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Course Information
Course Unit Title : Analysis I
Course Unit Code : MAT101
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 1
Semester : 1.Semester
Number of ECTS Credits Allocated : 6,00
Name of Lecturer(s) : ---
Course Assistants : ---
Learning Outcomes of The Course Unit : To define set and number conceptions
To define function and some special functions
To take limit at one point of functions
To analyze sequence and properties of sequences
To use the properties of continuous functions
To define derivative and applications of derivative
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Fundamental conceptions of mathematical analysis, set and number conceptions, functions and special functions, sequence of real numbers, convergence, upper and lower limits, properties of continuous functions, derivative, higher order derivative, geometric and physical meaning of the derivative, derivative and some related theorems, indefinite limits, drawing curves.
Languages of Instruction : Turkish-English
Course Goals : To define set and number conceptions
To define function and some special functions
To take limit at one point of functions
To analyze sequence and properties of sequences
To use the properties of continuous functions
To define derivative and applications of derivative
Course Aims : To give fundamental conceptions of mathematical analysis and limit, continuity, derivative and applications of derivative in single-valued functions.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook :
Additional Resources : Balcı, M., ?Analiz I?, Balcı Yayınları, 2001.
Stoll, M. ?Introduction to Real Analysis?, Addison Wesley, New York, 2001.
Ross, K.A., ''Elementary Analyis, the theory of Calculus'', Springer-Verlag, New York,1980.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
16 6 96  
Time Of Studying Out Of Class :
16 3 48  
Homeworks :
1 10 10  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 10 10  
Finals :
1 10 10  
Workload Hour (30) :
30  
Total Work Charge / Hour :
174  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
0 0
Quiz :
0 0
Homework :
0 0
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
0
The ratio of the term to success :
0
The ratio of final to success :
0
TOTAL :
0
Weekly Detailed Course Content
Week Topics  
1 Sets (operations of set, open sets, closed sets, limit points, etc.,)
 
2 Sets of numbers ( Natural numbers, Integers, Rational numbers, Real numbers and their properties.)
 
3 Mathematical induction, conceptions of functions , some special functions
 
4 Sequence of real numbers, boundedness, convergence, sequences of Real numbers, sınırlılık, yakınsaklık, Bolzano-Weierstrass theorem, monotone sequences
 
5 Limit superior and inferior of a sequence
 
6 Limits and continuity of a Functions
 
7 Continuous functions, uniform continuity
 
8 Derivative, Rules of derivative
 
9 Methods of derivative
 
10 The geometric and physical meaning of the derivative, derivative and some related theorems
 
11 Theorems related to derivative
 
12 To compute the indefinite limits
 
13 Differentials and draw the curves (Cartesian coordinates)
 
14 To draw the curves ( Polar Coordinates)