Ondokuz Mayıs Üniversitesi Bilgi Paketi - Ders Kataloğu

# Description of Individual Course Units

 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
1. Students offer solutions to problems encountered in the application individually or as a group.
2. Students connect with the subjects based on these definitions.
3. Students know definitions of cluster and function.
Mode of Delivery
Formal Education
Prerequisites and co-requisities
None
Recommended Optional Programme Components
None
1)Calculus for Business, Economics and Social Sciences, 9th Edition; R. A. Barnett/M: R: Ziegler/ K. E. Byleen, Prentice-Hall
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