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

IMÖ201 | Analysis-I | 927001 | 2 | 3 | 8 |

Level of Course Unit

First Cycle

Objectives of the Course

The purpose of the course is to be able to examine development of limit, differential and integral calculus of theoretical structure in univariate functions and to gain skills in its interpreting.

Name of Lecturer(s)

Yrd. Doç. Dr. Mevlüde Doğan

Learning Outcomes

- Students offer solutions to problems encountered in the application individually or as a group.
- Students connect with the subjects based on these definitions.
- Students know definitions of cluster and function.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Recommended or Required Reading

1)Calculus for Business, Economics and Social Sciences, 9th Edition; R. A. Barnett/M: R: Ziegler/ K. E. Byleen, Prentice-Hall

2)Calculus: A Complete Course, 7th Edition; R. A. Adams, Addison-Wesley.

3)Calculus With Analytic Geometry, C. H. Edwards, Prentice –Hall.

4) J.A.Fridy: Introductory Analysis, The Theory of Calculus, Academic Pres, 1987, USA.

5) K.A.Ross: Elementary Analysis, The Theory of Calculus, Springer Verlag, 1980, NewYork.

6) B.Yurtsever: Matematik Analiz Dersleri, Cilt I(ikinci kısım), 1981. Ekonomist yayınevi, Ankara

7)Marsden J. E., Elementary Classical Analysis, W.H.Freeman Comp,1974

2)Calculus: A Complete Course, 7th Edition; R. A. Adams, Addison-Wesley.

3)Calculus With Analytic Geometry, C. H. Edwards, Prentice –Hall.

4) J.A.Fridy: Introductory Analysis, The Theory of Calculus, Academic Pres, 1987, USA.

5) K.A.Ross: Elementary Analysis, The Theory of Calculus, Springer Verlag, 1980, NewYork.

6) B.Yurtsever: Matematik Analiz Dersleri, Cilt I(ikinci kısım), 1981. Ekonomist yayınevi, Ankara

7)Marsden J. E., Elementary Classical Analysis, W.H.Freeman Comp,1974

Planned Learning Activities and Teaching Methods

Language of Instruction

Turkish

Work Placement(s)

None

Course Contents

Progressions. Basic definitions and examples.Monotone progressions. Examples. Convergent, divergent progressions and their geometric meanings. Limited sequences. Zillion and Infinitesimal progressions. General theorems about sequences and practice tasks. Determination of characters of progressions. Examination of convergence of sequences. Practice of theorems. Limit conception of univariate functions and its practice. Perfect limits. Limit calculation techniques. Types of continuity and discontinuity. Properties of continuous functions. Concept of derivative in univariate functions. Geometrical and physical interpretation of derivative. Rules of derivation. Features of derivation. Derivate of functions given in the form of closed and parametric ones. Derivative of inverse and compound functions. Differential of function and its practice. High-ordered derivatives. Finite theorem of Taylor. Theorem of Role and Average Value Theorem. L'Hospital rule and limit calculations according to this rule. Practice for derivative:
Ascending and descending intervals of function. Concavity direction of a curve. Bending points. Asymptotes. Extreme points of function.. Analyse of function and graphic drawing. Examples. Absolute extreme points of a function. Maximum and minimum problems. Concept of integral, indefinite integrals, integration techniques( some special transformations and integration of rational functions) Practice for indefinite integrals. Partial integration. Integration of trigonometric functions. Concept of definite integral. Lower, Upper and Riemann

Weekly Detailed Course Contents

Week | Theoretical | Practice | Laboratory |

1. | Limit Concept and Applications in One Variable Functions | ||

2. | Continuity Concepts and Applications in One Variable Functions, The Types of discontinuity | ||

3. | Derivatives Concepts in One Variable Functions and the rules of derivatives | ||

4. | Trigonometric, logarithmic, exponential, hyperbolic functions | ||

5. | Higher order derivatives, extreme and absolute extreme points of functions | ||

6. | Extreme Problems and their applications in various fields | ||

7. | Rolle and Mean Value Theorem, Finite Taylor Theorem | ||

8. | L'Hospital Rule and limit computing with the aid of this rule | ||

9. | Mid-term | ||

10. | Differential and Linear Increase | ||

11. | The concept of integral, indefinite integrals | ||

12. | The techniques of integral | ||

13. | Definite integrals | ||

14. | Field and volume measurements with definite integral and their applications |

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 | 3 | 3 |

Final Examination | 1 | 3 | 3 |

Attending Lectures | 14 | 6 | 84 |

Tutorial | 11 | 10 | 110 |

SUM | 200 |