11111

COURSE INTRODUCTION AND APPLICATION INFORMATION


ete.cs.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall
Prerequisites
 MATH 153To succeed (To get a grade of at least DD)
Course Language
Course Type
Required
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • the student have learnt and grasp 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. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices
  • get acquainted with the concepts of Linear Independence and Bases; Dimension; Nullspace, Rowspace, and Column Space; Wronskians;
  • have learnt the Systems of Linear Equations, Determinants, Matrices, and Matrix Operations, Inverses of Matrices;
  • be able to solve problems dealing with Separable Differential Equations, Exact Differential Equations, Linear Differential Equations;
  • be able to use the techniques of Reduction of Order, and Numerical Solutions of Ordinary Differential Equations;
  • Be able to employ the Methods of Undetermined Coefficients, and the Method of Variation of Parameters effectively for the solution of ODEs;
Course Description

 



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
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
2
20
Portfolio
Homework / Assignments
8
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
25
Final Exam
1
35
Total

Weighting of Semester Activities on the Final Grade
65
Weighting of End-of-Semester Activities on the Final Grade
35
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
2
32
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
2
Field Work
Quizzes / Studio Critiques
2
2
Portfolio
Homework / Assignments
8
2
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
2
Final Exams
1
2
    Total
88

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 Have sufficient background in mathematics, basic sciences and other related engineering areas and to be able to use this background in the problems of the electrical and electronics  engineering. X
2 Be able to identify, formulate and solve electrical and electronics engineering-related problems by using state-of-the-art methods, techniques and equipment. X
3 Be able to analyze an electrical and electronics system, system components or process, and to design with realistic limitations to meet the requirements using modern design techniques. X
4 Be able to choose and use the required techniques and tools for electrical and electronics engineering applications; to use technical symbols and drawings for communication. X
5

Be able to design and do simulation and/or experiment, collect and analyze data and interpret the results.   

X
6

Be able to work independently and participate in multidisiplinary teams.

X
7

Be conscious of project management, office applications, workers’ health, environment and work safety; awareness of professional and ethical responsibilities and the legal consequences of engineering applications.

X
8

Be able to access information, to do research and use data bases and other information sources.

X
9

Be able to communicate both in oral and written form in English at a minimum level of European Language Portfolio Global Scale Level B1.

10

Have an aptitude, capability and inclination for life-long learning.

11

To be able to use a second foreign language at intermediate level.

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

 

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