INDUSTRIAL ENGINEERING
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT3012 Numerical Analysis Fall 2 2 3 6
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Must Course
Course Level: Bachelor
Mode of Delivery: Hybrid
Course Coordinator : Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Course Lecturer(s): Dr. UTKU GÜLEN
Dr. Öğr. Üyesi ERKUT ARICAN
RA ÇİĞDEM ERİŞ
Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Course Objectives: Numerical Analysis 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 system of equations, interpolation, curve fitting using least-squares method integration, eigenvalue, and singular value decomposition. And also they should develop some experience in the implementation of numerical methods by using MATLAB.

Learning Outputs

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. Calculate maximum eigenvalues and corresponding eigenvectors and to calculate singular value decomposition of a matrix and apply it on image processing
8. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory.

Course Content

The course studies algorithms and computer techniques for solving mathematical problems. They do all computations using MATLAB.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Introduction to Numerical Analysis: kinds of problems we solve. Error analysis, round-off and truncation errors. Taylor Theorem and Taylor series.
2) Loss of Significance Big O notation
3) Solution of Nonlinear Equations, i.e. f(x)=0. Bracketing Methods for Locating a Root. Bisection (Method of Bolzano). False-position (Regula-Falsi) Method.
4) Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics)
5) Solution of Linear Systems of Equations. Properties of Vectors and Matrices. Upper-Triangular Linear Systems. Gaussian Elimination and Pivoting.
6) Triangular Factorization (LU Decomposition)
7) Iterative Methods for Linear Systems. Jacobi Method. Gauss-Sedidel Method.
8) Iterative Methods for Linear Systems Gauss-Sedidel Method. Diagonally dominant matrix. Errors is solving linear systems.
9) System of Nonlinear Equations (Newton’s Method)
10) Interpolation and Polynomial Approximation. Introduction to Interpolation. Lagrange Approximation.
11) Newton Interpolation Polynomials. Piecewise Linear Interpolation, Cubic Spline Functions
12) Curve Fitting (Applications from heat transfer and electrical engineering). Least-Squares Approximation. Linearization of Nonlinear Relationships.
13) Eigenvalues and Eigenvectors. The power method
14) Singular Value decomposition. Applications from Image Processing

Sources

Course Notes: Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill
References: • J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013. • Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris. • John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3 • Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013. • İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6. • Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Attendance % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes 3 % 10
Homework Assignments 1 % 10
Presentation % 0
Project % 0
Seminar % 0
Midterms 1 % 35
Preliminary Jury % 0
Final 1 % 45
Paper Submission % 0
Jury % 0
Bütünleme % 0
Total % 100
PERCENTAGE OF SEMESTER WORK % 55
PERCENTAGE OF FINAL WORK % 45
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 2 28
Laboratory 14 2 28
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 14 2 28
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 95

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Build up a body of knowledge in mathematics, science and industrial engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. 5
2) Identify, formulate, and solve complex engineering problems; select and apply proper analysis and modeling methods for this purpose. 3
3) Design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. The ability to apply modern design methods to meet this objective.
4) Devise, select, and use modern techniques and tools needed for solving complex problems in industrial engineering practice; employ information technologies effectively. 3
5) Design and conduct experiments, collect data, analyze and interpret results for investigating the complex problems specific to industrial engineering.
6) Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working independently.
7) Demonstrate effective communication skills in both oral and written English and Turkish. Writing and understanding reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instructions.
8) Recognize the need for lifelong learning; show ability to access information, to follow developments in science and technology, and to continuously educate him/herself.
9) Develop an awareness of professional and ethical responsibility, and behaving accordingly. Information about the standards used in engineering applications.
10) Know business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development.
11) Know contemporary issues and the global and societal effects of modern age engineering practices on health, environment, and safety; recognize the legal consequences of engineering solutions.
12) Develop effective and efficient managerial skills.