

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 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
ndimensional 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 
: 
TurkishEnglish

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
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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.

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Workload Hour (30)

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Assessment Methods and Criteria
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Weekly Detailed Course Content
Week

Topics

1

ndimensional Euclidean space, definition, Euclidean distance or Euclidean metric, topological structures



2

Sequences in ndimensional Euclidean space, convergence of sequences in ndimensional Euclidean space, BolzanoWeierstrass 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



























































































