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Course Information
Course Unit Title : Advanced Analysis
Course Unit Code : 01MAT5161
Type of Course Unit : Optional
Level of Course Unit : Second 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 : Convexity and derivative of mutivariable real functions
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Euclid Sapce and Convexity: Ortonormal bases, Sets and Functions, Linear functions, hyperplanes, convex sets, convex and concav functions, continuity of convex functions, extremum values.
Differentation of real valued functions: directed derivative, partial derivative, differentiable functions, Mean value theorem, Functions in the calss of C(q), High order partial derivatives, Functions in the class of C(infinity).
Languages of Instruction : Turkish-English
Course Goals : To introduce the convexity and differentation of mutivarible functions.
Course Aims : To introduce the convexity and differentation of mutivarible functions.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook : i-) Fleming, Wendell, Functions of Several Variables, Springer-Verlag, New York 1977
Additional Resources :
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) :
14 3 42  
Time Of Studying Out Of Class :
15 4 60  
Homeworks :
3 15 45  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
177  
Course's ECTS Credit :
6      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
1 100
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 :
100
The ratio of the term to success :
50
The ratio of final to success :
50
TOTAL :
100
Weekly Detailed Course Content
Week Topics  
1 General description.
 
2 Ortonormal bases
 
3 Sets and Functions d conculusions.
 
4 Linear functions, hyperplanes
 
5 Convex and concav functions
 
6 Continuation of convex and concav functions
 
7 Continuity of convex functions
 
8 Differentation of real valued functions: directed derivative
 
9 Differentiable functions
 
10 Mean value theorem
 
11 Functions in the calss of C(q)
 
12 High order partial derivatives
 
13 Functions in the class of C(infinity)
 
14 Review and conculusions.