|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 Coordinator||Prof.Dr. Gonca AYIK|
Using Riemann integrability criteria, Recognize integrable functions,Using Fundamental theorem of calculus, using Darbox theorem, using inverse and implicit function theorem
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.
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|Textbook||Principle 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.