CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ANALYSIS I | MAT101 | FALL | 4+2 | Fac./ Uni. | C | 7 |

Learning Outcomes | 1-To be able to explain basic theorems and their proofs related to limit, continuity and derivative of functions of one variable 2-To be able to apply computation techniques related to limit, continuity and derivative of functions of one variable 3-To be able to calculate maximum, minimum and inflection points of functions of one variable 4-To be able to sketch the graphs of functions of one variable 5-To be able to solve maximum and minimum problems |

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 | 5 | 10 |

Short-Term Exams (exam + preparation) | 10 | 2 | 5 | 10 |

Midterm exams (exam + preparation) | 30 | 1 | 10 | 10 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 15 | 15 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 199 | |||

Total Workload (hours) / 30 (s) | 6,63 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Real numbers, absolute value, equations and inequalities, basic definitions related to functions | |

2 | Polinomials, rational functions, piecewise defined functions, trigonometric functions, exponential and logarithmic functions | |

3 | Limit of functions, one sided limis, limit theorems | |

4 | Limits at infinity, infinite limits, undetermined condtitions, examples related to limits | |

5 | Limits of trigonometric, exponential, and logarithmic functions | |

6 | Continuous functions, basic properties of continuous functions | |

7 | Properties of continuous functions defined on a closed and bounded interval | |

8 | Uniform continuity | |

9 | The notion of derivative, rules of taking derivatives, chain rule, higher order derivatives, derivatives of exponential and logarithmic functions | |

10 | Chain rule, higher order derivatives | |

11 | Derivatives of exponential and logarithmic functions, implicit differentiation, derivatives of parametric functions | |

12 | Mean-value theorem, increasing and decreasing functions | |

13 | Maximum and minimum values, concavity and inflection points, second derivative test, asymptotes, sketcing graphs | |

14 | Maximum, Minimum problems, related rates, L`hospital rule |

Prerequisites | - |

Language of Instruction | Turkish |

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

Instructors | - |

Assistants | - |

Resources | Teori ve Çözümlü Problemlerle Analiz I, Binali Musayev, Murat Alp, Nizami Mustafayev, İsmail Ekincioğlu, Seçkin Yayıncılık, 2007 |

Supplementary Book | 1. Yüksek Matematik 1, Hüseyin Halilov, Alemdar Hasanoğlu, Mehmet Can, Literatür Yayıncılık, 2009. 2. Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert, John Wiley & Sons 3. Calculus, Robert A. Adams, Addison-Wesley |

Document | - |

Goals | Teaching basic theorems and their proofs related to limit, continuity and derivative of functions in one variable |

Content | Real numbers, absolute value, equations and inequalities, basic definitions related to functions, polinomials, rational functions, piecewise defined functions, trigonometric functions, exponential and logarithmic functions, limits of functions, limit theorems, limits at infinity, infinite limits, undetermined condtitions, limits of trigonometric, exponential, and logarithmic functions, continuous functions, properties of continuous functions defined on a closed and bounded interval, uniform continuity, the notion of derivative, rules of taking derivatives, chain rule, higher order derivatives, derivatives of exponential and logarithmic functions, implicit differentiation, derivatives of parametric functions, Mean-value theorem, increasing and decreasing functions, maximum and minimum values, first derivative test, concavity and inflection points, second derivative test, asymptotes, sketcing graphs, maximum-minumum problems, related rates, L`hospital rule. |

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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