ECTS - Numerical Methods for Engineers

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 veya MATH231)
Course Language English
Course Type Elective Courses
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Experiment, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives 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.
Course Learning Outcomes 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.
Course Content 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.
Other Sources 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

Requirements Number Percentage of Grade
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
Percentage of Final Work 100
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Gain sufficient knowledge in mathematics, science and computing; be able to use theoretical and applied knowledge in these areas to solve engineering problems related to information systems. X
2 To be able to identify, define, formulate and solve complex engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose. X
3 Designs a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; applies modern design methods for this purpose.
4 To be able to develop, select and use modern techniques and tools required for the analysis and solution of complex problems encountered in information systems engineering applications; to be able to use information technologies effectively.
5 Designs and conducts experiments, collects data, analyzes and interprets results to investigate complex engineering problems or research topics specific to the discipline of information systems engineering.
6 Can work effectively in disciplinary and multidisciplinary teams; can work individually.
7 a. Communicates effectively both orally and in writing; writes effective reports and understands written reports, prepares design and production reports, makes effective presentations, gives and receives clear and understandable instructions. b. Knows at least one foreign language.
8 To be aware of the necessity of lifelong learning; to be able to access information, to be able to follow developments in science and technology and to be able to renew himself/herself continuously.
9 a. Acts in accordance with the principles of ethics, gains awareness of professional and ethical responsibility. b. Gains knowledge about the standards used in information systems engineering applications.
10 a. Gains knowledge about business life practices such as project management, risk management and change management. b. Gains awareness about entrepreneurship and innovation. c. Gains knowledge about sustainable development.
11 a. To be able to acquire knowledge about the universal and social effects of information systems engineering applications on health, environment and safety and the problems of the era reflected in the field of engineering. b. Gains awareness of the legal consequences of engineering solutions.

ECTS/Workload Table

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
Total Workload 77