CANKIRI KARATEKIN UNIVERSITY Bologna Information System

Course Information

Course's Contribution to Prog.

ECTS- Workload Calculation Tool

Program Information

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

Advanced Analysis II | MATH202 | SPRING | 4+2 | C | 7 |

Learning Outcomes | 1-Defines the concept of multiple integrals. 2-Calculates double and triple integrals. 3-Calculates line integrals. 4-Uses calculation techniques of surface integral. |

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 | 0 | 0 | 0 | 0 |

Short-Term Exams (exam + preparation) | 10 | 1 | 6 | 6 |

Midterm exams (exam + preparation) | 40 | 1 | 10 | 10 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 12 | 12 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 196 | |||

Total Workload (hours) / 30 (s) | 6,53 ---- (7) | |||

ECTS Credit | 7 |

Week | Topics | Study Metarials |

1 | Basic definitions and theorems related to multiple integrals | R1) Lecture Notes |

2 | Reducing multiple integrals to consecutive integrals, changing variables in multiple integrals | R1) Lecture Notes |

3 | Improper multiple integrals and comparison test for convergence , changing variables in improper multiple integrals | R1) Lecture Notes |

4 | Double integrals, converting regions in double integrals, double integrals in polar coordinates | R1) Lecture Notes |

5 | Applications of double integrals: finding area and volume, center of mass, moment of inertia | R1) Lecture Notes |

6 | Triple integrals, spherical and cylindirical coordinates, triple improper integrals | R1) Lecture Notes |

7 | Application of triple integrals: volume, center of mass, moment of inertia | R1) Lecture Notes |

8 | Midterm exams | |

9 | Curves in n-dimensional space, parametrization of curves, basic definitions related to line integrals, line integrals of scalar and vector fields | R1) Lecture Notes |

10 | Line integrals in 3 dimensional space, path of independence, exact differentials, line integrals in plane | R1) Lecture Notes |

11 | Green`s theorem, multiple connected regions | R1) Lecture Notes |

12 | Surfaces in nth-dimensional space, parametrization of surfaces, smooth surfaces, directions in surfaces | R1) Lecture Notes |

13 | Surface integrals of scalar and vector fields | R1) Lecture Notes |

14 | Divergence and Stoke`s Theorem | R1) Lecture Notes |

15 | Applications of line and surface integrals | R1) Lecture Notes |

Prerequisites | - |

Language of Instruction | English |

Coordinator | Prof. Dr. Hüseyin Irmak |

Instructors | - |

Assistants | - |

Resources | R1) Robert, A. A., Essex, C. (2007). Calculus: A Complete Course (7th Ed.). Pearson Education, Canada. R2) Stewart, J. (2015). Calculus (8th Ed.). Cengage Learning, Boston. R3) Hass, J.R., Heil, C.E., Weir, M.D. (2017). Thomas` Calculus (14 Ed.). Pearson, London. |

Supplementary Book | - |

Goals | To teach the basic properties of multiple integrals, double and triple integrals, applications of line integrals and surface integrals. |

Content | Double integrals, triple integrals, line integrals, surface integrals, Green`s and Stokes` Theorems. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 4 |

2 | To have the ability of abstract thinking | 2 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 4 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 2 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | - |

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 | - |

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

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 | - |

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 | - |

Çankırı Karatekin Üniversitesi Bilgi İşlem Daire Başkanlığı @
2017 - Webmaster