8	104
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	10	10
Others	0	0	0
Final Exams	1	12	12
Total WorkLoad			210
Total workload/ 30 hr			7
ECTS Credit of the Course			7

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

	PQ1	PQ3	PQ4	PQ5	PQ6	PQ7	PQ8
LO1	5	5	3	5	5	4	2
LO2	5	5	4	5	5	5	2
LO3	5	5	3	5	3	4	2
LO4	5	5	3	5	3	5	2
LO5	5	5	4	5	5	5	2
LO6	5	5	4	5	5	4	2
LO7	5	5	4	5	5	3	2
LO8	5	5	4	5	4	3	2

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High