

Course Information
Course Unit Title 
: 
Analysis III 
Course Unit Code 
: 
MAT201 
Type of Course Unit 
: 
Compulsory 
Level of Course Unit

: 
First Cycle 
Year of Study

: 
2 
Semester

: 
3.Semester 
Number of ECTS Credits Allocated

: 
8,00 
Name of Lecturer(s) 
: 


Course Assistants 
: 


Learning Outcomes of The Course Unit 
: 
Infinite series, series and sequences of fuctions, kinds of convergence, Taylor  Maclaurin series, vector valued functions

Mode of Delivery 
: 
FaceToFace

Prerequisities and Corequisities Courses 
: 
Unavailable

Recommended Optional Programme Components 
: 
Unavailable

Course Contents 
: 
Infinite series, convergence tests for positive series, sequences and series of functions, uniform convergence, Power series, Taylor series , Maclaurin series, vector valued functions and multivariable calculus.

Languages of Instruction 
: 
TurkishEnglish

Course Goals 
: 
Learning of the foundation principles of Mathematical Analysis.

Course Aims 
: 
The main purpose of this course is to introduce the foundation principles of Mathematical Analysis.

WorkPlacement 

Not Available


Recommended or Required Reading
Textbook

: 
S. Pehlivan, M. Gürdal, Analiz,S.D.U publications 2. edition, 2008, 2. baskı ISBN: 975792976X.
J. Lewin, An Interactive Introduction to Mathematical Analysis, Cambridge Press, 2003
R. Haggarty, Fundamentals of Mathematical Analysis, AddisonWesley Publishers Ltd. 1989
S..T. Douglass : Introduction to Mathematical Analysis, Addison Wesley, 1996,
M. Stoll : Introduction to Real Analysis, Addison Wesley,2000.

Additional Resources

: 
http://en.wikipedia.org/wiki/Main_Page http://arxiv.org/archive/math

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

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Course Duration (Excluding Exam Week)

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Time Of Studying Out Of Class

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Homeworks

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Presentation

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Project

:


Lab Study

:


Field Study

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Visas

:


Finals

:


Workload Hour (30)

:


Total Work Charge / Hour

:


Course's ECTS Credit

:



Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

: 

Quiz

: 

Homework

: 

Attendance

: 

Application

: 

Lab

: 

Project

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Workshop

: 

Seminary

: 

Field study

: 




TOTAL

: 

The ratio of the term to success

: 

The ratio of final to success

: 

TOTAL

: 


Weekly Detailed Course Content
Week

Topics

1

Infinite series, convergence tests for positive series, comparison tests, integral test



2

D' Alembert' s ratio test, Cauchy's root test, Kummer test, Raabe test, etc..



3

Series of arbitrary terms, Alternating series test, Abel's partial summation, Abel, Dedekind and Dirichlet's tests



4

Absolute and conditional convergence, rearrangement of series



5

Multiple of infinite series, Cauchy's product Cesaro summability (if time remains)



6

Uniform convergence, Dini's theorem, Uniform convergence and differentiation



7

Uniform convergence and integration, Tests for uniform convergence (Weierstrass's MTest, Abel and Dirichlet tests )



8

Power series, The radius and interval of convergence, Taylor series representation of functions, AscoliArzela Theorem (if time remains). Differentiation and integration of power series, Algebra of power series



9

Taylor series and applications , Taylor polynomials and Maclaurin formula, Lagrange's , Lagrange's , Cauchy's and Integral forms of the remainders for Taylor's Theorem



10

Generalized integrals and types, Laplace transform; definition, Laplace transforms of some functions, inverse Laplace transform



11

some properties of Laplace transform and applicatios.



12

Integral Functions; Gamma Function, definition and properties, Beta function, alternative form, Relationship between gamma function and beta function, and some applications of these functions



13

Vector valued functions, limits, continuity and derivatives of vector functions, geometric interpretation of a vector derivative



14

Definition of gradient, divergence and curl. Applications. Vector interprretation of Jacobians. Orthogonal curvilinear coordinates. Special curvilinear coordinates



























































































