SE 366 | Course Introduction and Application Information

Course Name
Numerical Analysis
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
SE 366
Fall/Spring
3
0
3
8

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives This course is an introduction level overview to the numerical analysis. The primary objective of the course is to develop the understanding of numerical algorithms and skills to implement algorithms to solve mathematical problems on the computer.
Course Description The students who succeeded in this course;
  • will be able to create solutions for both linear and non-linear problems
  • will be able to use iterative approaches to analysis problems
  • will be able to produce proper algorithms to solve complex problems
  • will be able to apply numerical methods to real world engineering applications
  • will be able to identify complex mathematical problems
Course Content Floating point arithmetic, computational linear algebra, iterative solution to nonlinear equations, interpolation, numerical solution of ODEs, computer subroutine packages

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Introduction, errors and stability of numerical calculations, condition number, big O notation Lecture notes
2 The solution of linear equations, vectors and matrices, linear triangular systems, Gaussian elimination, pivoting Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
3 LU factorization, Cholesky factorization, QR factorization Numerical Analysis by Timothy Sauer, 2006, Pearson
4 The solution of nonlinear equations, iterations, fixed point iterations, root bracketing and bisection method Numerical Analysis by Timothy Sauer, 2006, Pearson
5 Secant method, Newton-Rapson method, Newton-Rapson method with constraints Numerical Analysis by Timothy Sauer, 2006, Pearson
6 Interpolation of functions and polynomial approximations: Taylor polynomial, Lagrange polynomial, Chebyshev polynomial Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
7 Midterm Exam
8 Curve fitting, splines, method of undetermined coefficients Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
9 Curve fitting, linear least squares, nonlinear least squares, data linearization Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
10 Numerical differentiation and integration, finite differences, quadratures, trapezoid and Simpson quadratures Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
11 Numerical optimization, optimality conditions, steepest descent method, conjugate gradients Numerical Analysis by Timothy Sauer, 2006, Pearson
12 Solution of Ordinary Differential Equations: Euler’s method, Heun’s method, Taylor series and Runge-Kutta methods Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
13 Systems of ODEs and boundary value problems, method of finite differences, finite differences and solutions of PDE Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004
14 Eigenvalues and singular values, singular value decomposition Numerical Analysis by Timothy Sauer, 2006, Pearson
15 Review of the semester
16 Review of the semester

 

Course Notes/Textbooks

Numerical Methods using MATLAB by Mathews and Fink, Pearson, 2004

Steven, C. Chapra. Applied Numerical Methods With Matlab: For Engineers And Scientists. Tata McGraw Hill Education Private Limited, 2007

Suggested Readings/Materials

Numerical Analysis by Timothy Sauer, 2006, Pearson; Numerical Methods for Engineers and Scientists: An Introduction with Applications using MATLAB by Gilat and Subramaniam, Wiley;

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Homework / Assignments
8
30
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
30
Final / Oral Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
6
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
Including exam week: 16 x total hours
16
3
48
Laboratory / Application Hours
Including exam week: 16 x total hours
16
Study Hours Out of Class
16
5
Field Work
Quizzes / Studio Critiques
Homework / Assignments
8
4
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
35
Final / Oral Exam
1
35
    Total
230

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 Adequate knowledge in Mathematics, Science and Software Engineering; ability to use theoretical and applied information in these areas to model and solve Software Engineering problems X
2 Ability to identify, define, formulate, and solve complex Software Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose
3 Ability to design, implement, verify, validate, measure and maintain a complex software system, process or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern methods for this purpose
4 Ability to devise, select, and use modern techniques and tools needed for Software Engineering practice
5 Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Software Engineering problems
6 Ability to work efficiently in Software Engineering disciplinary and multi-disciplinary teams; ability to work individually
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9 Awareness of professional and ethical responsibility
10 Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development
11 Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Software Engineering solutions

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest