# 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 Area Elective 3 1 0 3 5
Pre-requisite Course(s)
MATH275 Linear Algebra
Course Language English Elective 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 in mathematics, science and computing fields; ability to apply theoretical and practical knowledge of these fields in solving engineering problems related to information systems. X
2 Ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. X
3 Ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; 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 information systems engineering applications; ability to use information technologies effectively.
5 Ability to gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the information systems discipline.
6 Ability to work effectively in inter/inner disciplinary teams; ability to work individually.
7 a. Effective oral and written communication skills in Turkish; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions. b. Knowledge of at least one foreign language; ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8 Recognition of the need for lifelong learning; the ability to access information and follow recent developments in science and technology with continuous self-development.
9 a. Ability to behave according to ethical principles, awareness of professional and ethical responsibility. b. Knowledge of the standards utilized in information systems engineering applications.
10 a. Knowledge on business practices such as project management, risk management and change management. b. Awareness about entrepreneurship, and innovation. c. Knowledge on sustainable development.
11 a. Knowledge of the effects of information systems engineering applications on the universal and social dimensions of health, environment, and safety. b. Awareness of the legal consequences of engineering solutions.

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