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Course Information
Course Unit Title : Analysis IV
Course Unit Code : MAT202
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 2
Semester : 4.Semester
Number of ECTS Credits Allocated : 8,00
Name of Lecturer(s) : ---
Course Assistants : ---
Learning Outcomes of The Course Unit : To understand the foundation principles of Mathematical Analysis
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : n-dimensional Euclidean space, definition, Euclidean distance or Euclidean metric, topological structures, Multiple Integrals, cylindrical and spherical coordinates, applications of double integrals and triple integrals, applications of multiple integrals. Line integrals: Line integrals of vector fields, alternative forms, properties, closed curves, dependence on path of integration, exact differentials in three independent variables, Green?s theorem. Surfaces and suface integrals: Gauss divergence theorem, Green?s theorem in the plane, Stokes?s theorem. Fourier series: Convergence of the mean, trigonometric series, convergence of trigonometric series, Dirichlet conditions, Fourier coefficients, Cesaro summability of Fourier series, Fourier integrals, Eliptic functions, Introduction to measure: Measure of open sets, inner and outer measure, properties of measurable sets, measurable functions, Lebesgue integral of a bounded functions
Languages of Instruction : Turkish-English
Course Goals : Learning of the theory of multivariable calculus
Course Aims : The main purpose of this course is to introduce the foundation principles of Mathematical Analysis. ( multivariable calculus and application)
WorkPlacement   Not Available
Recommended or Required Reading
Textbook : S. Pehlivan, M. Gürdal: Analiz IV Ders Notları
Additional Resources : M. Balcı: Matematik Analiz 2, Balcı Yayınları, 2001.
M. Balcı, Ali Ural: Çözümlü Matematik Analiz 2, Balcı Yayınları, 2001.
T.S Kennan: Premier of Modern Analysis, Springer- Verlag, 1983.
R. G. Bartle, D. R. Sherbert: Introduction to Real Analysis, John Wiley and Sons, Inc., 1992.
S..T. Douglass: Introduction to Mathematical Analysis, Addison Wesley, 1996.
M. Stoll: Introduction to Real Analysis, Addison Wesley, 2000
K.A. Stroud: Further Engineering Mathematics, Macmillan, 1998.
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 6 84  
Time Of Studying Out Of Class :
14 6 84  
Homeworks :
2 15 30  
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 :
228  
Course's ECTS Credit :
8      
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 n-dimensional Euclidean space, definition, Euclidean distance or Euclidean metric, topological structures
 
2 Sequences in n-dimensional Euclidean space, convergence of sequences in n-dimensional Euclidean space, Bolzano-Weierstrass theorem
 
3 Multivariable functions, definition, definition and range sets, vector valued functions and application , limits, continuity and derivatives of vector functions
 
4 Graphics of multivariable functions, limits and continuity in multiple dimensions
 
5 Partial derivatives, chain rule, higher order partial derivatives
 
6 Partial derivatives using Jacobians. Transformations, Extramum (maxima and minima) functions of more than one variable
 
7 Definitions and applications gradient, diverjans, and curl . Jacobians?in vektör yorumu, Dik koordinat sistemi ve özel koordinat sistemleri, İntegral altında türev alma
 
8 Definition and some properties of the double and triple integrals, , Fubini theorems
 
9 Applications of double integrals, the gravitation attraction of a disc, moments and centres of mass, moment of inertia
 
10 Applications of triple integrals
 
11 Line integrals of vector fields, alternative forms, properties, closed curves, line integral with respect to arc length, parametric equations, dependence on path of integration, exact differentials in three independent variables, Green?s theorem
 
12 Surfaces and suface integrals, Parametric surfaces, Gauss divergence theorem, Green?s theorem in the plane, Stokes?s theorem
 
13 Fourier series, trigonometric series, convergence of trigonometric series, Dirichlet conditions, Fourier coefficients, Cesaro summability of Fourier series, Fourier integrals, additional topics
 
14 Eliptic functions, standard forms of first and second kinds, complete elliptic functions, alternative forms. Introduction to measure