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

TYS205 | Engineering Mathematics | 927001 | 2 | 3 | 5 |

Level of Course Unit

First Cycle

Objectives of the Course

The aim is to Provide students a knowledge on the basic concepts and applications of high mathematics.

Name of Lecturer(s)

Prof. Dr. İmanverdi EKBERLİ

Learning Outcomes

- Receives basic mathematical knowledge in the field of agriculture and irrigation structures.
- Araştırma sonuçlarına bağlı olarak maksimizasyon ve minimizasyon doğrusal programlama modellerinin yapılması becerilerine sahip olur.
- Toprakların su, tuz vb. gibi parametrelerinin değişimini ifade eden denklemlerin incelenmesi için derekli teorik bilgilere sahip olur.
- Maintains base for implementation of functions with multiple variables into the research results and base for implementation of differenteial functions in application of some soil procedures.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Recommended or Required Reading

1. Bronson, R., 1989. Matris İşlemleri (Teori ve problemleri). Schaun serisinden çevri editörü Prof. Dr. H. Hilmi Hacisalihoğlu. Nobel yayın dağıtım LTD. ŞTİ,Ankara.2. Alpha C.Chiang, 1999. Matematiksel İktisadın Temel Yöntemleri. Gazi büro kitabevi, Ankara.3. Tulunay, Y., 1987. Matematik Programlama ve İşletme Uygulamaları. Bayrak matbaacılık, İstanbul.4. Evsahiboğlu,N., 1994. Mühendislik Matematiği. Ankara Üniversitesi Ziraat Fakültesi Yayınları No: 1339. Ders kitabı: 388.5. Edward T. Dowling, 1993. İşletme ve İktisad İçin Matematiksel Yöntemler (Teori ve Problemler). Schaum serisinden çevri, Nobel yayın dağıtım LTD. ŞTİ, Ankara.

Planned Learning Activities and Teaching Methods

Language of Instruction

Turkish

Work Placement(s)

None

Course Contents

Matrices. The vectors as special matrices. The sum and substraction of the matrix. Multiplication by a scalar and matrix multiplication.Further features of the product matrix. Different aspects of matrix algebra. Inverse matrices and their properties. Determinants. Determinants calculation (Triangle and Laplace rule). Basic properties of determinants. The calcuation of Inverse matrix of determinants. Rank of the matrix. The calculation of matris rank with a methodology of surroinding minors and conversion to angular matrix. Systems of linear equations. Kroneker-Kapelle theory. grammar and Solution of linear equation system through Gauss-Jordan method . A homogeneous system of linear equations. Definition of functions with several ariables. Limit and limit rules. Continuity.The concept of partial derivatives. Geometric implication of partial derivatives. Exponential partial derivatives. Composite functions and their derivatives. Total diferantials. The condition of being full Diferantial. Exponential total diferantials. Implicit differentiation.The maximum and minimum values of functions with several variables. Lagrangian multiplier method. To linear programming and linear programming model. Graphical method, the solution of linear programming models. The solution of linear programming models of maximization with Simplex method. The solution of linear programming models of miminization with Sipmlex method. Duality. Dual model and its solution.

Weekly Detailed Course Contents

Week | Theoretical | Practice | Laboratory |

1. | Matrices. The vectors as special matrices. The sum and substraction of the matrix. Multiplication by a scalar and matrix multiplication. | ||

2. | Further features of the product matrix. Different aspects of matrix algebra. Inverse matrices and their properties. | ||

3. | Determinants. Determinants calculation (Triangle and Laplace rule). Basic properties of determinants. | ||

4. | The calcuation of Inverse matrix of determinants. Rank of the matrix. The calculation of matris rank with a methodology of surroinding minors and conversion to angular matrix | ||

5. | Systems of linear equations. Kroneker-Kapelle theory. grammar and Solution of linear equation system through Gauss-Jordan method . A homogeneous system of linear equations. | ||

6. | Definition of functions with several ariables. Limit and limit rules. Continuity. | ||

7. | The concept of partial derivatives. Geometric implication of partial derivatives. Exponential partial derivatives. Composite functions and their derivatives. | ||

8. | Total diferantials. The condition of being full Diferantial. Exponential total diferantials. Implicit differentiation. | ||

9. | Mid-term exam. | ||

10. | The maximum and minimum values of functions with several variables. Lagrangian multiplier method. | ||

11. | To linear programming and linear programming model. | ||

12. | Graphical method, the solution of linear programming models. | ||

13. | The solution of linear programming models of maximization with Simplex method. | ||

14. | The solution of linear programming models of miminization with Sipmlex method. Duality. Dual model and its solution. | ||

15. |

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 (%) |

SUM | 0 | |

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 | 2 | 2 |

Attending Lectures | 14 | 2 | 28 |

Problem Solving | 10 | 2 | 20 |

Self Study | 13 | 2 | 26 |

Individual Study for Mid term Examination | 13 | 2 | 26 |

Individual Study for Final Examination | 13 | 2 | 26 |

SUM | 130 |