| SOFTWARE ENGINEERING | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3012 | Numerical Analysis | Spring | 2 | 2 | 3 | 6 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Hybrid |
| Course Coordinator : | Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN |
| Course Lecturer(s): |
Dr. UTKU GÜLEN Dr. Öğr. Üyesi ERKUT ARICAN RA ÇİĞDEM ERİŞ Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN |
| Recommended Optional Program Components: | None |
| Course Objectives: | Numerical Analysis is concerned with the mathematical derivation, description and analysis of obtaining numerical solutions of mathematical problems. We have several objectives for the students. Students should obtain an intuitive and working understanding of some numerical methods for the basic problems of numerical analysis. They should gain some appreciation of the concept of error and of the need to analyze and predict it. Topics cover linear and nonlinear system of equations, interpolation, curve fitting using least-squares method integration, eigenvalue, and singular value decomposition. And also they should develop some experience in the implementation of numerical methods by using MATLAB. |
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The students who have succeeded in this course; 1. Define errors, big O notation, use Taylor’s theorem 2. Solve nonlinear algebraic equations 3. Solve linear systems and to use iterative methods for linear systems 4. Solve systems of nonlinear algebraic equations 5. Use interpolation methods and polynomial approximation for a given data, piecewise linear interpolation and spline function interpolation; 6. Use least-squares method for curve fitting 7. Calculate maximum eigenvalues and corresponding eigenvectors and to calculate singular value decomposition of a matrix and apply it on image processing 8. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory. |
| The course studies algorithms and computer techniques for solving mathematical problems. They do all computations using MATLAB. |
| Week | Subject | Related Preparation |
| 1) | Introduction to Numerical Analysis: kinds of problems we solve. Error analysis, round-off and truncation errors. Taylor Theorem and Taylor series. | |
| 2) | Loss of Significance Big O notation | |
| 3) | Solution of Nonlinear Equations, i.e. f(x)=0. Bracketing Methods for Locating a Root. Bisection (Method of Bolzano). False-position (Regula-Falsi) Method. | |
| 4) | Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics) | |
| 5) | Solution of Linear Systems of Equations. Properties of Vectors and Matrices. Upper-Triangular Linear Systems. Gaussian Elimination and Pivoting. | |
| 6) | Triangular Factorization (LU Decomposition) | |
| 7) | Iterative Methods for Linear Systems. Jacobi Method. Gauss-Sedidel Method. | |
| 8) | Iterative Methods for Linear Systems Gauss-Sedidel Method. Diagonally dominant matrix. Errors is solving linear systems. | |
| 9) | System of Nonlinear Equations (Newton’s Method) | |
| 10) | Interpolation and Polynomial Approximation. Introduction to Interpolation. Lagrange Approximation. | |
| 11) | Newton Interpolation Polynomials. Piecewise Linear Interpolation, Cubic Spline Functions | |
| 12) | Curve Fitting (Applications from heat transfer and electrical engineering). Least-Squares Approximation. Linearization of Nonlinear Relationships. | |
| 13) | Eigenvalues and Eigenvectors. The power method | |
| 14) | Singular Value decomposition. Applications from Image Processing |
| Course Notes / Textbooks: | Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill |
| References: | • J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013. • Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris. • John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3 • Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013. • İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6. • Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7 |
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 3 | % 10 |
| Homework Assignments | 1 | % 10 |
| Midterms | 1 | % 35 |
| Final | 1 | % 45 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 55 | |
| PERCENTAGE OF FINAL WORK | % 45 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 2 | 28 |
| Laboratory | 14 | 2 | 28 |
| Study Hours Out of Class | 14 | 2 | 28 |
| Homework Assignments | 1 | 4 | 4 |
| Quizzes | 3 | 1 | 3 |
| Midterms | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Total Workload | 95 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Be able to specify functional and non-functional attributes of software projects, processes and products. | |
| 2) | Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems. | |
| 3) | Be able to develop a complex software system with in terms of code development, verification, testing and debugging. | 2 |
| 4) | Be able to verify software by testing its program behavior through expected results for a complex engineering problem. | 1 |
| 5) | Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation. | 2 |
| 6) | Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically. | |
| 7) | Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams. | 2 |
| 8) | Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems. | 1 |
| 9) | Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system. | 1 |
| 10) | Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities. | 5 |
| 11) | Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life. | |
| 12) | Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions. | |
| 13) | Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions. |