CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

INTRODUCTION TO REAL ANALYSIS | MAT207 | FALL | 4+0 | C | 6 |

Learning Outcomes | 1-To describe real valued sequences, cauchy sequences, functions sequences, series, power series, taylor series and maclaurin series. 2-To prove the basic theorems relating to real valued sequences, cauchy sequences, functions sequences, series, power series, taylor series and maclaurin series. 3-To apprehend properties or to do applications of sequences, functions sequences, series, power series, taylor series and maclaurin series. |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 4 | 56 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 18 | 18 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 174 | |||

Total Workload (hours) / 30 (s) | 5,8 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Foreknowledge | |

2 | Certain topological properties of real numbers | |

3 | Rean number sequences, related definitions, theorems, certain applications, upper-lower limits, and their applications | |

4 | Real Cauchy sequence, its definiton, related definitions and theorems | |

5 | Introduction to real series | |

6 | Convergence and divergence of series | |

7 | Tests for convergence and divergence of series | |

8 | Real function sequences, related definitions, theorems amd certain applications | |

9 | Real valued function series, related definitions, theorems and certain applications | |

10 | Introduction to power series | |

11 | Convergence and divergence of power series | |

12 | Weirstrass M-test and its applications | |

13 | Maclaurin series and their applications | |

14 | Taylor series and and pplications |

Prerequisites | Analiz I, Analiz II |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors |
1-)Bölüm Başkanı Hüseyin Irmak |

Assistants | - |

Resources | An introduction to real analysis, T. Terzioğlu, Matematik Vakfı yayınları, 2000. |

Supplementary Book | [1] Analiz, M. Balcı, Balcı Yayınları, ISBN: 978-975-6683-03-3, 2009. [2] The Elements of Real Analysis, R. G. Bartle, John Wiley and Sons, 1967 [3] Real analysis with Real Applications, K. R. Davidson, A. P. Donsig, Prentice Hall, 2002 [4] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons [5] Analiz, M. Balcı, Balcı Yayınlar, ISBN:978-9756683-02-6, 2008. |

Document | Ders Notları |

Goals | Real sayı dizlerini, Caouchy dizilerini, fonksiyon dizilerini, serileri, kuvvet serilerini ve fonksiyon serilerini tanıtmak ve bunlarla ilgili teoremlerin ispatlarını ve uygulamalarını öğretmek. |

Content | - |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 2 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 3 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 4 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 4 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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