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
Calculus: A complete Course, Robert A.
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
DERSN ADI (tr) : Analiz II
Name (en): Analysis II
Akademik Birim Academic Unit:
Fen Edebiyat Fakltesi Faculty of Arts And Sciences
Blm Department/Program:
Matematik
Mathematics
Dersin Kodu Code :
MAT 102
Zorunlu/Semeli Compulsive/Elective
Zorunlu
Compulsive
Snf Class:
1 Yaryl ( 1 / 2 ) Term 1/2 :
Bahar
Spring
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:
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:
Calculus: A complete Course, Robert A.
AdamsCalculus ve Analitik Geometri, Richard
A. Silverman
Calculus: A complete Course, Robert A.
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 : 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
After completion of this course students will be able to:
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
HAFTALIK DERS PROGRAMI (TRKE)
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]
WEEKLY COURSE PLAN (English)
Weeks TOPICS Preparation
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
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 X
institutions/courts
6 To be able to find solutions for the real life problems by analitical thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
DERSN ADI (tr) : Analtitk Geometri I
Name (en): Analytic Geometry I
Akademik Birim Academic Unit:
Fen Edebiyat Fakltesi Faculty of Arts And Sciences
Blm Department/Program:
Matematik
Dersin Kodu Code :
MAT 103 Zorunlu/Semeli Compulsive/Elective
Zorunlu
Snf Class:
1 Yaryl ( 1 / 2 ) Term 1/2 :
Gz Autumn
OM Kredisi : 3 AKTS Kredisi
ECTS Credit:
6
Dersin Dili Language:
Trke
H.Ders Saati : Class hour per week
Teorik/Theoretical
(hours per week)
Uygulama/Tutorial
(hours per week)
Laboratuvar/Laboratory
(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
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:
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
Materyalleri Materials
( Ek1-2 ):
Dier Other
Eitim-retim
Metodlar Teaching Methods
( Ek1-1 ):
Ders anlatm Oral lectures
DERS RENME IKTILARI (TRKE)
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
WEEKLY COURSE PLAN (English)
Weeks TOPICS Preparation
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati)
14 4 56
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 7 21
Final Snavna Hazrlanma 3 7 21
Varsa Dier
TOPLAM YK : 150
ECTS KREDS (Toplam Yk Saati / 25 (s) ) : 6
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 14 4 56
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 7 21
Final 3 7 21
If any other state please
TOTAL WORKLOAD : 150
ECTS Credit (Total Workload Hours / 25 (hours ) : 6
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 X
geliimlerine yardmc olabilmek
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 thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
DERSN ADI (tr) : Analtitk Geometri II
Name (en): Analytic Geometry II
Akademik Birim Academic Unit:
Fen- Edebiyat Fakltesi Faculty of Arts And Sciences
Blm Department/Program:
Matematik
Mathematics Dersin Kodu
Code : MAT 104 Zorunlu/Semeli
Compulsive/Elective
Zorunlu
Snf Class:
1 Yaryl ( 1 / 2 ) Term 1/2 :
Bahar
Spring
OM Kredisi : 3 AKTS Kredisi
ECTS Credit:
6
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)
2 2 -
RETM ELEMANLARI
1 :
Yrd.Do. Dr. etin CAMCI Contact
E-mail: [email protected]
Tel: 286 218 0018 / 1713
DERSN KATEGORS
Sadece bir kategori seilecektir. (X) 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:
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
Materyalleri Materials
( Ek1-2 ):
Dier Other
Eitim-retim
Metodlar Teaching Methods
( Ek1-1 ):
Ders anlatm Oral lectures
DERS RENME IKTILARI (TRKE)
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
YARIYIL DERS PROGRAMI (TRKE)
HAFTALIK KONU N HAZIRLIK
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
WEEKLY COURSE PLAN (English)
Weeks TOPICS Preparation
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati)
14 4 56
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 7 21
Final Snavna Hazrlanma 3 7 21
Varsa Dier
TOPLAM YK : 150
ECTS KREDS (Toplam Yk Saati / 25 (s) ) : 6
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 14 4 56
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 7 21
Final 3 7 21
If any other state please
TOTAL WORKLOAD : 150
ECTS Credit (Total Workload Hours / 25 (hours ) : 6
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 thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
DERSN ADI (tr) : Soyut Matematik I
Name (en): Abstract Mathematics I
Akademik Birim Academic Unit:
Fen Edebiyat Fakltesi Faculty of Arts And Sciences
Blm Department/Program:
Matematik
Dersin Kodu Code :
MAT 107 Zorunlu/Semeli Compulsive/Elective
Zorunlu
Snf Class:
1 Yaryl ( 1 / 2 ) Term 1/2 :
Gz Autumn
OM Kredisi : 3 AKTS Kredisi
ECTS Credit:
6
Dersin Dili Language:
Trke
H.Ders Saati : Class hour per week
Teorik/Theoretical
(hours per week)
Uygulama/Tutorial
(hours per week)
Laboratuvar/Laboratory
(hours per week)
2 2 -
RETM ELEMANLARI
Do. Dr. Erdal EKC Contact
E-Mail: [email protected]
DERSN KATEGORS Sadece bir kategori seilecektir. (X) 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
- -
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
Materyalleri Materials
( Ek1-2 ):
Dier Other
Eitim-retim
Metodlar Teaching Methods
( Ek1-1 ):
Ders anlatm Oral lectures
DERS RENME IKTILARI (TRKE)
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.
Ders anlatm Ara snav
3 : Bant kavramn tanmlayabilir ve fonksiyon kavramn tanmlayabilir.
Ders anlatm Ara snav
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 )
DEERLENDRME YNTEMLER (
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
Oral lectures Midterm exam
3 : Defines the concept of relation and the
concept of function
Oral lectures Midterm exam
4 : Investigates injectiveness, surjectiveness
of functions
Oral lectures Midterm exam
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
Oral lectures final exam
YARIYIL DERS PROGRAMI (TRKE)
HAFTALIK KONU N HAZIRLIK
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 :
WEEKLY COURSE PLAN (English)
Weeks TOPICS Preparation
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati)
14 4 56
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 7 21
Final Snavna Hazrlanma 3 7 21
Varsa Dier
TOPLAM YK : 150
ECTS KREDS (Toplam Yk Saati / 25 (s) ) : 6
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 14 4 56
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 7 21
Final 3 7 21
If any other state please
TOTAL WORKLOAD : 150
ECTS Credit (Total Workload Hours / 25 (hours ) : 6
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 thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
DERSN ADI (tr) : Soyut Matematik II
Name (en): Abstract Mathematics II
Akademik Birim Academic Unit:
Fen- Edebiyat Fakltesi Faculty of Arts And Sciences
Blm Department/Program:
Matematik
Dersin Kodu Code :
MAT 108 Zorunlu/Semeli Compulsive/Elective
Zorunlu
Snf Class:
1 Yaryl ( 1 / 2 ) Term 1/2 :
Bahar
Spring
OM Kredisi : 3 AKTS Kredisi
ECTS Credit:
6
Dersin Dili Language:
Trke
H.Ders Saati : Class hour per week
Teorik/Theoretical
(hours per week)
Uygulama/Tutorial
(hours per week)
Laboratuvar/Laboratory
(hours per week)
2 2 -
RETM ELEMANLARI
Do. Dr. Erdal EKC Contact
E-Mail: [email protected]
DERSN KATEGORS Sadece bir kategori seilecektir. (X) 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
- -
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
Materyalleri Materials
( Ek1-2 ):
Dier Other
Eitim-retim
Metodlar Teaching Methods
( Ek1-1 ):
Ders anlatm Oral lectures
DERS RENME IKTILARI (TRKE)
RETM YNTEMLER
( Ek1-1
)
DEERLENDRME YNTEMLER (
Ek1-3 )
1 : Seme aksiyomunu ve edeerlerini ifade edebilir.
Ders anlatm Ara snav
2 : kili ilem kavramnn tanmn yapabilir. Ders anlatm Ara snav
3 : Doal saylar kmesini, tam saylar kmesini ve rasyonel saylar kmesini belirleyebilir.
Ders anlatm Ara snav
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 )
DEERLENDRME YNTEMLER (
Ek1-3 )
1 : Explains the axiom of choose and its
equivalent forms
Oral lectures Midterm exam
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
Oral lectures Midterm exam
4 : Determines the concept of equipotent
sets and its examples
Oral lectures final exam
5 : Determines whether a given set is finite
or infinite
Oral lectures final exam
6 : Explains the concept of cardinality Oral lectures final exam
YARIYIL DERS PROGRAMI (TRKE)
HAFTALIK KONU N HAZIRLIK
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]
WEEKLY COURSE PLAN (English)
Weeks TOPICS Preparation
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati)
14 4 56
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 7 21
Final Snavna Hazrlanma 3 7 21
Varsa Dier
TOPLAM YK : 150
ECTS KREDS (Toplam Yk Saati / 25 (s) ) : 6
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 14 4 56
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 7 21
Final 3 7 21
If any other state please
TOTAL WORKLOAD : 150
ECTS Credit (Total Workload Hours / 25 (hours ) : 6
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 thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
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)
Laboratuvar/Laboratory
(hours per week)
4 2 -
RETM ELEMANLARI - LECTURERS
1 :
Do.Dr. Mehmet NAL Contact
E-mail: [email protected]
Tel:0 286 218 0018 / 1703
2 :
DERSN KATEGORS - TYPE
Sadece bir kategori seilecektir. (X) Choose only one type
Temel Meslek Dersleri x
Uzmanlk Alan Desleri
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.
Yksek Matematik, Halilov, H. , Can, M. (2001), Literatr Yaynclk. Diferensiyel ve ntegral Hesap, Frank Ayres, Jr. (1992), Nobel Yaynclk.
Eitim-retim
Materyalleri Materials
( Ek1-2 ):
Yok None
Eitim-retim
Metodlar
( Ek1-1 ):
Ders anlatm Lecturing
DERS RENME IKTILARI (TRKE)
Bu dersi baar ile tamamlayan renciler
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
After completion of this course students will be able to:
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
HAFTALIK DERS PROGRAMI (TRKE)
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati) 16 6 96
Staj
devler
Seminer
Proje
Aratrma yapma
Alan almas
n hazrlk (ders ncesinde derse hazrlanma iin harcanan sre)
15 4 60
Vaka ncelemesi
Ders d alma 16 2 32
Rapor sunma
Ksa snavlar
Sunum
Ara Snav/lara hazrlanma
Final Snavna Hazrlanma 2 6 12
Varsa Dier
TOPLAM YK : 200
AKTS KREDS (Toplam Yk Saati / 25 (s) ) : 8
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 16 6 96
Practice
Assignments
Seminar/workshop
Project
Fieldwork
Doing Research
Preparation 15 4 60
Case Study
Study Hours Out of Class 16 2 32
Microteaching (teacher training departments)
Quizzes
Presentation
Midterm Exams
Final 2 6 12
If any other state please
TOPLAM YK : 200
AKTS KREDS (Toplam Yk Saati / 25 (s) ) : 8
DEERLENDRME SSTEM
YARIYIL ALIMALAR SAYI KATKI PAYI
Derse Devam
Laboratuvar
Uygulama
Aratrma
Proje
Kk Snavlar
dev
Sunum
Seminer
Ara Snavlar 1 %40
TOPLAM Yaryl ii almalarn toplamnn %40 alnmaktadr.
YARIYIL SONU ALIMALAR SAYI KATKI PAYI
Final Snav 1 %60
Varsa Dier
TOPLAM : 2 100
EVALUATION CRITERIA
SEMESTER REQUIREMENTS NUMBER PERCENTAGE OF GRADE %
Course attendance
Laboratory
Practice
Research
Project
Quizzes
Assignments/Homeworks
Presentation
Seminars
Midterm(s) 1 %40
TOTAL(40% of the activities within the Semester)
ACTIVITIES AT THE END OF SEMESTER SAYI KATKI PAYI
Final Exams 1 %60
IF ANY OTHER (please state)
TOTAL 2 100
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 thinking
X
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)
COURSE SYLLABUS- DERS TANITIM BLGLER
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)
Laboratuvar/Laboratory
(hours per week)
4 2 -
RETM ELEMANLARI - LECTURERS
1 :
Do.Dr. Mehmet NAL Contact
E-mail: [email protected]
Tel:0 286 218 0018 / 1703
2 :
DERSN KATEGORS - TYPE
Sadece bir kategori seilecektir. (X) Choose only one type
Temel Meslek Dersleri x
Uzmanlk Alan Desleri
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:
Yksek Matematik, Halilov, H. , Can, M. (2001), Literatr Yaynclk. Diferensiyel ve ntegral Hesap, Frank Ayres, Jr. (1992), Nobel Yaynclk.
Yksek Matematik, Halilov, H. , Can, M. (2001), Literatr Yaynclk. Diferensiyel ve ntegral Hesap, Frank Ayres, Jr. (1992), Nobel Yaynclk.
Eitim-retim
Materyalleri Materials
( Ek1-2 ):
Yok None
Eitim-retim
Metodlar
( Ek1-1 ):
Ders anlatm Lecturing
DERS RENME IKTILARI (TRKE)
Bu dersi baar ile tamamlayan renciler
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
After completion of this course students will be able to:
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.
HAFTALIK DERS PROGRAMI (TRKE)
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
AKTVTELER SAYI SRES (saat) TOPLAM
Ders Saati (Snav haftas dahil 16 x toplam ders saati) 16 6 96
Staj
devler
Seminer
Proje
Aratrma yapma
Alan almas
n hazrlk (ders ncesinde derse hazrlanma iin harcanan sre)
15 4 60
Vaka ncelemesi
Ders d alma 16 2 32
Rapor sunma
Ksa snavlar
Sunum
Ara Snav/lara hazrlanma
Final Snavna Hazrlanma 2 6 12
Varsa Dier
TOPLAM YK : 200
AKTS KREDS (Toplam Yk Saati / 25 (s) ) : 8
ECTS WORKLOAD TABLE
ACTIVITIES Number Duration Total Workload
Class hours (Including Exam Week: 16 x Total Hours) 16 6 96
Practice
Assignments
Seminar/workshop
Project
Fieldwork
Doing Research
Preparation 15 4 60
Case Study
Study Hours Out of Class 16 2 32
Microteaching (teacher training departments)
Quizzes
Presentation
Midterm Exams
Final 2 6 12
If any other state please
TOPLAM YK : 200
AKTS KREDS (Toplam Yk Saati / 25 (s) ) : 8
DEERLENDRME SSTEM
YARIYIL ALIMALAR SAYI KATKI PAYI
Derse Devam
Laboratuvar
Uygulama
Aratrma
Proje
Kk Snavlar
dev
Sunum
Seminer
Ara Snavlar 1 %40
TOPLAM Yaryl ii almalarn toplamnn %40 alnmaktadr.
YARIYIL SONU ALIMALAR SAYI KATKI PAYI
Final Snav 1 %60
Varsa Dier
TOPLAM : 2 100
EVALUATION CRITERIA
SEMESTER REQUIREMENTS NUMBER PERCENTAGE OF GRADE %
Course attendance
Laboratory
Practice
Research
Project
Quizzes
Assignments/Homeworks
Presentation
Seminars
Midterm(s) 1 %40
TOTAL(40% of the activities within the Semester)
ACTIVITIES AT THE END OF SEMESTER SAYI KATKI PAYI
Final Exams 1 %60
IF ANY OTHER (please state)
TOTAL 2 100
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.