COMPUTER 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
MAT2045	Numerical Methods for Engineers	Fall	3	2	4	5

Basic information

Language of instruction:	English
Type of course:	Must Course
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Dr. Öğr. Üyesi LAVDİE RADA ÜLGEN
Course Lecturer(s):	Prof. Dr. NAFİZ ARICA
Course Objectives:	This course 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 systems of equations, interpolation, curve fitting using least-squares method, numerical differentiation and integration, discrete Fourier transformation, power method for eigenvalues and eigenvectors of matrix, singular value decomposition. Students should gain some experience in the implementation of numerical methods by using MATLAB.

Learning Outcomes

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. Approximate the dominant eigenvalue and corresponding eigenvector of the matrix and to calculate singular value decomposition of a matrix and apply it on image processing;
8. Approximate derivatives and integrals numerically and calculate discrete Fourier transformation
9. Implement numerical methods on MATLAB and test their programs behavior through expected results in accordance with the Numerical Analysis theory.

Course Content

Errors, numerical methods for nonlinear algebraic equations, direct and iterative methods for solving the system of linear equations, Newton's method for system of nonlinear equations, interpolation methods, curve fitting, cubic splines, eigenvalues and eigenvectors, singular value decomposition, numerical differentiation, numerical integration, discrete Fourier transform. All computations will be done by using MATLAB.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Errors, Taylor’s Theorem, Big O Notation.
2)	Bisection and False position methods for the solution of nonlinear algebraic equations.
3)	Fıxed point and Newton-Raphson methods for the solution of nonlinear algebraic equations.
4)	Gauss Elimination method with pivoting for the solution of linear systems.
5)	LU Factorization method with pivoting for the solution of linear systems.
6)	Jacobi and Gauss-Seidel iterative methods for the solution of linear systems.
7)	Newton’s method for the solution of systems of nonlinear equations.
8)	Interpolation using Lagrange and Newton polynomials.
9)	Interpolation using cubic splines.
10)	Curve fitting using least-squares method, linearization.
11)	Power method for approximation of the dominant eigenvalue of a matrix.
12)	Singular value decomposition
13)	Numerical differentiation and numerical integration
14)	Discrete Fourier Transform

Sources

Course Notes / Textbooks:	1. J. D. Faires, R. Burden, "Numerical Analysis", 9th edition, 2011 2. S. C. Chapra, "Applied Numerical Methods with MATLAB for Engineers and Scientists", 3rd edition, 2012.
References:

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	2	% 10
Homework Assignments	1	% 10
Midterms	1	% 35
Final	1	% 45
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	3	42
Application	14	2	28
Study Hours Out of Class	14	4	56
Homework Assignments	1	4	4
Quizzes	3	1	3
Midterms	1	2	2
Final	1	2	2
Total Workload			137

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)	Adequate knowledge in mathematics, science and computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.	5
2)	Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.	5
3)	Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; 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 computer engineering applications; ability to use information technologies effectively.
5)	Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or computer engineering research topics.
6)	Ability to work effectively within and multi-disciplinary teams; individual study skills.
7)	Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
8)	Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously.
9)	To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications.
10)	Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development.
11)	Knowledge of the effects of engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions.