Course unit title Level of course unit Course unit code Type of course unit Semester of course unit Local credit ECTS credit Syllabus
ANALYSIS Second cycle MAT 505 1 7.50 7.50 Print
   
Description of course unit
Prerequisites and course requisities No
Language of instruction Turkish
Coordinator DOÇ. DR. ADİVE NİHAL TUNCER
Lecturer(s) DOÇ. DR. ADİVE NİHAL TUNCER
Teaching assitant(s) -
Mode of delivery Face to face
Course objective The purpose of this course is to explain applying the techniques of the double, line and surface integrals, furthermore real-life examples of mathematical symbols is to express and analyze the resulting model
Course description Functions of several variables and limit, continuity and differentiability concepts of them, compound functions, implicit functions, maximum and minimum, line integrals, double and triple integrals and applications.

Course contents
1 Limits and continuity of functions of several variables
2 Partial derivatives of functions of several variables and High-order partial derivatives of functions of several variables
3 The concept of differentiation and total differential in functions of several variables, derivatives of closed functions
4 closed functions Theorems and proofs, Differentiation in any direction,
5 maximum and minimums, Side conditional extremums, Lagrange Multipliers methods
6 Jacobian matrices and Functional dependence
7 Midterm Exam
8 Vector fields, gradient, divergence and curl
9 Parameter dependent integrals, Leibnizt formules
10 Double integrals, Region conversions and applications
11 Triple integrals, Region conversions and applications.
12 Line integrals and Green Theorem and applications.
13 Surface integrals and fundamentals theorems of Surface integrals (Stokes theorems, Divergens theorems ve Gauss theorems))
14 Final Exam
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Learning outcomes of the course unit
1 To understand the structure of functions of several variables
2 To grasp limits and continuity of functions of several variables
3 To grasp total differential and makes applications
4 Calculates the extreme values under the additional conditions for a given function
5 To find partial derivatives and calculates the derivative in any direction of the ımplicit function.
6 Area and volume calculation with the help of a double integral
7 Volume calculation with the help of triple integrals
8 To learn line integral and calculate
9 To calculate surface area.
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*Contribution level of the course unit to the key learning outcomes
1 Have competence to use research methods and techniques available in Sociology and hold theoretical and practical knowledge.
2 Have competence to use written Sociology. Write with conciseness and clarity and apply the conventions of European Language Portfolio at a level of B2 to communicate effectively and support an idea.
3 Understand the link between sociology and other disciplines and carry out interdisciplinary research and study. Raise clear and precise questions, consider different points of view.
4 Generate solutions to the discipline specific problems of sociology and apply appropriate research techniques and methods to solve these problems. Also use theoretical and practical knowledge on an advanced level. Develop and draw upon sociological knowledge in order to analyse relevant contemporary issue(s)
5 Provide up-to-date information and generate novelties through an interdisciplinary study.
6 Carry out an independent and comprehensive research. Clearly present creative ideas and analytical information to a variety of audiences. able to lead such researches with expertise both on an institutional level and as part of a team when required.
7 As tutor to inform, educate and assist people. Also be able to identify, interpret and analyse society, cultural ideas, influences and artefacts. Contribute in raising-awareness to critical issues of culture and art within a society.
8 Collect, interpret, and use sociological data and have expertise to evaluate and to audit efforts at the understanding society.
9 Adopt critical approach to build, develop and revise knowledge/skills when necessary.
10 Use current sociology methods to research and provide analyses and syntheses based on critical thinking. Deliver the results of such independent, and scientifically conducted studies accurately and on time.
11 Convey the current developments in sociology to the groups and scholars in the department and other departments by supporting with quantitative and qualitative data . Make strategies, apply and revise them as needed. Use the latest information technologies.
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Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load
  Quantity Time (hour) Quantity*Time (hour)
Lectures (face to face teaching) 14 3 42
Study hours out of classroom (study before and after the class) 14 5 70
Homework 1 2 2
Presentation / seminar 2 3 6
Quiz 0 0 0
Preparation for midterm exams 14 2 28
Midterm exams 1 2 2
Project (term paper) 0 0 0
Laboratuar 0 0 0
Field study 0 0 0
Preparation for final exam 14 2 28
Final exam 1 2 2
Research 2 2 4
Total work load     184
ECTS     7.50

Assessment methods and criteria
Evaluation during semester Quantity Percentage
Midterm exam 1 70
Quiz 0 0
Homework 1 30
Semester total   100
Contribution ratio of evaluation during semester to success   40
Contribution ratio of final exam to success   60
General total   100

Recommended and required reading
Textbook • Mustafa BAYRAKTAR , ANALİZ, Ekim 2010, Nobel Yayınları. • Mustafa BALCI, Matematik Analiz, Cilt II, Ankara 1997. • WEBB, J.R.L., Functions of several variables, Ellis Harwood Limited, LONDON, 1991 Abdulkadir ÖZDEĞER-Nursun ÖZDEĞER, Çözümlü Analiz Problemleri, Cilt I-II,
Additional references İstanbul 1994. •PISKUNOV, N., Differential and integral calculus, Vol. I, Translated from the Russian by George YANKOVSK, Mir Publishers, MOSCOW, 1974.

Files related to the course unit