|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 Coordinator||Prof.Dr. Doğan DÖNMEZ|
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.
Limit, continuity, derivatives in functions. Sequences and series of functions.
|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||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|
|Textbook||Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert|
Principles of Mathematical Analysis, Walter Rudin