FACULTY OF ENGINEERING

Department of Electrical and Electronics 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
  MATH 153 To succeed (To get a grade of at least DD)
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives The main goal of this course is to cover practical mathematical methods important to engineering applications. It is expected that students already have a mathematical background, including undergraduate courses in calculus, linear algebra and differential equations. The course will start with vector differential and integral analysis. In general, this course will be focused on more advanced topics, including complex analysis, Laplace and the Fourier transform. The course aims to provide an understanding of the basic facts of complex analysis. An important goal of this course is to learn how to use computer to solve problems. Computational parts of the course include the use of the MatLab package.
Learning Outcomes The students who succeeded in this course;
  • Explain divergence, curl and gradient of scalar fields,
  • Analyse multi integrals, line integrals and surface integrals,
  • Employ Gauss theorem to flux integrals, Stokes' theorem to line integrals, and Green’s theorem to surface integrals,
  • Identify Cauchy-Riemann equations,
  • Define Taylor and Laurent series of simple functions,
  • Employ the residue theorem in the evaluation of complex integrals,
  • Describe the importance of Fourier series, and Fourier and Laplace transforms in applications.
Course Description Vector fields, gradient, curl, divergence. Multiple integrals, line integrals, surface integrals. Stokes' theorem in one, two, and three dimensions. Complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; Fourier analysis, Laplace transforms.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Vector Differential Calculus. Grad, Div, Curl Vectors in 2Space and 3Space Inner Product (Dot Product) Vector Product (Cross Product) Vector and Scalar Functions and Fields. Derivatives Curves. Arc Length. Curvature. Torsion Calculus Review: Functions of Several Variables. CHAPTER 9, Sect.9.19.6, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
2 Vector Differential Calculus. Grad, Div, Curl Gradient of a Scalar Field. Directional Derivative Divergence of a Vector Field Curl of a Vector Field CHAPTER 9, Sect.9.713.9, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
3 Vector Integral Calculus. Integral Theorems Line Integrals Path Independence of Line Integrals Calculus Review: Double Integrals. Green’s Theorem in the Plane Surfaces for Surface Integrals CHAPTER 10, Sect.10.1 10.5, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
4 Vector Integral Calculus. Integral Theorems Surface Integrals Triple Integrals. Divergence Theorem of Gauss Further Applications of the Divergence Theorem Stokes’s Theorem CHAPTER 10, Sect.10.6 10.9, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
5 Complex Numbers and Functions Complex Numbers. Complex Plane Polar Form of Complex Numbers. Powers and Roots Derivative. Analytic Function Cauchy–Riemann Equations. Laplace’s Equation CHAPTER 13, Sect.13.113.4, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
6 Complex Numbers and Functions Exponential Functio Trigonometric and Hyperbolic Functions Logarithm. General Power Review Questions and Problems CHAPTER 13, Sect.13.513.8, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
7 Complex Integration Line Integral in the Complex Plane Cauchy’s Integral Theorem CHAPTER 14, Sect.14.114.2, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
8 Complex Integration Cauchy’s Integral Formula Derivatives of Analytic Functions Review Questions and Problems CHAPTER 14, Sect.14.314.4, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
9 Power Series, Taylor Series Sequences, Series, Convergence Tests Power Series Functions Given by Power Series CHAPTER 15, Sect.15.115.3, Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
10 Power Series, Taylor Series Taylor and Maclaurin Series Uniform Convergence. Optional Review Questions and Problems CHAPTER 15, Sect.15.415.5 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
11 Laurent Series. Residue Integration Laurent Series Singularities and Zeros. Infinity Residue Integration Method Residue Integration of Real Integrals CHAPTER 16, Sect.16.116.4 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
12 Laplace Transforms Laplace Transform. Inverse Transform. Linearity. sShifting Transforms of Derivatives and Integrals. ODEs Unit Step Function. tShifting Short Impulses. Dirac’s Delta Function. Partial Fractions Convolution. Integral Equations CHAPTER 6, Sect.6.1 6.5 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
13 Laplace Transforms Differentiation and Integration of Transforms. Systems of ODEs Laplace Transform: General Formulas Table of Laplace Transforms CHAPTER 6, Sect.6.6 6.9 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
14 Fourier Analysis Fourier Series Functions of Any Period p = 2L Even and Odd Functions. HalfRange Expansions CHAPTER 11, Sect.11.116.3 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
15 Fourier Analysis Complex Fourier Series. Optional Forced Oscillations Approximation by Trigonometric Polynomials Fourier Integral CHAPTER 11, Sect.11.411.7 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
16 Fourier Analysis Fourier Cosine and Sine Transforms Fourier Transform. Discrete and Fast Fourier Transforms Tables of Transforms CHAPTER 11, Sect.11.811.10 Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005

 

Course Notes/Textbooks Erwin Kreyszig, "Advanced Engineering Mathematics 9th Ed. + Instructor's Manual 9 Ed."Publisher: John Wiley & Sons | ISBN: 0471728977 / 0471726478 | 9th Edition: 2005
Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
1
5
Portfolio
Homework / Assignments
1
5
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
50
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
Weighting of End-of-Semester Activities on the Final Grade
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
16
4
64
Field Work
0
Quizzes / Studio Critiques
1
5
5
Portfolio
0
Homework / Assignments
1
5
5
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
15
30
Final Exam
1
20
20
    Total
156

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science and Electrical and Electronics Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

X
2

To be able to identify, define, formulate, and solve complex Electrical and Electronics Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

X
3

To be able to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.

X
4

To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in Electrical and Electronics Engineering applications; uses computer and information technologies effectively.

X
5

To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Electrical and Electronics Engineering research topics.

X
6

To be able to work efficiently in Electrical and Electronics Engineering disciplinary and multi-disciplinary teams; to be able to work individually.

X
7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.

8

To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to Electrical and Electronics Engineering; to be aware of the legal ramifications of Electrical and Electronics Engineering solutions.

X
9

To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications

X
10

To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

X
11

To be able to collect data in the area of Electrical and Electronics Engineering, and to be able to communicate with colleagues in a foreign language. ("European Language Portfolio Global Scale", Level B1)

X
12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Electrical and Electronics Engineering.

X

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

 


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