CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ADVANCED ANALYSIS I | MAT201 | FALL | 4+2 | C | 7 |

Learning Outcomes | 1-To explain fundamental topological properties of r^n space. 2-To describe multivariable functions and basic concepts related to these functions. 3-To explain basic theorems and their proofs related to limit, continuity and derivatives of functions of multivariableatives. 4-To calculate partial derivatives and directional derivatives of functions of multivariable. 5-To find tangent plane and normal line of a surface. 6-To determine series expansions of multivariable functions. 7-To solve extremum value problems related to multivariable functions. |

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

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

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

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) | 220 | |||

Total Workload (hours) / 30 (s) | 7,33 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Basic properties of the topology of R^n | |

2 | Multivariable functions and their properties | |

3 | Limits and continuity of multivariable functions | |

4 | Basic differentiation rules, chain rule, gradient, directional derivatives | |

5 | The geometric meaning of differentials, tangent planes and normal lines | |

6 | Higher order partial derivatives, mean value theorem for multivariable functions | |

7 | Differentials, Jacobian matrices of multivariable functions | |

8 | Mean-value theorem for transformations | |

9 | Inverse transformations and inverse transformation theorem | |

10 | Implicit functions and implicite function theorem | |

11 | Extremum values of multivariable functions | |

12 | Maximum and minimum problems | |

13 | Extremum values with constraints, Lagrange multipliers method | |

14 | Vector and scalar fields, gradient, divergence, rotation |

Prerequisites | ANALYSIS I, ANALYSIS II |

Language of Instruction | Turkish |

Course Coordinator | Prof. Dr. Hüseyin IRMAK |

Instructors | - |

Assistants | - |

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

Supplementary Book | [1] Calculus, Robert A. Adams, Addison-Wesley. [2] Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons. |

Document | Lecture Notes |

Goals | To analyze basic topological properties of R^n, to extend the limit, continuity and derivative concepts to multivariable 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 | 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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