|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 Coordinator||Prof.Dr. Doğan DÖNMEZ|
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.
Induction, Real Numbers, Sequences, Series.
|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||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|
|Textbook||Temel Gerçel Analiz I ,A. Nesin, Nesin Matematik Köyü, Calculus, M. Spivak, Türk Matematik Vakfı Yayınları|
Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert
Principles of Mathematical Analysis, Walter Rudin