‘Fire Towers’ for Forest Fires
Prof. Dr. Celalettin Kozanoğlu and Prof. Dr. Murat Aşkar from Izmir University of Economics (IUE) have developed a ‘fire tower’ ...
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Department of Civil 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 | To be successful in MATH 153 (To have received at least DD grade) | |||||
| 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 |
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| National Occupational Classification Code | - | |||||
| Course Coordinator |
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| Course Lecturer(s) |
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| Assistant(s) | - | |||||
| Course Objectives | Introduction to Complex Algebra. Representation of Complex Numbers. Euler Formula. Complex Functions. Analytical Functions. Matrices. System of Linear Equations. Gauss-Elimination Method. Linear Dependency and Independence. Vector Spaces. Determinants. Inverse Matrix. Eigenvalue Problem and Diagonalization. First and Second Order Differential Equations. Linear Constant Coefficient Differential Equations. Euler Method. Separable and Ordinary Differential Equations. Modeling Engineering Problems with Differential Equations. System of Linear Differential Equations. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning Outcomes |
The students who succeeded in this course;
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| Course Description | Complex Numbers and Their Geometric Representations. Analytical Functions and Properties. Cauchy-Riemann Equations. Laplace Equation. Euler Formula. Line Integral in the Complex Plane. Cauchy Integral Theorem. Matrices and Vectors. Matrix Operations. Systems of Linear Equations. Gauss Elimination. Linear Independence. Matrix Order. Vector Space. Linear System Solutions. Cramer's Rule. Determinants. Eigenvalues and Eigenvalue Vectors. Orthogonal Matrices. Eigenvalue Basis Vectors. Diagonalization. Gram-Schmidt Orthogonalization Method. Basic Concepts in Differential Equations. Modeling. Euler Method. Separable and Ordinary Differential Equations (OTD). First and Second Order Homogeneous Linear Differential Equations. Linear Differential Equations with Constant Coefficients. Modeling Engineering Problems with Differential Equations. System of Linear Differential Equations. Modeling and Solution of Systems of Linear Differential Equations. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Related Sustainable Development Goals |
-
|
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|
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 | Complex numbers and Geometric Representation. Polar Form. Receiving strength and finding root. Derivative. Analytical Function. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.1, 13.2, 13.3) | 99a7db87 |
| 2 | Cauchy-Riemann Equation. Laplace Equation. Exponential , Logarithmic, Trigonometric and Hyperbolic Functions. Euler's Formula | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 13.4, 13.5, 13.6, 13.7) | 99a7db87 |
| 3 | Line Integral in the Complex Plane, Cauchy Integral Theorem, Derivative of Analytic Functions | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 14.1, 4.2, 14.3, 14.4) | 99a7db87 |
| 4 | Matrices, Vectors. Addition, Multiplication by constant number, Matrix Multiplication. Linear Equation System. Gauss Elimination Method | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.1, 7.2, 7.3) | 3afdd132 |
| 5 | Linearly Independent Vectors. Order of Matrices. Vector Spaces. Solution of Linear Systems. Issues of Existence and Uniqueness. Second and Third Degree Determinants. Inverse Matrix. Cramer's Rule. Gauss-Jordan Elimination Method | 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) | 3afdd132 |
| 6 | Vector Spaces, Inner Product Spaces, Linear Transformation. Matrix Eigenvalue Problems. Finding Eigenvalue and Eigenvectors. Perpendicular Vectors. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 7.9, 8.1) | d36ea250 |
| 7 | Midterm Exam | - | - |
| 8 | Applications of Eiegenvalue Problems. Symmetric and Skewed Symmetric and Orthogonal Vectors | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.2, 8.3) | d36ea250 |
| 9 | Eigenbase Vectors. Diagonalization. Second Degree Forms. Gram-Schmidt Perpendicular Generation Method | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 8.4) | d36ea250 |
| 10 | Differential Equations. Basic Concepts. Modeling. Euler Method. Separable Ordinary Differential Equations (STD). | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.1, 1.2, 1.3) | 84d33c7b |
| 11 | Complete Ordinary Differential Equations. Linear Ordinary Differential Equations. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 1.4, 1.5, 1.7) | 84d33c7b |
| 12 | Homogeneous Quadratic and Linear Ordinal Differential Equations. Non-homogeneous Ordinal Differential Equations. Applications. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.1, 2.2, 2.4) | 84d33c7b |
| 13 | Homogeneous Linear Ordinary Differential Equations, Constant Coefficient Linear Differential Equations and Systems | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 2.6, 2.7, 2.8, 2.9) | ad7fac02 |
| 14 | Systems of Ordinary Differential Equations, Systems of Ordinary Differential Equations in Engineering Applications. Fixed Coefficient Sytems. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 3.1, 3.2, 3.3) | ad7fac02 |
| 15 | Using Complex Numbers, Matrices, Differential Equations in Solving Engineering Problems. | Erwin Kreyszig, "Advanced Engineering Mathematics" 10th Ed, Wiley 2011. ISBN: 978-0-470-45836-5. (Sec. 4.1, 4.2, 4.3) | 8b254dc6 |
| 16 | Final Exam | - | - |
| Course Notes/Textbooks | Erwin Kreyszig "Advanced Engineering Mathematics" 10th Ed Wiley 2011. ISBN: 978-0-470-45836-5. |
| Suggested Readings/Materials | "Diiferential Equations and Linear Algebra" 3/E Edwards & Penney 2010 Prentice Hall ISBN: 978-0-138-14102-8 |
EVALUATION SYSTEM
| Semester Activities | Number | Weighting | LO1 | LO2 | LO3 | LO4 | LO5 | LO6 |
| Quizzes / Studio Critiques | 3 | 20 | X | X | X | X | X | |
| Homework / Assignments | 1 | 5 | X | X | X | X | X | |
| Midterm | 1 | 35 | 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 | 3 | 48 |
| Field Work | - | - | - |
| Quizzes / Studio Critiques | 3 | 5 | 15 |
| Portfolio | - | - | - |
| Homework / Assignments | 5 | 4 | 20 |
| Presentation / Jury | - | - | - |
| Project | - | - | - |
| Seminar / Workshop | - | - | - |
| Oral Exams | - | - | - |
| Midterms | 1 | 9 | 9 |
| Final Exam | 1 | 24 | 24 |
| Total | 180 |
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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