COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Real Analysis * MT   332 6 3 3 5

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. Gonca AYIK
Instructors
Prof.Dr.GONCA AYIK1. Öğretim Grup:A
Prof.Dr.GONCA AYIK2. Öğretim Grup:A
 
Assistants
Goals
Using Riemann integrability criteria, Recognize integrable functions,Using Fundamental theorem of calculus, using Darbox theorem, using inverse and implicit function theorem
Content
Riemann integral, Properties of Riemann integral, Fundamental theorem of calculus, Integral as a limit, improper integral, uniform convergence, intercahange of limits, Inverse and implicit function theorem.

Learning Outcomes
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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
X
10
Uses effective scientific methods and appropriate technologies to solve problems
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.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Reimann Integral Review of the relevant pages from sources
2 Reimann integrability Review of the relevant pages from sources
3 Integrable functions Review of the relevant pages from sources
4 Solving problem Review of the relevant pages from sources
5 Properties of Riemann integral Review of the relevant pages from sources
6 Integrability of continuous and monotone functions. Review of the relevant pages from sources
7 Fundamental theorem of calculus Review of the relevant pages from sources
8 Mid-term exam Review and problem solving
9 Taylor´ s formula Review of the relevant pages from sources
10 Darboux theorem Review of the relevant pages from sources
11 Improper Integral Review of the relevant pages from sources
12 Functions of several variables Review of the relevant pages from sources
13 Inverse function theorem Review of the relevant pages from sources
14 Implicit function theorem Review of the relevant pages from sources
15 Implicit function theorem Review of the relevant pages from sources
16-17 Final exam Review and problem solving

Recommended or Required Reading
TextbookPrinciple of Mathematical Analysis,Walter Rudin,McGraw-Hill, 1976.
Analiz I,II, Erdal Coşkun, Alp Yayınevi, 2002.
Introduction To Real Analysis , Robert G. Bartle, Donald R. Bartle,Wiley, 1992.
Additional Resources