Course Unit Code | Course Unit Title | Type of Course | Year | Semester | ECTS |

TBMAT104 | Mathematics-II | 927006 | 1 | 2 | 5 |

Level of Course Unit

First Cycle

Objectives of the Course

To teach applications of mathematics

Name of Lecturer(s)

Matematik Bölümü Öğretim Üyeleri

Learning Outcomes

- Learns the concept of integral in functions.
- Will be able to understand two and three variable functions and their properties.
- Will be able to know the concept of derivative in two and three variable functions and will be able to apply it to engineering problems.
- Can do various applications of integral. apply to engineering problems.
- Learn two and three dimensional space vectors.
- Learn the concept of limit and continuity in two and three variable functions.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

Language of Instruction

Turkish

Work Placement(s)

None

Course Contents

Extremums of functions, mean value and Rolle's theorem, applications, first and second differentiation condition for extremum, absolute extremum, concavity and curve plot, applied optimization problems, Newton's method, indefinite integral, change of variable, partial integration, partial fractions, special change of variable, trigonometric integration, Riemann's definite integral, limits of finite sums, fundamental theorem of calculus and properties of definite integral, calculation of area, volume calculation by shell and disk method, arc length, calculation of surface area, moment and calculation of center of mass

Weekly Detailed Course Contents

Week | Theoretical | Practice | Laboratory |

1. | Extremums of functions | ||

2. | Mean value and Rolle's theorem, applications | ||

3. | First and second differentiation condition for extremum, absolute extremum, concavity and curve plot | ||

4. | Applied optimization problems, Newton's method, indefinite integral | ||

5. | Change of variable, partial integration, partial fractions | ||

6. | Special change of variable, trigonometric integration | ||

7. | Riemann's definite integral, limits of finite sums | ||

8. | Fundamental theorem of calculus and properties of definite integral | ||

9. | Midterm | ||

10. | Calculation of area | ||

11. | Volume calculation by shell and disk method | ||

12. | Arc length | ||

13. | Calculation of surface area | ||

14. | Moment | ||

15. | Calculation of center of mass | ||

16. | Final |

Assessment Methods and Criteria

Term (or Year) Learning Activities | Quantity | Weight (%) |

Midterm Examination | 1 | 100 |

SUM | 100 | |

End Of Term (or Year) Learning Activities | Quantity | Weight (%) |

Final Examination | 1 | 100 |

SUM | 100 | |

Term (or Year) Learning Activities | 40 | |

End Of Term (or Year) Learning Activities | 60 | |

SUM | 100 |

Workload Calculation

Activities | Quantity | Time(hours) | Total Workload(hours) |

Midterm Examination | 1 | 2 | 2 |

Final Examination | 1 | 3 | 3 |

Individual Study for Mid term Examination | 1 | 60 | 60 |

Individual Study for Final Examination | 1 | 60 | 60 |

SUM | 125 |