COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Advanced Calculus II * MT   242 4 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
To comprehend fully the structure of and prove the properties of the real numbers analytically which were used in MT131 and MT 132 . Thus, equipped with the basic infrastructure of real-analysis, the student is able to comprehend advamced abstract concepts of analysis.
Content
Limit, continuity, derivatives in functions. Sequences and series of functions.

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 Limits of functions and properties. Reading the relevant pages from sources
2 Limit theorems Reading the relevant pages from sources
3 Continuous functions and properties. Reading the relevant pages from sources
4 Continuous functions on intervals. Reading the relevant pages from sources
5 Uniform continuity Reading the relevant pages from sources
6 Continuity of Monotone and inverse functions Reading the relevant pages from sources
7 Derivative, differential. Reading the relevant pages from sources
8 Mid-term exam Review topics discussed in the lecture notes and sources
9 The mean value theorem and its applications Reading the relevant pages from sources
10 Taylor's theorem and its applications Reading the relevant pages from sources
11 Sequences and series of functions Reading the relevant pages from sources
12 Pointwise and uniform convergence, applications Weierstrass M-test Reading the relevant pages from sources
13 Changing the order of limit in sequences of functions Reading the relevant pages from sources
14 Relationship between the derivative of the limit and the limit of the derivatives in sequences of functions Reading the relevant pages from sources
15 Power series Reading the relevant pages from sources
16-17 Final exam Review topics discussed in the lecture notes and sources

Recommended or Required Reading
TextbookIntroduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert
http://math.cu.edu.tr/Dersler/MT242/MT242.htm
Additional Resources
Principles of Mathematical Analysis, Walter Rudin