# Numerical Methods for Engineers (MATH380) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Numerical Methods for Engineers MATH380 5. Semester 3 1 0 3 5
Pre-requisite Course(s)
MATH275 Linear Algebra
Course Language İngilizce Service Courses Taken From Other Departments Lisans Face To Face Lecture, Experiment, Problem Solving. This undergraduate course is designed for engineering students. The objective of this course is to introduce some numerical methods that can be used to solve mathematical problems arising in engineering that can not be solved analytically. The philosophy of this course is to teach engineering students how methods work so that they can construct their own computer programs. The students who succeeded in this course; solve a non-linear equation in science and engineering by using the MATLAB programming. solve a linear system by using a suitable method in science and engineering via the MATLAB programming. find the eigenvalues and eigenvectors of a given matrix. learn how to use the interpolation. learn how to derive the approximations for the derivatives. learn the approximate computation of an integral using numerical techniques. Solution of nonlinear equations, solution of linear systems, eigenvalues and eigenvectors, interpolation and polynomial approximation, least square approximation, numerical differentiation, numerical integration.

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 1. Preliminaries: Approximation, Truncation, Round-off errors in computations. pp. 2 - 41
2 2. Solution of Nonlinear Equations 2.1. Fixed Point 2.2. Bracketing Methods for Locating a Root pp. 41 - 51
3 2.3. Initial Approximation and Convergence Criteria 2.4. Newton-Raphson and Secant Methods pp. 62 - 70
4 2.6. Iteration for Non-Linear Systems (Fixed Point for Systems) 2.7. Newton Methods for Systems pp. 167 - 180
5 3. Solution of Linear Systems 3.3. Upper-Triangular Linear Systems (Lower-Triangular) 3.4. Gaussian Eliminatian and Pivoting pp. 120 - 137
6 3.5. Triangular Factorization (LU) pp. 141 - 153
7 Midterm
8 3.7. Doğrusal sistemler için iteratif metotlar (Jacobi / Gauss Seidel Metotları) pp. 156 - 165
9 11. Eigenvalues and Eigenvectors 11.2. Power Method (Inverse Power Method) pp. 588 – 592 pp. 598 - 608
10 4. Interpolation and Polynomial Approximation 4.2. Introduction to Interpolation 4.3. Lagrange Approximation and Newton Approximation pp. 199 - 228
11 5. Curve Fitting 5.1. Least-squares Line pp. 252 - 259
12 5.3. Spline fonksiyonları ile interpolasyon pp. 279 - 293
13 6. Numerical Differentiation 6.1. Approximating the Derivative 6.2. Numerical Differentiation Formulas pp. 320 - 348
14 7. Numerical Integration 7.1. Introduction to Quadrature 7.2. Composite Trapezoidal and Simpson’s Rule pp. 352 - 374
15 Review
16 Genel Sınav

### Sources

Course Book 1. J. H. Mathews, K. D. Fink, Numerical Methods Using Matlab, 4th Edition, Prentice Hall, 2004. 2. S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd Edition, Mc Graw Hill Education, 2012. 3. A. Gilat, V. Subramaniam, Numerical Methods for Engineers and Scientists: An introduction with Applications Using MATLAB, 3rd Edition, John Wiley & Sons, Inc. 2011.

### Evaluation System

Attendance/Participation - -
Laboratory 2 10
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 5 100
 Percentage of Semester Work 0 100 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.)
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. X
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines. X
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions.
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory 16 1 16
Application
Special Course Internship
Field Work
Study Hours Out of Class 14 2 28
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 13 13