COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Advanced Calculus I * MT   241 3 4 4 7

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Doğan DÖNMEZ
Instructors
Prof.Dr.ALİ ARSLAN ÖZKURT1. Öğretim Grup:A
Prof.Dr.ALİ ARSLAN ÖZKURT2. Öğretim Grup:A
 
Assistants
Goals
The student who has learned the analytical techniques in general in the MT131 and MT 132 courses, will learn the structure of real numbers with all their proofs in this course. Thus, the student will be provided with the basic background of real-analytic concepts and will be able to comprehend the concepts of advanced analysis.
Content
Induction, Real Numbers, Sequences, Series.

Learning Outcomes
-


Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Induction and inequalities Required readings
2 Algebraic and order properties of real numbers Required readings
3 Completeness property of real numbers Required readings
4 Consequences of completeness property Required readings
5 Topology of real numbers Required readings
6 Convergence and limits of sequences Required readings
7 Limit theorems for sequences. Required readings
8 Mid-term exam Review of topics discussed in the lecture notes and sources
9 Monotone sequences and properties. Required readings
10 Subsquences and the Bolzano-Weierstrass Theorem Required readings
11 Cauchy sequences and completeness in terms of Cauchy sequences of real numbers Required readings
12 Divergent sequences and their properties. Required readings
13 Infinite series and convergence Required readings
14 Convergence tests for series with positive terms Required readings
15 Conditional convergence, absolute convergence and convergence tests Required readings
16-17 Final exam Review of topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookTemel Gerçel Analiz I ,A. Nesin, Nesin Matematik Köyü, Calculus, M. Spivak, Türk Matematik Vakfı Yayınları
Additional Resources
Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert
Principles of Mathematical Analysis, Walter Rudin
http://math.cu.edu.tr/Dersler/MT241/MT241.htm