MATEMATİK II DERS TANITIM VE UYGULAMA BİLGİLERİ

Kodu	Dersin Adı	Yarıyıl	Süresi(T+U)	Kredisi	AKTS Kredisi
MAT106	MATEMATİK II	2	5	4	6

DERS BİLGİLERİ
Dersin Öğretim Dili :	Türkçe
Dersin Düzeyi	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Dersin Türü	Zorunlu
Dersin Veriliş Şekli	-
Dersin Koordinatörü	Prof. HAMDİ ALPER ÖZYİĞİT
Dersi Veren Öğretim Üyesi/Öğretim Görevlisi
Ders Ön Koşulu	Yok

AMAÇ VE İÇERİK
Amaç:	It is aimed for students to recognize multivariable functions, to be able to transfer the concepts of limit continuity and derivatives obtained in univariate functions to multivariable functions, to interpret their graphs, and to calculate surface area and volume with different methods with the help of integral.
İçerik:	Area Between Curves, Lengths of Plane Curves, Finding Volume by Slicing and Rotation around an Axis, Finding Volume with Cylindrical Shells, Areas of Rotational Surfaces, Generalized Integrals, Multivariable Functions, Limits and Continuity in High Dimensions, Partial Derivatives, Chain Rule, Direction Derivatives and Gradient Vectors. , Tangent Planes and Differentials, Extreme Values ​​and Saddle Points, Second Derivative Test for Extreme Values, Double Integrals and Area, Volume Applications, Double Integrals in Polar Form, Variable Conversion in Multiple Integrals

DERSİN ÖĞRENME ÇIKTILARI (Öğrenciler, bu dersi başarı ile tamamladıklarında aşağıda belirtilen bilgi, beceri ve/veya yetkinlikleri gösterirler.)
Recognizes multivariable functions and their graphs. (Bloom 1, Knowledge)
Uses partial derivative steps correctly. (Bloom 3, Application)
Defines and interprets Directional Derivative and Gradient Vector. (Bloom 1, Knowledge, Bloom 2, Understand)
Solves the problems of finding extrema and saddle points of graphs of two-variable functions. (Bloom 3, Application)
Transfers a given function to polar form. (Bloom 3, Application)
Compares different methods of calculating volume with the help of integral. (Bloom 2, Understand)
Solves area, volume and arc length calculation problems with the help of definite integral. (Bloom 3, Application)
Solves area and volume calculation problems with the help of double integral. (Bloom 3, Application)

HAFTALIK DERS KONULARI VE ÖNGÖRÜLEN HAZIRLIK ÇALIŞMALARI
Hafta	Ön Hazırlık	Konular	Yöntem
1	Students create a positive impression in the preparatory work related to course topics	Sigma Notation and Limits of Finite Sums,The Definite Integral, The Fundamental Theorem of Calculus, Basic Integration Formulas, Integration by Parts,	Lecture-Discussion
2	Topic started on the preparation of problems and solutions	Integration of Rational Functions by Partial Fractions, Trigonometric Integrals, Trigonometric Substitutions	Lecture-Discussion
3	Topic started on the preparation of problems and solutions	Substitution and Area Between Curves, Lengths of Plane Curves	Lecture-Discussion
4	Topic started on the preparation of problems and solutions	Volumes by Slicing and Rotation About an Axis, Volumes by Cylindrical Shells, Areas of Surfaces of Revolution	Lecture-Discussion
5	Topic started on the preparation of problems and solutions	Improper Integrals	Lecture-Discussion
6	Topic started on the preparation of problems and solutions	Functions of Several Variables	Lecture-Discussion
7	Topic started on the preparation of problems and solutions	Limits and Continuity in Higher Dimensions	Lecture-Discussion
8	-	MID-TERM EXAM	-
9	Topic started on the preparation of problems and solutions	Partial Derivatives, The Chain Rule	Lecture-Discussion
10	Topic started on the preparation of problems and solutions	Directional Derivatives and Gradient Vectors, Tangent Planes and Differentials	Lecture-Discussion
11	Topic started on the preparation of problems and solutions	Extreme Values and Saddle Points	Lecture-Discussion
12	Topic started on the preparation of problems and solutions	Double Integrals, Area and Volume	Lecture-Discussion
13	Topic started on the preparation of problems and solutions	Double Integrals in Polar Form, Substitutions in Multiple Integrals	Lecture-Discussion
14	Topic started on the preparation of problems and solutions	Applications	Lecture-Discussion
15	-	-	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

KAYNAKLAR
P.F.Smith, W.R. Congley, Diferansiyel ve İntegral Hesap.
Prof.Dr.Ahmet Karadeniz, Yüksek Matematik Problemleri.
Murtaza Çalı, Diferansiyel ve İntegral Hesap.
George B. Thomas, Calculus and Analytic Geometry.
Naci İskender, Yüksek Matematik.

ÖLÇME VE DEĞERLENDİRME
Yarıyıl İçi Yapılan Çalışmaların Ölçme ve Değerlendirmesi	Etkinlik Sayısı	Katkı Yüzdesi	Açıklama

(0) Etkisiz	(1) En Düşük	(2) Düşük	(3) Orta	(4) İyi	(5) Çok İyi
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Able to adopt math and science knowledge to the problems of Mechatronic Engineering.					4

KNOWLEDGE
Factual
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Can use the scientific methods to solve problems of Mechatronic Engineering.						5
2	Able to plan experiment, build hardware, collect data using modern devices and analyze data.	0

SKILLS
Cognitive
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Can define, scientize and solve the actual mechatronics problems.	0

SKILLS
Practical
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Use modern tools such as softwares in engineering design and analysis.	0

OCCUPATIONAL
Autonomy & Responsibility
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Prone to work in interdisciplinary teams and be a team leadership.	0

OCCUPATIONAL
Learning to Learn
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Able to find solutions that meet technical and economical expectations when designing a system with components.	0
2	Can approach with a global perspective to Mechatronics Engineering.	0
3	Able to keep up to date of self-awarness in the field.	0
4	Can follow academic and industrial developments related Mechatronics Engineering.	0

OCCUPATIONAL
Communication & Social
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Able to work in the field, interdisciplinary and multidisciplinary environments.	0
2	Have written and verbal communication skills in Turkish and English.	0

OCCUPATIONAL
Occupational and/or Vocational
	Program Yeterlilikleri/Çıktıları	Katkı Düzeyi
		0	1	2	3	4	5
1	Have professional and ethical values and sensitive to these.	0
2	Sensitive to health and safety issues in Mechatronic Engineering.	0
3	Sensitive to social, environmental and economic factors in professional activities.	0

DERSİN İŞ YÜKÜ VE AKTS KREDİSİ
Öğrenme-Öğretme Etkinlikleri İş Yükü
Öğrenme-Öğretme Etkinlikleri	Etkinlik(hafta sayısı)	Süresi(saat sayısı)	Toplam İş Yükü
Lecture & In-Class Activities	14	4	56
Preliminary & Further Study	14	2	28
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	0	0	0
Assignment (Homework)	4	6	24
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	4	4	16
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	2	2
Preparation for the Final Exam	1	10	10
Mid-Term Exam	1	2	2
Preparation for the Mid-Term Exam	1	10	10
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	40	0	148