CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ADVANCED ANALYSIS II | MAT202 | SPRING | 4+2 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able to describe the concept of multiple integrals 2-To be able to calculate double and triple integrals 3-To be able to calculate line integrals 4-To be able to use calculation techniques of surface integrals |

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 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 228 | |||

Total Workload (hours) / 30 (s) | 7,6 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Basic definitions and theorems related to multiple integrals | |

2 | Reducing multiple integrals to consecutive integrals, changing variables in multiple integrals | |

3 | Improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals | |

4 | Double integrals, converting regions in double integrals, double integrals in polar coordinates | |

5 | Applications of double integrals: finding area and volume, center of mass, moment of inertia | |

6 | Triple integrals, spherical and cylindirical coordinates, triple improper integrals | |

7 | Application of triple integrals: volume, center of mass, moment of inertia | |

8 | Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields | |

9 | Line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane | |

10 | Green`s theorem, multiple connected regions | |

11 | Surfaces in nth dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces | |

12 | Surface integrals of scalar and vector fields | |

13 | Divergence and Stoke`s Theorem | |

14 | Applications of line and surface integrals |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors | - |

Assistants | - |

Resources | Teori ve Çözümlü Problemlerle Analiz IV, Binali Musayev, Nizami Mustafayev, Kerim Koca, Seçkin Yayıncılık, 2007 |

Supplementary Book | Calculus, Robert A. Adams, Addison-Wesley, 2002. |

Document | - |

Goals | Teaching the basic properties of multiple integrals, double and triple integrals, applications of line integrals and surface integrals |

Content | Basic definitions and theorems related to multiple integrals, reducing multiple integrals to consecutive integrals, changing variables in multiple integrals, improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals, double integrals,converting regions in double integrals, double integrals in polar coordinates, applications of double integrals: finding area and volume, center of mass, moment of inertia, Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields, line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane, Green?s theorem, multiple connected regions, surfaces in n dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces, surface integrals of scalar and vector fields, divergence and Stoke`s Theorem, applications of line and surface integrals. |

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 | 3 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 3 |

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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