Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH251

Course Name:

Analysis 1

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Prof. Dr. ŞÜKRÜ YALÇINKAYA

Course Lecturer(s):

Dr. Öğr. Üyesi İlker Savaş Yüce

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to generalize the results of calculus developed for certain types of classical functions to more general functions so that we can state and solve problems of some other areas of mathematics.
Course Content:	The content of the course consists of structural results needed to generalize the results of calculus to more general functions.

Learning Outcomes

The students who have succeeded in this course;
1) will be able to distinguish the Completeness axiom by understanding its consequences such as Monotone Convergence, Bolzano-Weierstrass and Heine-Borel Theorems.
2) will be able to use the definitions of continouos and uniform continouos functions and /or their sequential characterizations to prove their properties.
3) will be able to use the definition and the properties of a differentiable function.
4) will be able to understand the Riemann integrability of a bounded function on a bounded interval by means of Darboux sums and the Fundamental Theorems.
5) will be able to distinguish between pointwise and uniform convergence of the sequences of functions.

Course Flow Plan

Week	Subject	Related Preparation
1)	Real numbers, field and order properties, completeness
2)	Real numbers, field and order properties, completeness
3)	Countable and uncountable sets, metric spaces, compact sets
4)	Convergence in Metric spaces, connected sets,
5)	Numerical sequences, convergence, subsequences, Cauchy sequences, liminf, limsup
6)	"Series, ratio and root tests, power series, absolute convergence, addition and multiplication of series "
7)	Continuous functions, intermediate and extreme value theorems
8)	Midterm Exam
9)	Differentiation, mean value theorems, higher derivatives,
10)	Taylor theorem, L'Hospital's theorem
11)	Riemann-Stieltjes integral, properties of the integral
12)	Fundamental theorem of calculus, applications
13)	Uniform Continuity and uniform convergence,
14)	Arzela-Ascoli and Stone-Weierstrass theorems.

Sources

Course Notes / Textbooks:	W. Rudin: Principles of Mathematical Analysis
References:	T. Apostol: Mathematical Analysis

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	3

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	6		78
Application	13	0			0
Study Hours Out of Class	13	0	8		104
Midterms	1	0	25		25
Final	1	0	35		35
Total Workload					242