Ders Plani Icerigi New

COURSE SYLLABUS- DERS TANITIM BLGLER

DERSN ADI (tr) : Analiz I

Name (en): Analysis I

Akademik Birim Academic Unit:

Fen Edebiyat Fakltesi Faculty of Arts And Sciences

Blm Department/Program:

Matematik

Mathematics

Dersin Kodu Code :

MAT 101

Zorunlu/Semeli Compulsive/Elective

Zorunlu

Compulsive

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Gz Autumn

OM Kredisi : 5 AKTS Kredisi

ECTS Credit: 7

Dersin Dili Language:

Trke Turkish

H.Ders Saati : Class hour per week

Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)

Laboratuvar/Laboratory

(hours per week)

4 2 0

RETM ELEMANLARI

Yrd. Do. Dr. smail DEMR Contact

E-Mail: [email protected]

Tel:02862180018/1704

DERSN KATEGORS

Sadece bir kategori seilecektir. (X) Choose only one type

Temel Meslek Dersleri X

Uzmanlk Alan Desleri

Destek Dersleri

letiim ve Ynetim Becerileri Dersleri

Aktarlabilir Beceri Dersleri

ERK BLGLER

TRKE NGLZCE

n Koullar : Pre-requsites

Yok None

Dersin Tanmlamas

Course Description:

Reel saylar ve reel say kmeleri; Dzlemde kartezyen koordinatlar; Fonksiyonlar ve

grafikleri;Trigonometrik fonksiyonlar; Limit,

sreklilik ve trev; Belirsiz integral; stel ve logaritmik fonksiyon; Ters fonksiyonlar;

Hiperbolik fonksiyonlar; Trevin uygulamalar, Grafik izimleri

Real numbers and real number sets; Cartesian

coordinates in plane; Functions and their

graphs; Trigonometric functions; Limit;

Continuity and derivative; Indefinite integral;

Exponential and logarithmic functions;

Inverse functions; Hyperbolic functions;

Applications of derivative, Drawing graph.

Ana Ders Kitab:

Main Coursebook:

Calculus: A complete Course, Robert A.

AdamsCalculus ve Analitik Geometri, Richard

A. Silverman


AdamsCalculus ve Analitik Geometri,

Richard A. Silverman

Dier Kaynaklar :

Other references

Kalkls, James Stewart Kalkls, James Stewart

Eitim-retim

Materyalleri Materials

( Ek1-2 ):

Dier Other

Eitim-retim

Metodlar Teaching Methods

( Ek1-1 ):

Ders anlatm Lecturing

DERS RENME IKTILARI (TRKE)

Bu dersi baar ile tamamlayan renciler

1 : Kme kavram ve gerel saylar kmesini tanmak.

2 : Gerel saylar kmesi zerinde tanmlanan fonksiyonar temel zellikleri ile inceleme.

3 : Fonksiyonlarn limiti, sreklilii, trevi gibi kavramlar renme ve uygulamasn yapabilme

4 : Verilen bir fonksiyonun grafiini izebilme ve grafii yorumlayabilme.

5 : Trevin uygulamalarn renerek bunlarn analizini yapabilme.

LEARNING OUTCOMES

After completion of this course students will be able to:

1 : Learn concept of sets and Real numbers set.

2 : Understand the functions defined on real numbers set with properties.

3 : Understand concepts of limits, continuity, derivation of functions and applies.

4 : Draws graph of a given function and interperets graph.

5 : Learns application of derivation and this analyses.

HAFTALIK DERS PROGRAMI (TRKE)

Haftalar HAFTALIK KONULAR N HAZIRLIK

1 : Kme kavram, saylar [1], [2], [3]

2 : Fonksiyonlar; fonksiyonlarn tanm ve deer kmeleri [1], [2], [3]

3 : Fonksiyon grafikleri, zel fonksiyonlar [1], [2], [3]

4 : Fonksiyonlarn limiti, sa ve sol limitler, limitlerde cebirsel ilemler [1], [2], [3]

5 : Sonsuz limitler, epsilon-delta teknii le limit tanm [1], [2], [3]

6 : Sreklilik, srekli fonksiyonlarn zellikleri [1], [2], [3]

7 : Trev, trevin tanm, trev alma kurallar zincir kural [1], [2], [3]

8 : Kapal fonksiyonun trevi, Rolle teoremi, Ortalama deer teoremi [1], [2], [3]

9 : Arasnav [1], [2], [3]

10 : Ters fonksiyonlar, stel ve logaritmik fonksiyonlar [1], [2], [3]

11 : Ters trigonometrik fonksiyonlar.Hiperbolik fonksiyonlar [1], [2], [3]

12 : Trevin uygulamalar: Maksimum ve minumum deerler, Konkavlk, ekstrem deer problemleri

[1], [2], [3]

13 : Belirsiz ifadeler, L' Hospital Teoremi, Asimtotlar [1], [2], [3]

14 : Grafik izimleri [1], [2], [3]

WEEKLY COURSE PLAN (English)

Weeks TOPICS Preparation

1 : Concept of set, numbers [1], [2], [3]

2 : Functions, define and value sets of functions [1], [2], [3]

3 : Function graphs, special functions [1], [2], [3]

4 : Limit of functions, right and left limits [1], [2], [3]

5 : Infinite limits, definitions of limit with - technics [1], [2], [3]

6 : Continuity, properties of continues functions [1], [2], [3]

7 : Definition of derivative, Rules of derivation [1], [2], [3]

8 : Derivation of closed functions, Rolle theorem, Mean value theorem [1], [2], [3]

9 : Midterm exam [1], [2], [3]

10 : Inverse , exponential and logarithmic functions [1], [2], [3]

11 : Inverse trigonometric , hyperbolic functions [1], [2], [3]

12 : Applications of derivative: Maximum and minimum value, concavity,

extreme value problems [1], [2], [3]

13 : Indefinite expressions, L'Hospital Theorem, Asimptots [1], [2], [3]

14 : Graph drawing [1], [2], [3]

AKTS YK TABLOSU

AKTVTELER SAYI SRES (saat) TOPLAM

Ders Saati (Snav haftas dahil 16 x toplam ders saati)

14 6 84

Staj

devler

Seminer

Proje

Aratrma Yapma 13 2 26

Alan almas

n hazrlk (ders ncesinde derse hazrlanma iin harcanan sre)

Vaka ncelemesi

Ders d alma 13 2 26

Mikroretim (retmenlik program iin)

Ksa Snavlar

Sunum

Ara Snav/lara hazrlanma 3 6 18

Final Snavna Hazrlanma 3 7 21

Varsa Dier

TOPLAM YK : 175

ECTS KREDS (Toplam Yk Saati / 25 (s) ) : 7

ECTS WORKLOAD TABLE

ACTIVITIES Number Duration Total Workload

Class hours (Including Exam Week: 16 x Total Hours) 14 6 84

Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study

Study Hours Out of Class 13 2 26

Microteaching (teacher training

departments)

Quizzes

Presentation

Midterm Exams 3 6 18

Final 3 7 21

If any other state please

TOTAL WORKLOAD : 175

ECTS Credit (Total Workload Hours / 25 (hours ) : 7

DEERLENDRME SSTEM

YARIYIL ALIMALAR SAYI KATKI PAYI

Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40

TOPLAM Yaryl ii almalarn toplamnn %40 alnmaktadr.

YARIYIL SONU ALIMALAR SAYI KATKI PAYI

Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA

SEMESTER REQUIREMENTS NUMBER PERCENTAGE OF GRADE %

Course attendance

Laboratory

Practice

Research

Project

Quizzes

Assignments/Homeworks

Presentation

Seminars

Midterm(s) %40

TOTAL(40% of the activities within the Semester)

ACTIVITIES AT THE END OF SEMESTER

Final Exams 1 % 60

IF ANY OTHER please state

and 60% of the final exam

TOTAL

100

DERSN PROGRAM IKTILARINA KATKISI

PROGRAM IKTISI (ncelikle lgili Program kurulunca belirlenmi olan program ktlar bu ksma girilecek daha sonra katk dzeyleri belirtilecektir.)

* KATKI DZEY

1 2 3 4 5

1 rendii matematiksel yntemleri kullanarak, toplumsal sorunlarla ilgili tartmalara katlabilmek ve zm nerisi getirebilmek

X

2 Matematik alan ile ilgili verilerin toplanmas, yorumlanmas, duyurulmas aamalarnda bilimsel ve toplumsal deerleri gz nnde bulundurma yeterliliine sahip olmak.

X

3 Matematik alannn gerektirdii lde bilgisayar yazlm ve programlama bilgisi edinebilmek

4 Mesleki ynden sorumluluk duygusuna ve etik deerlere sahip olmak X

5 Matematik ile ilgili sektrlerde, sorumluluu altnda alanlarn geliimlerine yardmc olabilmek

X

6 Gnlk hayatta karlat problemler karsnda analitik dnme yetenei ile zm bulabilmek

X

7 Soyut dnme yeteneini kullanabilmek X

8 Matematik alanndaki son gelimeleri takip edebilecek dzeyde matematik bilgisine ulaabilmek

X

9 Meslektalaryla iletiim kurabilecek ve alanndaki yabanc dilde yaynlanm almalar takip edebilecek dzeyde yabanc dil bilgisine sahip olabilmek

10 alma arkadalarna uyum salayabilmek, grup almasna katlabilmek

X

11 Matematik alanndaki bilimsel bir materyali tartabilmek, yazabilmek ve bilgi sahibi bir dinleyici grubuna szl olarak sunabilmek

X

12 Yeterli seviyede alan bilgisine sahip olmak ve bilgisini eitim-retim srecinde verimli kullanabilmek

X

13 Matematikle ilgili elde edilen verileri istatistiksel olarak deerlendirip yorumlayabilmek

14 Farkl bilim alanlarndaki problemleri matematiksel modellemek, analiz etmek ve zme katkda bulunabilmek

X

15

*(1-ok az , 2- Az , 3- Orta , 4-yi, 5-ok iyi ) derecede katk

CONTRIBUTION OF COURSE LEARNING OUTCOMES TO PROGRAM OUTCOMES

PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5

1 By using learned mathematical techniques, to be able to interact with the social problems and offer solution suggestions

X

2 To be able to take into consideration of social and scientific values when collecting, analyzing and announcing the mathematical datas.

X

3 To be able to gain sufficient computer and programming knowledge at a stage which is needed in field of Mathematics

4 To have sense of responsibility and ethical values within professional aspects

X

5 To be able to help the progress of emploees at Mathematical institutions/courts

X

6 To be able to find solutions for the real life problems by analitical X

thinking

7 To be able to use conceptual skills X

8 To be able to achieve the mathematical background in order to follow recent developments in mathematics

X

9 To be able to know the foreign language in related area and be able to use it to communicate with his/her colleagues and to follow periodic literature

10 To be able to fit in collegues and be able to join the group works X

11 To be able to negotiate a scientific material in the field of mathematics and write and present it to interested communities

X

12 To be able have field information at a sufficient level and be able to use it during the education process in an efficient way

X

13 To be able to evaluate and comment on the mathematical results statistically

14 To be able to make mathematical modelling of the problems in different fields of sciences and be able to make corresponding analysis and so to contribute to the solutions

X

15

*(1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest)


DERSN ADI (tr) : Analiz II

Name (en): Analysis II




Matematik

Mathematics

Dersin Kodu Code :

MAT 102

Zorunlu/Semeli Compulsive/Elective

Zorunlu

Compulsive

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Bahar

Spring


ECTS Credit: 7


Trke Turkish


Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

4 2 0

RETM ELEMANLARI

Yrd. Do. Dr. smail DEMR Contact


Tel:02862180018/1704

DERSN KATEGORS


Temel Meslek Dersleri X


Destek Dersleri



ERK BLGLER

TRKE NGLZCE


Yok None

Dersin Tanmlamas

Course Description:

Riemann integrali; Belirsiz integraller, Analizin

temel teoremi; ntegral alma yntemleri; Belirli integralin uygulamalar; Konikler; Parametrik ve kutupsal eriler, Diziler, Seriler ve Yaknsaklk Testleri

Riemann integral; Indefinite integrals;

Fundamental theorem of Analysis; Methods

of integration; Applications of indefinite

integral. Conics, parametric and polar curves,

Sequences, series and convergence tests

Ana Ders Kitab:

Main Coursebook:


AdamsCalculus ve Analitik Geometri, Richard

A. Silverman


AdamsCalculus ve Analitik Geometri,

Richard A. Silverman

Dier Kaynaklar :

Other references

Kalkls, James Stewart Kalkls, James Stewart

Eitim-retim


( Ek1-2 ):

Dier Other

Eitim-retim


( Ek1-1 ):




1 : Belirsiz integralleri ve integral alma yntemlerini iyi renme

2 : Alt ve st Riemann toplamlarn renme

3 : Alt ve st Riemann toplamlarn kullanarak belirli integral bulabilme

4 : ntegral teknikleri ve belirli integralin uygulamalarn renme

5 : Has olmayan integralleri renir

6 : Diziler ve serilerin zelliklerini ve yaknsaklk testlerini iyi renme

7 : Taylor ve Maclaurin serileri ile Fonksiyonlarn seriye almlarn iyi renme.

LEARNING OUTCOMES


1 : Learns indefinite integrals and integration methods

2 : Learns lower and upper Riemann sums

3 : Finds definite integrals by using Lover and upper Riemann sums

4 : Understands integral techniques and applications of definite integration

5 : Learns improper integrals

6 : Learns properties of Sequences and series and convergence tests

7 : Taylor and Maclaurin series and Series expansion of functions


Haftalar HAFTALIK KONULAR N HAZIRLIK

1 : Belirsiz ntegraller. Toplamlarn limiti olarak alanlar [1], [2], [3]

2 : Alt ve st Riemann toplamlar. Riemann integrali [1], [2], [3]

3 : Belirli integralin zellikleri. Analizin temel teoremi [1], [2], [3]

4 : Deiken deitirme yntemi. Trigonometrik integraller [1], [2], [3]

5 : Ksmi integral yntemi. Basit kesirlere ayrma yntemi [1], [2], [3]

6 : Alan hesab, hacim hesab [1], [2], [3]

7 : Eri uzunluu hesab. Dnel yzeylerin alan [1], [2], [3]

8 : Has olmayan integraller [1], [2], [3]

9 : Arasnav [1], [2], [3]

10 : Diziler, Serilerin yaknsakl, yaknsaklk testleri [1], [2], [3]

11 : Mutlak ve koullu yaknsaklk [1], [2], [3]

12 : Kuvvet serileri [1], [2], [3]

13 : Taylor ve Maclaurin serileri [1], [2], [3]

14 : Fonksiyonlarn seriye almlar [1], [2], [3]



1 : Indefinite integrals, as the limit of the total areas [1], [2], [3]

2 : Lower and upper Riemann sums, Riemann integral [1], [2], [3]

3 : Properties of definite integral. Fundamental theorem of Analysis [1], [2], [3]

4 : Substitution method. Trigonometric integrals. [1], [2], [3]

5 : Partial integration method. Simple fractional allocation method. [1], [2], [3]

6 : Area and volume calculation [1], [2], [3]

7 : Calculation of curve length. Area of a surface of revolations [1], [2], [3]

8 : Improper integrals. [1], [2], [3]

9 : Midterm Exam [1], [2], [3]

10 : Sequences, Convergence of series. Convergence tests. [1], [2], [3]

11 : Absolute and conditional convergence [1], [2], [3]

12 : Power series [1], [2], [3]

13 : Taylor and Maclaurin series [1], [2], [3]

14 : Series expansion of functions [1], [2], [3]

AKTS YK TABLOSU



14 6 84

Staj

devler

Seminer

Proje


Alan almas


Vaka ncelemesi

Ders d alma 13 2 26


Ksa Snavlar

Sunum



Varsa Dier

TOPLAM YK : 175


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study



departments)

Quizzes

Presentation


Final 3 7 21




DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) %40



Final Exams 1 % 60



TOTAL

100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X

5 To be able to help the progress of emploees at Mathematical X

institutions/courts

6 To be able to find solutions for the real life problems by analitical thinking

X



X




X


X



X

15



DERSN ADI (tr) : Analtitk Geometri I

Name (en): Analytic Geometry I




Matematik

Dersin Kodu Code :

MAT 103 Zorunlu/Semeli Compulsive/Elective

Zorunlu

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Gz Autumn


ECTS Credit:

6


Trke


Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

2 2 -

RETM ELEMANLARI

1 :

Yrd. Do. Dr. etin CAMCI Contact

E-mail: [email protected]

Tel: 286 218 0018/1713

2 :

DERSN KATEGORS

Sadece bir kategori seilecektir. (X) Temel Meslek Dersleri X


Destek Dersleri



ERK BLGLER

TRKE NGLZCE


Yok None

Dersin Tanmlamas

Course Description:

Dzlemsel koordinatlar ; dik koordinatlar, paralel koordinatlar, kutupsal koordinatlar, homojen

koordinatlar, uzayda dik koordinatlar. Vektrler ; ynlendirilmi doru paralar ve vektrler

cebrine giri, lineer baml ve lineer bamsz vektrler, skaler arpm, vektrel arpm, karma

arpm, dzlemde vektrler. Dzlemde Koordinat Dnmleri; telemeler, dnmeler, dik

koordinat sisteminden paralel koordinat sistemine

gei, afin dnmler. Eriler; dzlemsel erilerin snflandrlmas, cebirsel eri rnekleri,

konikler, dzlemde ikinci derece erileri, eri aileleri, konik demetleri

Coordinates in planes; vertical coordinates;

parallel coordinates, polar coordinates;

homogen coordinates, vertival coordinates in

space;Vectors;Introductuon to vector

algebra;linearly depandent and independent

vectors; scalar product; vectoral product;

coordinate mappings in plane , affin

mappings; Curves; Classification of plane

curves; conics

Ana Ders Kitab:

Main Coursebook:

1. Analitik Geometri,Hacsaliholu, H. H. (2000) 2. Uzay Analitik Geometri, Sezginman ., Abac M. (1999)

1. Analitik Geometri,Hacsaliholu, H. H. (2000)

2. Uzay Analitik Geometri, Sezginman ., Abac M. (1999)

Dier Kaynaklar :

Other references

Yok None

Eitim-retim


( Ek1-2 ):

Dier Other

Eitim-retim


( Ek1-1 ):

Ders anlatm Oral lectures


1 : Dzlemsel koordinatlar snflandrabilir.

2 : Vektrlerin cebirsel ilemlerini yapabilir.

3 : Lineer bamllk tanmn yapabilir.

4 : Skaler ve vektrel arpm yapabilir.

5 : Dzlemde koordinat dnmleri yapabilir.

6 : teleme ve dnme fonksiyonlarn bulabilir.

7 : Erileri ve konikleri tanmlayabilir, zelliklerini aratrabilir.

LEARNING OUTCOMES

1 :

Classificate coordinates in plane.

2 : Does algebric operations on vectors

3 : Defines linear independence concept.

4 : Calculates scalar and vectoral products.

5 : Makes mappings on planes.

6 : Finds rotation and transition functions.

7 : Defines curves and conics and also analyses their properties.

YARIYIL DERS PROGRAMI (TRKE)

HAFTALIK KONU N HAZIRLIK

1 : Dzlemsel koordinatlar ; dik koordinatlar, paralel koordinatlar, kutupsal koordinatlar, homojen koordinatlar, uzayda dik koordinatlar

2 : Dzlemsel koordinatlar ; dik koordinatlar, paralel koordinatlar, kutupsal koordinatlar, homojen koordinatlar, uzayda dik koordinatlar

3 : Vektrler ; ynlendirilmi doru paralar ve vektrler cebrine giri

4 : Lineer baml ve lineer bamsz vektrler

5 : Skaler arpm, vektrel arpm, karma arpm

6 : Skaler arpm, vektrel arpm, karma arpm

7 : Dzlemde Koordinat Dnmleri

8 : Dzlemde Koordinat Dnmleri

9 : Arasnav

10 : telemeler, dnmeler

11 : Eriler; dzlemsel erilerin snflandrlmas

12 : Eriler; dzlemsel erilerin snflandrlmas

13 : Konikler, dzlemde ikinci derece erileri, eri aileleri, konik demetleri

14 : Konikler, dzlemde ikinci derece erileri, eri aileleri, konik demetleri



1 : Coordinates in plane, vertical coordinates, parallel coordinates, polar

coordinates, vertical coordinates in space

2 : Coordinates in plane, vertical coordinates, parallel coordinates, polar

coordinates, vertical coordinates in space

3 : Vectors, directed line segment and vector algebra

4 : Lenearly dependent and independent vectors

5 : Scalar product, vectorel product, mixed scalar product

6 : Scalar product, vectorel product, mixed scalar product

7 : Coordinate mappings in Plane

8 : Coordinate mappings in Plane

9 : Midterm Exam

10 : Transition and rotation

11 : Curves, classification of curves in plane

12 : Curves, classification of curves in plane

13 : Conics , quadratic curves in plane; curve familiy; conic bunches

14 : Conics , quadratic curves in plane; curve familiy; conic bunches

AKTS YK TABLOSU



14 4 56

Staj

devler

Seminer

Proje


Alan almas


Vaka ncelemesi

Ders d alma 13 2 26


Ksa Snavlar

Sunum



Varsa Dier

TOPLAM YK : 150


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study



departments)

Quizzes

Presentation


Final 3 7 21




DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) %40



Final Exams 1 % 60



TOTAL

100



* KATKI DZEY

1 2 3 4 5


X


X



5 Matematik ile ilgili sektrlerde, sorumluluu altnda alanlarn X

geliimlerine yardmc olabilmek


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X


X


X



X




X


X



X

15



DERSN ADI (tr) : Analtitk Geometri II

Name (en): Analytic Geometry II


Fen- Edebiyat Fakltesi Faculty of Arts And Sciences


Matematik

Mathematics Dersin Kodu

Code : MAT 104 Zorunlu/Semeli

Compulsive/Elective

Zorunlu

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Bahar

Spring


ECTS Credit:

6


Trke Turkish


Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

2 2 -

RETM ELEMANLARI

1 :

Yrd.Do. Dr. etin CAMCI Contact


Tel: 286 218 0018 / 1713

DERSN KATEGORS

Sadece bir kategori seilecektir. (X) Temel Meslek Dersleri X


Destek Dersleri



ERK BLGLER

TRKE NGLZCE


Yok None

Dersin Tanmlamas

Course Description:

Uzayda doru ve dzlem; doru, dzlem, drtyzlnn hacmi, uzayda simetri, uygulamalar.

Yzeyler; yzeyin vektrel denklemi, yzeyin grafii, kre, silindir, koni, regle yzeyler, dnel yzeyler, ikinci dereceden yzeyler, uzay erileri. Uzayda

Koordinat Sistemleri; silindirik koordinatlar, kresel koordinatlar, kutuplar koordinatlar. n-boyutlu Uzayda

Analitik Geometri; IRn de nokta ve vektr kavram, IRn de doru, IRn de hiper dzlem, IRn de eri, IRn

de hiperdzeyler, baz zel yzeyler

Quotient spaces, First countable spaces,

Second countable spaces, Lindelf spaces, Separable spaces, The separation

axioms, Regular spaces, Norml spaces,

completely regular spaces, Tychonoff

spaces, Sequences and convergence in

topological spaces, Sequentially

continuity, Compact spaces, Tychonoff

theorem, Heine Borel theorem,

Connected spaces.

Ana Ders Kitab:

Main Coursebook:

1. Analitik Geometri,Hacsaliholu, H. H. (2000) 2. Uzay Analitik Geometri, Sezginman ., Abac M. (1999)

1. Analitik Geometri,Hacsaliholu, H. H. (2000)

2. Uzay Analitik Geometri, Sezginman ., Abac M. (1999)

Dier Kaynaklar :

Other references

Yok None

Eitim-retim


( Ek1-2 ):

Dier Other

Eitim-retim


( Ek1-1 ):



1 : Uzayda doru ve dzlemi tanmlayabilir.

2 : Kre, silindir, koni yzey grafiklerini izebilir.

3 : 2. dereceden yzeyleri ve uzay erilerinin zelliklerini belirleyebilir.

4 : Uzayda koordinat sistemlerini birbirine dntrebilir.

5 : Rn de nokta ve vektr kavramn renir.

6 : Rn de eri izimi yapabilir.

LEARNING OUTCOMES

1 : Defines line and plane in space

2 :

Graphs sphere, conics

3 : Analyse second order surface and curves at space

4 : Maps coordinat systems to polar coordinate system.

5 : Learns point and vector concepts at IRn

6 : . Draw curves at IRn



1 : Uzayda doru ve dzlem

2 : Doru, dzlem, uzayda simetri

3 : Yzeyler; yzeyin vektrel denklemi, yzeyin grafii

4 : Kre, Silindir

5 : Dnel yzeyler, ikinci dereceden yzeyler

6 : Uzay erileri

7 : Uzayda Koordinat Sistemleri

8 : Silindirik koordinatlar, kresel koordinatlar, kutuplar koordinatlar

9 : Arasnav

10 : n-boyutlu Uzayda Analitik Geometri

11 : IR^n de nokta ve vektr kavram

12 : IR^n de doru

13 : IR^n de hiper dzlem, IR^n de eri

14 : Baz zel yzeyler



1 : The axiom of choose and its equivalent forms

2 : The axiom of choose and its equivalent forms

3 : Binary operation

4 : Binary operation

5 : Natural numbers

6 : Natural numbers

7 : Integers

8 : Various examples

9 : Midterm Exam, Various examples

10 : Rational numbers

11 : Finite sets, Infinite sets

12 : Finite sets, Infinite sets

13 : Equipotent sets, cardinal numbers

14 : Equipotent sets, cardinal numbers

AKTS YK TABLOSU



14 4 56

Staj

devler

Seminer

Proje


Alan almas


Vaka ncelemesi

Ders d alma 13 2 26


Ksa Snavlar

Sunum



Varsa Dier

TOPLAM YK : 150


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study



departments)

Quizzes

Presentation


Final 3 7 21




DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) %40



Final Exams 1 % 60



TOTAL

100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X


X


X



X




X


X



X

15



DERSN ADI (tr) : Soyut Matematik I

Name (en): Abstract Mathematics I




Matematik

Dersin Kodu Code :


Zorunlu

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Gz Autumn


ECTS Credit:

6


Trke


Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

2 2 -

RETM ELEMANLARI

Do. Dr. Erdal EKC Contact


DERSN KATEGORS Sadece bir kategori seilecektir. (X) Temel Meslek Dersleri X


Destek Dersleri



ERK BLGLER

TRKE NGLZCE


- -

Dersin Tanmlamas

Course Description:

nermeler, ispat yntemleri, kme Kavram, kmeler ailesi, arpm kmeler, bantlar, fonksiyonlar, bire-bir, rten fonksiyonlar ve eitleri, fonksiyonlarn bilekesi, denklik bantlar, denklik snflar ve paralanma, blm kmeleri, sralama bantlar, ksmi sralama, tam sralama, iyi sralama bilgilerini renir.

Gets basic knowledgements about

propositions, proof methods, concept

of set, family of sets, product sets,

relations, functions, injective,

surjective functions and their types,

composite functions, equivalence

relations, equivalence classes and

partition, quotient sets, order relations,

partial ordering, total ordering, well

ordering.

Ana Ders Kitab:

Main Coursebook:

[1] Soyut Matematik, O. zer, D. oker, K. Ta, Anadolu niv., 1994.

[2] Soyut Matematie Giri, T. Karaay, Bakent niv., 2009.

1. Soyut Matematik, O. zer, D. oker, K. Ta, Anadolu niv., 1994.

2. Soyut Matematie Giri, T. Karaay, Bakent niv., 2009.

[3] Soyut Matematik, S. Akka, H. H. Hacsaliholu, Z. zel, A. Sabuncuolu, Gazi niversitesi, 1988.

3. Soyut Matematik, S. Akka, H. H. Hacsaliholu, Z. zel, A. Sabuncuolu, Gazi niversitesi, 1988.

Dier Kaynaklar :

Other references

- -

Eitim-retim


( Ek1-2 ):

Dier Other

Eitim-retim


( Ek1-1 ):



RETM YNTEMLER (

Ek1-1 )

DEERLENDRME YNTEMLER (

Ek1-3 )

1 : nerme kavramn ifade edebilir ve ispat yntemlerini uygulayabilir.

Ders anlatm Ara snav

2 : Kme kavramn aklayabilir ve arpm kmeler kavramn ifade edebilir.


3 : Bant kavramn tanmlayabilir ve fonksiyon kavramn tanmlayabilir.


4 : Verilen bir fonksiyonun bire-bir ve

rtenliini aratrabilir. Ders anlatm Ara snav

5 : Bileke fonksiyon oluturabilir. Denklik bantsn tanmlayabilir. Sralama bants zelliklerini sayabilir

Ders anlatm Final

6 : Ksmi sralama, tam sralama ve iyi sralama kavramlarn aklayabilir

Ders anlatm Final

LEARNING OUTCOMES

RETM YNTEMLER (

Ek1-1 )


Ek1-3 )

1 : Explains the concept of propositon and

applies the proof methods.

Oral lectures Midterm exam

2 : Explains the concept of set and the

concept of product sets


3 : Defines the concept of relation and the

concept of function


4 : Investigates injectiveness, surjectiveness

of functions


5 : Determines composite functions. Defines

Oral lectures final exam

the concept of equivalence relation and

explains the properties of order relation

6 : Explains the concepts of partial ordering,

total ordering and well ordering




1 : nermeler

[1], [2], [3]

2 : nermeler [1], [2], [3]

3 : spat Yntemleri

[1], [2], [3]

4 : Kme kavram [1], [2], [3]

5 : Kmeler ailesi, arpm kmeler

[1], [2], [3]

6 : Kmeler ailesi, arpm kmeler [1], [2], [3]

7 : Bantlar [1], [2], [3]

8 : Fonksiyonlar [1], [2], [3]

9 : Arasnav, Fonksiyonlar

[1], [2], [3]

10 : Fonksiyonlar [1], [2], [3]

11 : denklik bantlar, denklik snflar ve paralanma [1], [2], [3]

12 : denklik bantlar, denklik snflar ve paralanma [1], [2], [3]

13 : sralama bantlar, ksmi sralama, tam sralama, iyi sralama [1], [2], [3]

14 :

eitli rnekler

[1], [2], [3]

15 : Final

[1], [2], [3]

16 :



1 : Propositions

[1], [2], [3]

2 : Propositions

[1], [2], [3]

3 : Proof methods [1], [2], [3]

4 : Concept of set [1], [2], [3]

5 : Family of sets, product sets [1], [2], [3]

6 : Family of sets, product sets [1], [2], [3]

7 : Relations [1], [2], [3]

8 : Functions [1], [2], [3]

9 : Midterm Exam, Functions [1], [2], [3]

10 : Functions [1], [2], [3]

11 : Equivalence relations, Equivalence classes and partition [1], [2], [3]

12 : Equivalence relations, Equivalence classes and partition [1], [2], [3]

13 : Partial ordering, Total ordering, Well ordering [1], [2], [3]

14 : Various examples [1], [2], [3]

15 : Final [1], [2], [3]

16 :

AKTS YK TABLOSU



14 4 56

Staj

devler

Seminer

Proje


Alan almas


Vaka ncelemesi

Ders d alma 13 2 26


Ksa Snavlar

Sunum



Varsa Dier

TOPLAM YK : 150


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study



departments)

Quizzes

Presentation


Final 3 7 21




DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) %40



Final Exams 1 % 60



TOTAL

100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X


X


X



X




X


X



X

15



DERSN ADI (tr) : Soyut Matematik II

Name (en): Abstract Mathematics II


Fen- Edebiyat Fakltesi Faculty of Arts And Sciences


Matematik

Dersin Kodu Code :


Zorunlu

Snf Class:

1 Yaryl ( 1 / 2 ) Term 1/2 :

Bahar

Spring


ECTS Credit:

6


Trke


Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

2 2 -

RETM ELEMANLARI

Do. Dr. Erdal EKC Contact


DERSN KATEGORS Sadece bir kategori seilecektir. (X) Temel Meslek Dersleri X


Destek Dersleri



ERK BLGLER

TRKE NGLZCE


- -

Dersin Tanmlamas

Course Description:

Seme Aksiyomu ve edeerleri, ikili ilemler, doal saylar, tam saylar, rasyonel saylar, esayl olma, sonlu kmeler, sonsuz kmeler, nicelik saylar bilgilerini renir.

Gets basic knowledgements about

axiom of choose and its

equivalent forms, binary

operation, natural numbers,

integers, rational numbers,

equipotent sets, finite sets, infinite

sets, cardinal numbers.

Ana Ders Kitab:

Main Coursebook:

[1] Soyut Matematik, O. zer, D. oker, K. Ta, Anadolu niv., 1994.

[2] Soyut Matematie Giri, T. Karaay, Bakent niv., 2009.

[3] Soyut Matematik, S. Akka, H. H. Hacsaliholu, Z. zel, A. Sabuncuolu, Gazi niversitesi, 1988.

1. Soyut Matematik, O. zer, D. oker, K. Ta, Anadolu niv., 1994.

2. Soyut Matematie Giri, T. Karaay, Bakent niv., 2009.

3. Soyut Matematik, S. Akka, H. H. Hacsaliholu, Z. zel, A. Sabuncuolu, Gazi niversitesi, 1988.

Dier Kaynaklar :

Other references

Eitim-retim


( Ek1-2 ):

Dier Other

Eitim-retim


( Ek1-1 ):



RETM YNTEMLER

( Ek1-1

)


Ek1-3 )

1 : Seme aksiyomunu ve edeerlerini ifade edebilir.


2 : kili ilem kavramnn tanmn yapabilir. Ders anlatm Ara snav

3 : Doal saylar kmesini, tam saylar kmesini ve rasyonel saylar kmesini belirleyebilir.


4 : Esayl olma kavramn ve rneklerini belirleyebilir.

Ders anlatm Final

5 : Verilen bir kmenin sonlu yada sonsuz olup olmadn belirleyebilir.

Ders anlatm Final

6 : Nicelik saylar kavramn aklayabilir. Ders anlatm Final

LEARNING OUTCOMES

RETM YNTEMLER (

Ek1-1 )


Ek1-3 )

1 : Explains the axiom of choose and its

equivalent forms


2 : Defines the concept of binary operation Oral lectures Midterm exam

3 : Determines the set of natural numbers,

the integers and the set of rational

numbers


4 : Determines the concept of equipotent

sets and its examples


5 : Determines whether a given set is finite

or infinite


6 : Explains the concept of cardinality Oral lectures final exam



1 : Seme Aksiyomu ve edeerleri

[1], [2], [3]

2 : Seme Aksiyomu ve edeerleri [1], [2], [3]

3 : lem [1], [2], [3]

4 : lem [1], [2], [3]

5 : Doal saylar [1], [2], [3]

6 : Doal saylar [1], [2], [3]

7 : Tam saylar [1], [2], [3]

8 : eitli rnekler [1], [2], [3]

9 : Arasnav, eitli rnekler [1], [2], [3]

10 : Rasyonel saylar [1], [2], [3]

11 : Sonlu kmeler, sonsuz kmeler [1], [2], [3]

12 : Sonlu kmeler, sonsuz kmeler [1], [2], [3]

13 : Esayl olma, Nicelik saylar [1], [2], [3]

14 : Esayl olma, Nicelik saylar [1], [2], [3]

15 : Final [1], [2], [3]



1 : The axiom of choose and its equivalent forms [1], [2], [3]

2 : The axiom of choose and its equivalent forms [1], [2], [3]

3 : Binary operation [1], [2], [3]

4 : Binary operation [1], [2], [3]

5 : Natural numbers [1], [2], [3]

6 : Natural numbers [1], [2], [3]

7 : Integers [1], [2], [3]

8 : Various examples [1], [2], [3]

9 : Midterm Exam, Various examples [1], [2], [3]

10 : Rational numbers [1], [2], [3]

11 : Finite sets, Infinite sets [1], [2], [3]

12 : Finite sets, Infinite sets [1], [2], [3]

13 : Equipotent sets, cardinal numbers [1], [2], [3]

14 : Equipotent sets, cardinal numbers [1], [2], [3]

15 : Final [1], [2], [3]

AKTS YK TABLOSU



14 4 56

Staj

devler

Seminer

Proje


Alan almas


Vaka ncelemesi

Ders d alma 13 2 26


Ksa Snavlar

Sunum



Varsa Dier

TOPLAM YK : 150


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork 13 2 26

Doing Research

Preparation

Case Study



departments)

Quizzes

Presentation


Final 3 7 21




DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) %40



Final Exams 1 % 60



TOTAL

100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X


X


X



X




X


X



X

15



DERSN ADI (tr) : Analiz III

Course Name (en): Analysis III

Akademik Birim : Academic Unit:

Fen Edebiyat Fakltesi Faculty of Arts and Sciences

Blm : Department/Program

Matematik

Mathematics

Dersin Kodu: Code:

MAT 201

Zorunlu:

Compulsive: X

Semeli: Elective:

Snf: Class:

2 Yaryl ( 1 / 2 ):

Term (1/2):

Gz Autumn

OM Kredisi : 5 AKTS Kredisi:

ECTS Credit: 8

Dersin Dili: Language

Trke Turkish

H.Ders Saati: Class hour per week

Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

4 2 -

RETM ELEMANLARI - LECTURERS

1 :

Do.Dr. Mehmet NAL Contact


Tel:0 286 218 0018 / 1703

2 :

DERSN KATEGORS - TYPE


Temel Meslek Dersleri x


retmenlik Meslek Bilgisi

Genel Kltr

Alan Bilgisi Dersleri

VARSA DER BELRTNZ :

ERK BLGLER

TRKE/TURKISH NGLZCE/ENGLISH

n Koullar: Prerequisites:

Yok None

Dersin Tanmlamas:

Course Description:

R^n nin topolojisi, IR^n deki diziler ve serileri,

Fonksiyon serilerinin yaknsaklk ve dzgn yaknsaklk testleri, ok deikenli fonksiyonlarda limit ve sreklilik, Ksmi trevler, Ynl trevler, Gradiyent, Teet dzlem denklemi, Maksimum ve minimum deerler.

Topology of IR^n (n>1), sequences and series on IR^n , Tests of convergence and

uniform convergence of functions sequences,

Functions of several variables, Limits and

continuity. Partial derivatives, Directional

derivatives, Gradients, Equations of tangent

plane, Maximum and Minimum values.

Ana Ders Kitab:

Main Course Book

Calculus ve Analitik Geometri, Sherman, K.

Stein. (1997), Literatr Yaynclk. Calculus ve Analitik Geometri, Sherman, K.

Stein. (1997), Literatr Yaynclk.

Dier Kaynaklar:

Other References:

Yksek Matematik, Halilov, H. , Can, M. (2001), Literatr Yaynclk. Diferensiyel ve ntegral Hesap, Frank Ayres, Jr. (1992), Nobel Yaynclk.


Eitim-retim


( Ek1-2 ):

Yok None

Eitim-retim

Metodlar

( Ek1-1 ):




1 : IRn (n 1) in Eucledian uzay olmasn tanmlayabilir, taban kavramn renir.

2 : IRn deki dizilerin yaknsakln ve serilerin yaknsakln inceleyebilir.

3 : Fonksiyon serilerinin yaknsaklk ve dzgn yaknsaklk testlerini uygulayabilir.

4 : Ksmi trevler, ynl trevler, diferansiyel ve tanjant dzlemi tanmlayabilir.

5 : ok deikenli fonksiyonlarnn limit ve srekliliini inceleyebilir.

6 : Ksmi trevler, ynl trevler ve trevlerin srekliliini inceleyebilir.

7 : Zimcir kuraln renir, maksimim, minimum problemlerini zebilir.

LEARNING OUTCOMES


1 : Defines structure of IRn (n>1) and learns concept of base

2 : Dissects of convergence of sequences in IRn and convergence of series in IRn

3 : Applicabilties convergence and uniform

4 : Defines partial derivatives, directional derivatives, differential and tangent plane equation to a curve

5 : Analysables functions of several variables; limits and continuity convergence tests of function series

6 : Analysables continuity of partial derivatives, directional derivatives and derivatives.

7 : Learns chain rule and solves maximum and minimum problem


Haftalar HAFTALIK KONU N HAZIRLIK

1 : IRn in yaps ve taban kavram

2 : IRn iindeki dizilerin yaknsakl

3 : IRn iindeki serilerin yaknsakl

4 : Fonksiyon serilerinin yaknsakl ve yaknsaklk testleri

5 : ok deikenli fonksiyonlarda limit ve sreklilik

6 : Ksmi trevler, ynl trevler

7 : Ynl trev ve ksmi trev arasndaki ilikiler

8 : Diferansiyellenebilmenin matris gsterimi

9 : Arasnav

10 : Teet dzlem denklemi

11 : Zincir kural

12 : Aradeer teoremi

13 : Maksimim ve minimum problemleri

14 : Maksimim ve minimum problemleri

WEEKLY COURSE PLAN

Weeks TopIcs Preparation

1 : Structure of IRn (n>1) and concept of base

2 : Convergence of sequences in IR^n

3 : Convergence of series in IR^n

4 : Convergence tests of function series

5 : Limit and continuity for functions

6 : Partial derivatives, directional derivatives

7 : Relations between directional derivative and partial derivative

8 : Matrix representation of differentiable mappings

9 : Midterm Exam

10 : Tangent plane equation to a curve

11 : Chain rule and applications

12 : Mean-Value theorem

13 : Maximum and minimum problem

14 : Maximum and minimum problem

AKTS YK TABLOSU


Ders Saati (Snav haftas dahil 16 x toplam ders saati) 16 6 96

Staj

devler

Seminer

Proje

Aratrma yapma

Alan almas


15 4 60

Vaka ncelemesi

Ders d alma 16 2 32

Rapor sunma

Ksa snavlar

Sunum

Ara Snav/lara hazrlanma


Varsa Dier

TOPLAM YK : 200

AKTS KREDS (Toplam Yk Saati / 25 (s) ) : 8

ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork

Doing Research

Preparation 15 4 60

Case Study


Microteaching (teacher training departments)

Quizzes

Presentation

Midterm Exams

Final 2 6 12


TOPLAM YK : 200


DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar 1 %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 2 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) 1 %40


ACTIVITIES AT THE END OF SEMESTER SAYI KATKI PAYI

Final Exams 1 %60

IF ANY OTHER (please state)

TOTAL 2 100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


X



X


X


X



X




X


X



X

15



DERSN ADI (tr) : Analiz IV

Course Name (en): Analysis IV

Akademik Birim : Academic Unit:

Fen Edebiyat Fakltesi Faculty of Arts and Sciences

Blm : Department/Program

Matematik

Mathematics

Dersin Kodu: Code:

MAT 202

Zorunlu:

Compulsive: X

Semeli: Elective:

Snf: Class:

2 Yaryl ( 1 / 2 ):

Term (1/2):

Bahar

Spring

OM Kredisi : 5 AKTS Kredisi:

ECTS Credit: 8

Dersin Dili: Language

Trke Turkish

H.Ders Saati: Class hour per week

Teorik/Theoretical

(hours per week)

Uygulama/Tutorial

(hours per week)


(hours per week)

4 2 -

RETM ELEMANLARI - LECTURERS

1 :

Do.Dr. Mehmet NAL Contact


Tel:0 286 218 0018 / 1703

2 :

DERSN KATEGORS - TYPE


Temel Meslek Dersleri x


retmenlik Meslek Bilgisi

Genel Kltr

Alan Bilgisi Dersleri

VARSA DER BELRTNZ :

ERK BLGLER

TRKE/TURKISH NGLZCE/ENGLISH

n Koullar: Prerequisites:

Yok None

Dersin Tanmlamas:

Course Description:

Katl integraller; Has olmayan katl integraller; ki ve katl integraller; Silindirik ve kresel koordinatlar, Katl integralin uygulamalar, Dorusal ntegral; Yzeyler ve yzey integralleri

Multiple integrals, Improper multiple

integrals, triple and double integrals,

Cylindrical and Spherical Coordinates,

Applications of multiple integrals, Linear

integral, Surfaces and integrals of surface..

Ana Ders Kitab:

Main Course Book

Calculus ve Analitik Geometri, Sherman, K.

Stein. (1997), Literatr Yaynclk. Calculus ve Analitik Geometri, Sherman, K.

Stein. (1997), Literatr Yaynclk.

Dier Kaynaklar:

Other References:



Eitim-retim


( Ek1-2 ):

Yok None

Eitim-retim

Metodlar

( Ek1-1 ):




1 : Katl integralleri tanmlayabilir.

2 : Has olmayan katl integralleri hesaplayabilir.

3 : Ortalama ntegral teoremini ispatlayabilir.

4 : Kutupsal koordinatlarda katl integrallerde uygulama yapabilir.

5 : katl integralleri zebilir.

6 : Blge ve dzlemler arasnda oluan kat cisimlerin hacimlerini hesaplayabilir.

7 : Silindirik koordinat ve silindirik koordinat dnmlerini yapabilir.

LEARNING OUTCOMES


1 : Defines multiple integrals

2 : Calculation improper multiple integrals

3 : Proves avarage integral theorem

4 : Practices multiple integral in polar coordinates

5 : Solves triple integrals

6 : Calculation volumes of solids where between area and plane

7 : Makes cylindrical and spherical coordinate mapping.


Haftalar HAFTALIK KONU N HAZIRLIK

1 : Katl integraller

2 : Katl integrallerin zellikleri

3 : Belirsiz katl integraller

4 : Katl integrallerle ilgili problem zmleri

5 : Pozitif fonksiyonlarn has olmayan integralleri

6 : Pozitif fonksiyonlarn has olmayan integralleri

7 : Problem zmleri

8 : Kutupsal koordinatlarda katl integraller

9 : Arasnav

10 : Alan hesab

11 : katl integraller

12 : Yzeylerin parametrelenmesi ve dndrlmesi

13 : Kat cisim hacimleri

14 : Silindirik ve kresel koordinat dnmleri

WEEKLY COURSE PLAN

Weeks TopIcs Preparation

1 : Multiple integrals

2 : Properties of multiple integrals

3 : Improper multiple integrals

4 : Solved problems for multiple integrals

5 : Improper integrals of positive functions

6 : Improper integrals of positive functions

7 : Solved problems

8 : Multiple integrals in Polar coordinates

9 : Midterm Exam

10 : Area calculation

11 : Triple integrals

12 : Revolution of surfaces and parameters

13 : Volumes of solids

14 : Cylindrical and Spherical coordinate mapping.

AKTS YK TABLOSU


Ders Saati (Snav haftas dahil 16 x toplam ders saati) 16 6 96

Staj

devler

Seminer

Proje

Aratrma yapma

Alan almas


15 4 60

Vaka ncelemesi

Ders d alma 16 2 32

Rapor sunma

Ksa snavlar

Sunum

Ara Snav/lara hazrlanma


Varsa Dier

TOPLAM YK : 200


ECTS WORKLOAD TABLE



Practice

Assignments

Seminar/workshop

Project

Fieldwork

Doing Research

Preparation 15 4 60

Case Study


Microteaching (teacher training departments)

Quizzes

Presentation

Midterm Exams

Final 2 6 12


TOPLAM YK : 200


DEERLENDRME SSTEM


Derse Devam

Laboratuvar

Uygulama

Aratrma

Proje

Kk Snavlar

dev

Sunum

Seminer

Ara Snavlar 1 %40



Final Snav 1 %60

Varsa Dier

TOPLAM : 2 100

EVALUATION CRITERIA


Course attendance

Laboratory

Practice

Research

Project

Quizzes


Presentation

Seminars

Midterm(s) 1 %40


ACTIVITIES AT THE END OF SEMESTER SAYI KATKI PAYI

Final Exams 1 %60

IF ANY OTHER (please state)

TOTAL 2 100



* KATKI DZEY

1 2 3 4 5


X


X




X


X



X



X


X


X



X

15



PROGRAMME OUTCOMES

* KATKI DZEY

1 2 3 4 5


X


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