FACULTY OF ENGINEERING

Department of Electrical and Electronics Engineering

EEE 281 | Course Introduction and Application Information

Course Name
Engineering Mathematics I
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
EEE 281
Fall
2
2
3
6

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 Vector spaces, bases, GramSchmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices. Solution of firstorder ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Laplace transform methods; convolution and delta function. Matrix methods for the solution of ODEs: eigenvalues and eigenvectors, matrix exponentials, variation of parameters. MATLAB is introduced for problem sets.
Learning Outcomes The students who succeeded in this course;
  • Explain the foundations of Vector spaces, bases, Gram-Schmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form,
  • Analyse first-order differential equations; seperable differential equations, linear differential equations and higher order linear differential equations,
  • Apply the methods of undetermined coefficients, and the method of variation of parameters for the solution of ordinary differential equations,
  • Apply the techniques of reduction of order for the numerical solutions of ordinary differential equations,
  • Use Laplace Transform to solve initial value problems,
  • Analyse the problems of differential equations with many unknowns through linear algebra and applied matrix theory.
Course Description Vector spaces, bases, GramSchmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices. Solution of firstorder ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Laplace transform methods; convolution and delta function. Matrix methods for the solution of ODEs: eigenvalues and eigenvectors, matrix exponentials, variation of parameters. MATLAB is introduced for problem sets.

 



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 Matrices and Determinants / Dizey ve Belirteçler Systems of Linear Equations. Matrices and Matrix Operations. Inverses of Matrices. Kısım 1. / Chapter 1 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
2 Special Matrices and Additional Properties of Matrices. Determinants. Further Properties of Determinants. Proofs of Theorems on Determinants. Kısım 1. / Chapter 1 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
3 Vector Spaces / Vektör Uzayları Vector Spaces. Subspaces and Spanning Sets. Linear Independence and Bases. Dimension; Nullspace, Rowspace, and Column Space. Wronskians Kısım 2. / Chapter 2 . • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
4 First Order Ordinary Differential Equations / Birinci Mertebeden Türevli Denklemler Introduction to Differential Equations. Separable Differential Equations. Exact Differential Equations. Linear Differential Equations. Kısım 3. / Chapter 3 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
5 More Techniques for Solving First Order Differential Equations. Modeling With Differential Equations. Reduction of Order. The Theory of First Order Differential Equations. Numerical Solutions of Ordinary Differential Equations. Kısım 3. / Chapter 3 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
6 Linear Differential Equations / Doğrusal Türevli Denklemler The Theory of Higher Order Linear Differential Equations. Homogenous Constant Coefficient Linear Differential Equations. The Method of Undetermined Coefficients. The Method of Variation of Parameters. Some Applications of Higher Order Differential Equations Kısım 4. / Chapter 4 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
7 Linear Transformations, Eigenvalues, and Eigenvectors / Doğrusal Dönüşümler, Özdeğerler, ve Özvektörler Linear Transformations. The Algebra of Linear Transformations; Differential Operators and Differential Equations. Matrices for Linear Transformations. Kısım 5. / Chapter 5 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
8 Eigenvectors and Eigenvalues of Matrices. Similar Matrices, Diagonalization, and Jordan Canonical Form.Eigenvectors and Eigenvalues of Linear Transformations Kısım 5. / Chapter 5 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
9 Systems of Differential Equations / Türevli Denklem Sistemleri The Theory of Systems of Linear Differential Equations. Homogenous Systems with Constant Coefficients: The Diagonalizable Case. Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
10 Homogenous Systems with Constant Coefficients: The Nondiagonalizable Case. Nonhomogenous Linear Systems. Nonhomogenous Linear Systems Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
11 Converting Differential Equations to First Order Systems. Applications Involving Systems of Linear Differential Equations. 2x2 Systems of Nonlinear Differential Equations. Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
12 Laplace Transform / Laplace Dönüşümü Definition and Properties of the Laplace Transform. Solving Constant Coefficient Linear Initial Value Problems with Laplace Transforms Kısım 7. / Chapter 7 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
13 The Step Functions, Impulse Functions and the Delta Function. Convolution Integrals. Systems of Linear Differential Equations. Kısım 7. / Chapter 7 . • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
14 Power Series Solutions to Linear Differential Equations / Doğrusal Türevli Denklemlerin Serilerle Çözümü Introduction to Power Series Solutions. Series Solutions for Second Order Linear Differential equations. Kısım 8. / Chapter 8 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
15 Euler Type Equations. Series Solutions Near a Regular Singular Point.. Kısım 8. / Chapter 8 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
16 Inner Product Spaces / Dahili Çarpım Uzayları Inner Product Spaces. Orthonormal Bases Schur's Theorem and Symmetric Matrices. Kısım 9. / Chapter 9 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122

 

Course Notes/Textbooks • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
Suggested Readings/Materials • Differential Equations and Linear Algebra, 3/E, Edwards & Penney, ©2010, PrenticeHall, Published:10/10/2008, ISBN10: 0136054250, ISBN13: 9780136054252 • Differential Equations and Linear Algebra, 3/E, Goode & Annin, ©2008 PrenticeHall, Published:03/13/2007, ISBN10: 0130457949, ISBN13: 9780130457943 • Elementary Differential Equations, 6/E, Edwards & Penney ©2008, Pearson, ISBN10: 0132397307, ISBN13: 9780132397308• Differential Equations and Linear Algebra, 3/E, Edwards & Penney, ©2010 , PrenticeHall, Published:10/10/2008ISBN10: 36054250, ISBN13: 9780136054252 • Advanced Modern Engineering Mathematics, 3/E, James & James, ©2004 , PrenticeHall, Published:07/21/2005, ISBN10: 0130454257, ISBN13: 9780130454256 • Advanced Engineering Mathematics, 2/E, Greenberg ©1998 , PrenticeHall, Published: 01/08/1998, ISBN10: 0133214311, ISBN13: 9780133214314

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
2
50
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
3
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
4
64
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
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
2
10
20
Final Exam
1
30
30
    Total
178

 

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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