CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ANALYSIS II | MAT102 | SPRING | 4+2 | Fac./ Uni. | C | 7 |

Learning Outcomes | 1-To be able to explain fundamental theorems and their proofs related to definite and indefinite integrals of functions of one variable 2-To be able to apply calculation methods for definite and indefinite integrals of functions of one variable 3-To be able to calculate area in the plane, arclength of a curve and surface areas and volumes of revolutions by using definite integral 4-To be able to explain the basic theorems and their proofs related to sequences and series 5-To be able to examine the convergence of sequences and series 6-To be able to find taylor series expansion of a function |

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 | Antiderivatives and indefinite integral, basic integral formulas : changing variables | |

2 | Integration by parts, writing in simple fractions, inverse substitution | |

3 | Riemannian sums, Riemannian (definite) integral and its properties | |

4 | Mean-value theorem for integrals | |

5 | Fundamental theorem of differential and integral computation | |

6 | Applications of definite integral : area between two curves, Arclenght | |

7 | Surface area and volumes of revolutions | |

8 | Classifying improper integrals, tests for convergence | |

9 | Sequences in real numbers, convergence of sequences | |

10 | Monotone sequences, subsequences, Bolzano Weierstrass Theorem, Cauchy criteria | |

11 | Infinite series and their convergence, tests for absolute convergence: coparison test, ratio test integral test | |

12 | Absolute Convergence tests: ratio, root test, integral test, conditionally convergent series integral, alternating series | |

13 | Power series, radius and interval of convergence of power series | |

14 | Taylor`s Theorem, Taylar series and their applications |

Prerequisites | - |

Language of Instruction | Turkish |

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

Instructors | - |

Assistants | - |

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

Supplementary Book | 1. Yüksek Matematik 2, 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 | To teach integral, sequence and series notions and computational methods for these topics for single variable functions |

Content | Antiderivatives and indefinite integral, basic integral formulas : changing variables, integration by parts, writing in simple fractions, inverse substitution. Rieamannian sums, Rieamannian (definite) integral and its properties, Mean-value theorem for integrals, Fundamental theorem of differential and integral computation. Applications of definite integral : area between two curves, Arclenght, surface area and volumes of revolutions, classifying improper integrals, tests for convergence, sequences in real numbers, convergence of sequences, monotone sequences, subsequences, Bolzano Weierstrass Theorem, Cauchy criteria, infinite series and their convergence, tests for absolute convergence: coparison test, ratio test integral test, conditionally convergent series integral, alternating series, alternating series test, power series, radius and interval of convergence of power series, Taylor`s Theorem, Taylar series and their applications |

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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