| 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 |
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| 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;
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| 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. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 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 |
| Semester Activities | Number | Weighting |
| Participation | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | 1 | 20 |
| Portfolio | ||
| Homework / Assignments | 1 | 5 |
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 2 | 35 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | ||
| Weighting of End-of-Semester Activities on the Final Grade | ||
| Total |
| 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 | 4 | 64 |
| Field Work | |||
| Quizzes / Studio Critiques | 1 | 5 | |
| Portfolio | |||
| Homework / Assignments | 1 | 5 | |
| Presentation / Jury | |||
| Project | |||
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 2 | 15 | |
| Final Exams | 1 | 20 | |
| Total | 156 |
| # | 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. | |||||
| 6 | To be able to work efficiently in Civil Engineering disciplinary and multi-disciplinary teams; to be able to work individually. | |||||
| 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 engineering; to be aware of the legal ramifications of engineering solutions. | |||||
| 9 | To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications. | |||||
| 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. | |||||
| 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; | |||||
| 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 Civil Engineering. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
