Department of Civil Engineering

EEE 282 | Course Introduction and Application Information

Course Name

Engineering Mathematics II

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
EEE 282	SPRING	2	2	3	5

Prerequisites	None
Course Language	English
Course Type	Required (Core Course)
Course Level	First Cycle
Mode of Delivery	Face-To-Face
Teaching Methods and Techniques of the Course	Lecture Presentation Problem Solving
National Occupational Classification Code	-
Course Coordinator	Prof. Dr. Murat Aşkar
Course Lecturer(s)	Prof. Dr. Murat Aşkar
Assistant(s)	-

Course Objectives

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.

Learning Outcomes

The students who succeeded in this course;

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

Course Description

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.

Related Sustainable Development Goals

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
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		-

Course Notes/Textbooks	Erwin Kreyszig "Advanced Engineering Mathematics" 10th Ed Wiley 2011. ISBN: 978-0-470-45836-5.
Suggested Readings/Materials	"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.

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4	LO5	LO6
Quizzes / Studio Critiques	3	20	X	X	X
Homework / Assignments	1	5	X	X	X	X	X	X
Midterm	1	35	X	X	X	X	X
Final Exam	1	40	X	X	X	X	X	X
Total	6	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	4	64
Laboratory / Application Hours	-	-	-
Study Hours Out of Class	16	2	32
Field Work	-	-	-
Quizzes / Studio Critiques	3	4	12
Portfolio	-	-	-
Homework / Assignments	5	4	20
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	1	8	8
Final Exam	1	14	14
		Total	150

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
			1	2	3	4	5
No program competency data found.

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

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