ÇAĞ UNIVERSITY
FACULTY OF ARTS AND SCIENCES
Learning Outcomes of the
Course
Code
Course Title
Credit
ECTS
MAT 411
Real Analysis
3 (3-0)
5
Prerequisites
None
Language of Instruction
Mode of Delivery
Face to face
English
Type and Level of Course
Compulsory/4.Year/Fall Semester EQF- Level 6
Lecturers
Name(s)
Contacts
Lecture Hours
Office Hours
Course Coordinator Asist. Prof..Dr. Ayfer Kurt
[email protected]
Th:9-12
Mon. &Th. 14-16
Others
Course Objective
To investigate the fundamental concepts of analysis for real functions of a single variable,
including properties of real numbers,sequences and series,continuity and limits,
differentiation, integration
Relationship
Students who have completed the course successfully should
be able to
Prog. Output
Net Effect
1
demonstrate to do mathematical analysis dealing with the set of
1, 3, 7, 9
3, 4, 4, 5
real numbers.
2
relate the real analysis to complex analysis
1, 3, 9
4, 4, 5
3
obtain analytical skills to be able to prove theories related with
2, 3, 9
4, 5, 5
analytic properties of real functions, sequences including
convergence and smoothness
4
comprehend the concepts related with theory of real numbers
1, 3
5, 4
5
1, 3
5, 5
comprehend in comparison of real analysis and complex
analysis
Course Description: The analysis of the set of real numbers. Analytic properties of real functions,
limits,continuity and sequences including convergence and smoothness.
Course Contents:( Weekly Lecture Plan )
Weeks
Topics
Preparation
Teaching Methods
1
Lectures
Preliminaries sets and functions.
Textbook Ch.1
2
Lectures
Mathematical induction, finite and infinite sets
Textbook Ch.1
3
Lectures
The algebraic and order properties of R,
Textbook Ch.2
absolute value and real line
4
Lectures
The completeness property of R, applications
Textbook Ch.2
of the supremum property
5
Lectures
Sequences and their limits, limit theorems,
Textbook Ch.3
Monotone sequences
6
Lectures
Sequences and their limits, limit theorems,
Textbook Ch.3
Monotone sequences
7
Lectures
Subsequences and the Bolzano-Wierstrass
Textbook Ch.3
Theorem
8
The Cauchy Criterion, properly divergent
Lectures
sequences, introduction to infinite series
Textbook Ch.3
9
Lectures
Limits of functions,
Textbook Ch.4
10
Lectures
Limit theorems.
Textbook Ch.4
Some Extensions of the Limit Concept.
11
Lectures
Textbook Ch.4
12
Lectures
Continuous functions, combinations of
Textbook Ch.5
continuous functions
13
Lectures
Continuous functions on intervals
Textbook Ch.5
14
Lectures
Uniform continuity, continuity, monotone and
Textbook Ch.5
Inverse Functions.
Textbook
Related links
Recommended Reading
Material Sharing
REFERENCES
Bartle, Robert G. and Sherbert, Donald R. (2000). Introduction to Real Analysis (3
ed.). New York: John Wiley and Sons. ISBN 0-471-32148-6.
http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml
Dangello, Frank and Seyfried, Michael (1999). Introductory Real Analysis. Brooks
Cole. ISBN 978-0395959336
Activities
Midterm Exam
Quizzes
Homework
Effect of The Activities
Effect of The Final Exam
Contents
Hours in Classroom
Hours out Classroom
Homeworks
Quizzes
Midterm Exam
Fieldwork
Final Exam
Number
1
ASSESSMENT METHODS
Effect
40%
Notes
40%
60%
ECTS TABLE
Number
14
14
Hours
3
4
Total
42
56
1
20
20
1
30
Total
Total / 30
ECTS Credit
RECENT PERFORMANCE
30
148
148/30=4,80
5