COMPUTER 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 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | En |
Type of course: | Must Course |
Course Level: | Bachelor |
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: | 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 |
Attendance | 0 | % 0 |
Laboratory | 0 | % 0 |
Application | 0 | % 0 |
Field Work | 0 | % 0 |
Special Course Internship (Work Placement) | 0 | % 0 |
Quizzes | 2 | % 10 |
Homework Assignments | 1 | % 10 |
Presentation | 0 | % 0 |
Project | 0 | % 0 |
Seminar | 0 | % 0 |
Midterms | 1 | % 35 |
Preliminary Jury | 0 | % 0 |
Final | 1 | % 45 |
Paper Submission | 0 | % 0 |
Jury | 0 | % 0 |
Bütünleme | % 0 | |
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 |
Laboratory | 0 | 0 | 0 |
Application | 14 | 2 | 28 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 4 | 56 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 1 | 4 | 4 |
Quizzes | 3 | 1 | 3 |
Preliminary Jury | 0 | 0 | 0 |
Midterms | 1 | 2 | 2 |
Paper Submission | 0 | 0 | 0 |
Jury | 0 | 0 | 0 |
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) | Adequate knowledge in mathematics, science and computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. | 5 |
2) | Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose. | 5 |
3) | Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose. | |
4) | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in computer engineering applications; ability to use information technologies effectively. | |
5) | Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or computer engineering research topics. | |
6) | Ability to work effectively within and multi-disciplinary teams; individual study skills. | |
7) | Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. | |
8) | Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously. | |
9) | To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications. | |
10) | Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development. | |
11) | Knowledge of the effects of engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions. |