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EEE 282 | Ders Tanıtım Bilgileri

Dersin Adı

Engineering Mathematics II

Kodu	Yarıyıl	Teori (saat/hafta)	Uygulama/Lab (saat/hafta)	Yerel Kredi	AKTS
EEE 282	SPRING	2	2	3	5

Ön-Koşul(lar)	EEE 281 - Engineering Mathematics I (MATH 154 and EEE 281 (At least FD)), MATH 154 - Calculus II (MATH 154 and EEE 281 (At least FD))
Dersin Dili	English
Dersin Türü	Zorunlu
Dersin Düzeyi	Lisans
Dersin Veriliş Şekli	Face-To-Face
Dersin Öğretim Yöntem ve Teknikleri	Lecture Presentation Problem Solving
Ulusal Meslek Sınıflandırma Kodu	-
Dersin Koordinatörü	Prof. Dr. Murat Aşkar
Öğretim Eleman(lar)ı	Prof. Dr. Murat Aşkar
Yardımcı(ları)	-

Dersin Amacı

Introduction to transformation techniques. Laplace transform. Use of Laplace transform in solving ordinary differential equations. Fourier Series. Fourier series expansion of periodic functions. Orthogonal series. Fourier transform. Discrete Fourier Transform and Fast Fourier Transform. z-transform. Solution of Discrete Difference Equations using z-transform. Vector operations. Application of transformation techniques and vector operations to engineering problems.

Öğrenme Çıktıları

Bu dersi başarıyla tamamlayabilen öğrenciler;

Ad	Açıklama	PC Alt	* Katkı Düzeyi
Ad	Açıklama	PC Alt	1	2	3	4	5
LO1	Determining the Laplace transform of continuous time signals	1.1		X
LO2	Solving ordinary differential equations using the Laplace transform	1.1			X
LO3	Finding Fourier Series expansions of periodic functions	1.1		X
LO4	Determining the steady state response of linear systems using the Fourier transform	1.1			X
LO5	Using the z-transform to find solutions to discrete systems	1.1		X
LO6	Use of transformation techniques and vector operations in solving engineering problems.	4	X

Ders Tanımı

Laplace transform. Fundamental properties. Laplace transform of elementary functions. s-shift theorem. Laplace transform of derivative and integral. Ordinary differential equations and Laplace transform. Unit step function. T-shift theorem. Impulse function. Partial fraction expansion. Convolution. Integral equations. Solving ordinary differential equations using Laplace transform. Fourier series. Arbitrary choice of period. Even and odd functions. Half-range expansion. Forced oscillations. Orthogonal functions. Orthogonal series. Generalized Fourier series. Fourier integral. Fourier cosine and sine transforms. Fourier transform. Discrete Fourier transform and fast Fourier transform. Discrete systems. Z-transform. Solution of difference functions using z-transform. Vectors. Inner product (dot product) Vector product (cross product). Use of transformation techniques and vector operations in engineering problems.

Dersin İlişkili Olduğu Sürdürülebilir Kalkınma Amaçları

Dersin Kategorisi	Temel Ders	X
	Uzmanlık/Alan Dersleri
	Destek Dersleri
	İletişim ve Yönetim Becerileri Dersleri
	Aktarılabilir Beceri Dersleri

HAFTALIK KONULAR VE İLGİLİ ÖN HAZIRLIK ÇALIŞMALARI

Hafta	Konular	Ön Hazırlık	Öğrenme Çıktısı
1	Introduction to transforms. The usage of vector calculus. Basic Concepts. Laplace Transform. Linearity.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.1, 13.2, 13.3)	94931ee4
2	s-Shifting Theorem (s-Shifting). Transforms of Derivatives and Integrals.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.4, 13.5, 13.6, 13.7)	94931ee4
3	ODEs and Laplace Transform. Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 14.1, 4.2, 14.3, 14.4)	94931ee4
4	Impulse function. Partial Fractions expansion.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.1, 7.2, 7.3)	94931ee4
5	Convolution. Integral Equations. Solutions of ODES using Laplace Transform.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.4, 7.5, 7.6, 7.7, 7.8)	dfcbb5d9
6	Fourier Series. Arbitrary Period. Even and Odd Functions. Half- Range Expansions.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.9, 8.1)	7adf1d58
7	Midterm Exam		-
8	Forced Oscillations. Approximation by Trigonometric Polynomials.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.2, 8.3)	7adf1d58
9	Orthogonal Functions. Orthogonal Series. Generalized Fourier Series.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.4); Class Notes	7adf1d58
10	Fourier Integral. Fourier Cosine and Sine Transforms.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.1, 1.2, 1.3)	4d6d5820
11	Fourier Transform. The steady state response of the linear systems using Fourier transform. Discrete and Fast Fourier Transforms.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.4, 1.5, 1.7)	4d6d5820
12	Discrete systems. Definition of z- transform	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.1, 2.2, 2.4)	4355c8ef
13	Solving difference equations by z-transform.	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.6, 2.7, 2.8, 2.9)	4355c8ef
14	Vectors in 2-Space and 3-Space. Inner Product (Dot Product). Vector Product (Cross Product).	Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 3.1, 3.2, 3.3)	162cec74
15	Application of transform techniques and vector operations to solve engineering problems.	Class Notes	162cec74
16	Final Exam		-

Ders Kitabı	Erwin Kreyszig "Advanced Engineering Mathematics" 10th Ed Wiley 2011. ISBN: 978-0-470-45836-5.
Önerilen Okumalar/Materyaller	"Differential Equations and Linear Algebra 3/E Edwards & Penney 2010 Prentice Hall ISBN: 978-0-138-14102-8 "Differential Equations and Linear Algebra" 3/E Goode & Annin 2008 Prentice Hall. ISBN: 978-0-130-45794-3.

DEĞERLENDİRME ÖLÇÜTLERİ

Yarıyıl Aktiviteleri	Sayı	Katkı Payı %	LO1	LO2	LO3	LO4	LO5	LO6
Küçük Sınav / Stüdyo Kritiği	3	20	X	X	X
Ödev	1	5	X	X	X	X	X	X
Ara Sınav	1	35	X	X	X	X	X
Final Sınavı	1	40	X	X	X	X	X	X
Toplam	6	100

AKTS / İŞ YÜKÜ TABLOSU

Yarıyıl Aktiviteleri	Sayı	Süre (Saat)	İş Yükü
Katılım	-	-	-
Teorik Ders Saati	16	4	64
Laboratuvar / Uygulama Ders Saati	-	-	-
Sınıf Dışı Ders Çalışması	16	2	32
Arazi Çalışması	-	-	-
Küçük Sınav / Stüdyo Kritiği	3	4	12
Portfolyo	-	-	-
Ödev	5	4	20
Sunum / Jüri Önünde Sunum	-	-	-
Proje	-	-	-
Seminer/Çalıştay	-	-	-
Sözlü Sınav	-	-	-
Ara Sınavlar	1	8	8
Final Sınavı	1	14	14
		Toplam	150

DERSİN ÖĞRENME ÇIKTILARININ PROGRAM YETERLİLİKLERİ İLE İLİŞKİSİ

#	PC Alt	Program Yeterlilikleri / Çıktıları	* Katkı Düzeyi
#	PC Alt	Program Yeterlilikleri / Çıktıları	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics		LO1 LO3 LO5	LO2 LO4
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.		LO6
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.