|
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
|
|
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
|
|
Program Outcomes |
Level of Contribution |
1) |
Be able to specify functional and non-functional attributes of software projects, processes and products. |
|
2) |
Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems. |
|
3) |
Be able to develop a complex software system with in terms of code development, verification, testing and debugging. |
2 |
4) |
Be able to verify software by testing its program behavior through expected results for a complex engineering problem. |
1 |
5) |
Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation. |
2 |
6) |
Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically. |
|
7) |
Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams. |
2 |
8) |
Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems. |
1 |
9) |
Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system. |
1 |
10) |
Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities. |
5 |
11) |
Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life. |
|
12) |
Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions. |
|
13) |
Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions. |
|