| MECHATRONICS ENGINEERING | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT2045 | Numerical Methods for Engineers | Fall | 3 | 2 | 4 | 5 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN |
| Course Lecturer(s): |
Prof. Dr. NAFİZ ARICA |
| Course Objectives: | This course 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 systems of equations, interpolation, curve fitting using least-squares method, numerical differentiation and integration, discrete Fourier transformation, power method for eigenvalues and eigenvectors of matrix, singular value decomposition. Students should gain some experience in the implementation of numerical methods by using MATLAB. |
|
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. Approximate the dominant eigenvalue and corresponding eigenvector of the matrix and to calculate singular value decomposition of a matrix and apply it on image processing; 8. Approximate derivatives and integrals numerically and calculate discrete Fourier transformation 9. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory. |
| Errors, numerical methods for nonlinear algebraic equations, direct and iterative methods for solving the system of linear equations, Newton's method for system of nonlinear equations, interpolation methods, curve fitting, cubic splines, eigenvalues and eigenvectors, singular value decomposition, numerical differentiation, numerical integration, discrete Fourier transform. All computations will be done by using MATLAB. |
| Week | Subject | Related Preparation |
| 1) | Errors, Taylor’s Theorem, Big O Notation. | |
| 2) | Bisection and False position methods for the solution of nonlinear algebraic equations. | |
| 3) | Fıxed point and Newton-Raphson methods for the solution of nonlinear algebraic equations. | |
| 4) | Gauss Elimination method with pivoting for the solution of linear systems. | |
| 5) | LU Factorization method with pivoting for the solution of linear systems. | |
| 6) | Jacobi and Gauss-Seidel iterative methods for the solution of linear systems. | |
| 7) | Newton’s method for the solution of systems of nonlinear equations. | |
| 8) | Interpolation using Lagrange and Newton polynomials. | |
| 9) | Interpolation using cubic splines. | |
| 10) | Curve fitting using least-squares method, linearization. | |
| 11) | Power method for approximation of the dominant eigenvalue of a matrix. | |
| 12) | Singular value decomposition | |
| 13) | Numerical differentiation and numerical integration | |
| 14) | Discrete Fourier Transform |
| Course Notes / Textbooks: | 1. J. D. Faires, R. Burden, "Numerical Analysis", 9th edition, 2011 2. S. C. Chapra, "Applied Numerical Methods with MATLAB for Engineers and Scientists", 3rd edition, 2012. |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 2 | % 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 | 3 | 42 |
| Application | 14 | 2 | 28 |
| Study Hours Out of Class | 14 | 4 | 56 |
| Homework Assignments | 1 | 4 | 4 |
| Quizzes | 3 | 1 | 3 |
| Midterms | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Total Workload | 137 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | Build up a body of knowledge in mathematics, science and Mechatronics Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. | |
| 2) | Identify, formulate, and solve complex Mechatronics Engineering problems; select and apply proper modeling and analysis methods for this purpose. | |
| 3) | Design complex Mechatronic systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. | |
| 4) | Devise, select, and use modern techniques and tools needed for solving complex problems in Mechatronics Engineering practice; employ information technologies effectively. | |
| 5) | Design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Mechatronics Engineering. | |
| 6) | Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Mechatronics-related problems. | |
| 7) | Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. | |
| 8) | Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. | |
| 9) | Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Mechatronics Engineering applications. | |
| 10) | Learn about business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. | |
| 11) | Acquire knowledge about the effects of practices of Mechatronics Engineering on health, environment, security in universal and social scope, and the contemporary problems of Mechatronics engineering; is aware of the legal consequences of Mechatronics engineering solutions. |