CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ANALYSIS II | MAT102 | SPRING | 4+2 | C | 8 |

Learning Outcomes | 1-To apprehend fundamental theorems and their proofs related to definitions and indefinite integrals of functions of one variable. 2-To apprehend calculation methods for definite and indefinite integrals of functions of one variable. 3-To calculate area in the plane, arclength of a curve and surface areas and volumes of revolutions by using definite integral. 4-To know improper integrals and investigate their convergence. |

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

Course Duration (Weeks x Course Hours) | 14 | 6 | 84 | |

Classroom study (Pre-study, practice) | 14 | 6 | 84 | |

Assignments | 10 | 2 | 8 | 16 |

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

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

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) | 234 | |||

Total Workload (hours) / 30 (s) | 7,8 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Introduction to antiderivatives and indefinite integral | |

2 | Basic integral formulas | |

3 | Rules for changing variables in integrals | |

4 | Changing variables and ceratin applications | |

5 | Integration by writing in simple fractions and inverse substitution | |

6 | Integration by parts and certain examples | |

7 | Recursion formulas for integration and ceratin examples | |

8 | Riemannian sums and Riemann (definite) integral | |

9 | Definite integral, its properties, Mean-value theorem and certain examples | |

10 | Fundamental theorem of differential and integral computation | |

11 | Applications of definite integral: Area between two curves and Arclenght | |

12 | Applications of definite integral: Surface area and volumes of revolutions | |

13 | Improper integrals and their types | |

14 | Tests for convergence relating to improper integrals |

Prerequisites | ANALYSIS I |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors |
1-)Doktor Öğretim Üyesi Gülsüm Ulusoy Ada |

Assistants | - |

Resources | Teori ve Çözümlü Problemlerle Analiz II, Binali Musayev, Murat Alp, Nizami Mustafayev, Seçkin Yayıncılık, 2007. |

Supplementary Book | [1] Analiz, M. Balcı, Balcı Yayınlar, ISBN:978-9756683-02-6, 2008. [2] Calculus, Robert A. Adams, Addison-Wesley. [3] Yüksek Matematik 1, Hüseyin Halilov, Alemdar Hasanoğlu, Mehmet Can, Literatür Yayıncılık, 2009. [4] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons. |

Document | Lecture Notes |

Goals | To teach integral, sequence and series notions and computational methods for these topics for single variable functions. |

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 | 4 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 2 |

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 | 2 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 2 |

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 | 3 |

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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