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Course Information

Course's Contribution to Prog.

ECTS- Workload Calculation Tool

Program Information

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

Introduction to Programming | MATH207 | 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 | 6 | 84 | |

Assignments | 5 | 0 | 0 | 0 |

Short-Term Exams (exam + preparation) | 0 | 0 | 0 | 0 |

Midterm exams (exam + preparation) | 30 | 1 | 16 | 16 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 65 | 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 | Real number sequences, related definitions, theorems, certain applications, upperlower 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 | Midterm exams | |

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

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

11 | Introduction to power series | |

12 | Convergence and divergence of power series | |

13 | Weirstrass M-test and its applications | |

14 | Maclaurin series and their applications | |

15 | Taylor series and and applications |

Prerequisites | ANALYSIS I, ANALYSIS II |

Language of Instruction | English |

Coordinator | Assoc. Prof. Dr. Faruk Polat |

Instructors | - |

Assistants | Assist. Prof. Dr. Mustafa ASLANTAŞ |

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. |

Goals | To teach real valued sequences, Cauchy sequences, function sequences, function series and power series, to teach the proofs and applications of the related theorems. |

Content | - |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 3 |

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

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

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

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 4 |

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 | - |

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

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

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 | - |

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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