CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ADVANCED ANALYSIS I | MAT201 | FALL | 4+2 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able to explain fundamental topological properties of r^n space 2-To be able to describe multivariable functions and basic concepts related to these functions 3-To be able to explain basic theorems and their proofs related to limit, continuity and derivatives of functions of multivariableatives 4-To be able to calculate partial derivatives and directional derivatives of functions of multivariable 5-To be able to find tangent plane and normal line of a surface 6-To be able to find series expansions of multivariable functions 7-To be able 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 | 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 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, Taylor`s formula, mean value theorem for multivariable functions | |

7 | Differentials, Jacobian matrices of multivariable functions | |

8 | Taylor`s formula, 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 | - |

Language of Instruction | Turkish |

Course Coordinator | Assoc. Prof. Dr. Faruk POLAT |

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 | - |

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

Content | Basic topological properties of R^n , functions in multivariables and their properties, limits of real valued functions in two variables and their continuity, partial derivaties and differentials of functions in multivariables, the relation between partial derivatives and continuity, Basic differentiation rules, chain rule, gradient of a function, directional derivatives, Geometric meaning of differentials, tangent plane and normal lines to a surface, higher order derivatives, Taylor?s Formula, Mean value Theorem for functions in multivariables, Vector valued functions, limits, continuity and differentials of vector valued functions, Jacobian matrices, higher order derivatives of transformations Mean value theorem for transformations, İnverse transformations and inverse transformation theorem, implicit functions and implicit function theorem, maximum and minimum of functions in multivariables, Lagrange multipliers, scaler and vector fields, divergence rotation, coordinates of orthogonal curves |

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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