FACULTY OF ENGINEERING
Department of Civil Engineering
EEE 281 | Course Introduction and Application Information
Course Name |
Engineering Mathematics I
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Code
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Semester
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Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
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ECTS
|
EEE 281
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Fall
|
2
|
2
|
3
|
6
|
Prerequisites |
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Course Language |
English
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Course Type |
Required
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Course Level |
First Cycle
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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;
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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. |
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Core Courses | |
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 Civil 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 Civil 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 engineering applications. |
X | ||||
5 | To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Civil Engineering research topics. |
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6 | To be able to work efficiently in Civil Engineering disciplinary and multi-disciplinary teams; to be able to work individually. |
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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. |
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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 engineering; to be aware of the legal ramifications of engineering solutions. |
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9 | To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications. |
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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. |
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11 | To be able to collect data in the area of Civil Engineering, and to be able to communicate with colleagues in a foreign language; |
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12 | To be able to speak a second foreign language at a medium level of fluency efficiently. |
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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 Civil Engineering. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
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