# Numerical Methods for Engineers (MATH380) Course Detail

Course Name Course Code Season Lecture Hours Application Hours 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 English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) 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 Adequate knowledge of mathematics, physical sciences and the subjects specific to engineering disciplines; the ability to apply theoretical and practical knowledge of these areas in the solution of complex engineering problems.
2 The ability to define, formulate, and solve complex engineering problems; the ability to select and apply proper analysis and modeling methods for this purpose.
3 The ability to design a complex system, process, device or product under realistic constraints and conditions in such a way as to meet the specific requirements; the ability to apply modern design methods for this purpose.
4 The ability to select, and use modern techniques and tools needed to analyze and solve complex problems encountered in engineering practices; the ability to use information technologies effectively.
5 The ability to design experiments, conduct experiments, gather data, and analyze and interpret results for investigating complex engineering problems or research areas specific to engineering disciplines. X
6 The ability to work efficiently in inter-, intra-, and multi-disciplinary teams; the ability to work individually.
7 (a) Sözlü ve yazılı etkin iletişim kurma becerisi; etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi. (b) En az bir yabancı dil bilgisi; bu yabancı dilde etkin rapor yazma ve yazılı raporları anlama, tasarım ve üretim raporları hazırlayabilme, etkin sunum yapabilme, açık ve anlaşılır talimat verme ve alma becerisi.
8 Recognition of the need for lifelong learning; the ability to access information, follow developments in science and technology, and adapt and excel oneself continuously.
9 Acting in conformity with the ethical principles; professional and ethical responsibility and knowledge of the standards employed in engineering applications.
10 Knowledge of business practices such as project management, risk management, and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development.
11 Knowledge of the global and social effects of engineering practices on health, environment, and safety issues, and knowledge of the contemporary issues in engineering areas; awareness of the possible legal consequences of engineering practices.
12 (a) Knowledge of (i) fluid mechanics, (ii) heat transfer, (iii) manufacturing process, (iv) electronics and control, (v) vehicle components design, (vi) vehicle dynamics, (vii) vehicle propulsion/drive and power systems, (viii) technical laws and regulations in automotive engineering field, and (ix) vehicle verification tests. (b) The ability to merge and apply these knowledge in solving multi-disciplinary automotive problems.
13 The ability to make use of theoretical, experimental, and simulation methods, and computer aided design techniques in automotive engineering field.
14 The ability to work in the field of vehicle design and manufacturing.

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