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;
  • be able to create solutions for both linear and non-linear problems
  • be able to use iterative approaches to analysis problems
  • be able to produce proper algorithms to solve complex problems
  • be able to identify complex mathematical problems
  • be able to apply numerical methods to real world engineering applications.
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
Oral Exams
Midterm
1
30
Final 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
Theoretical 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
Oral Exam
Midterms
1
35
Final Exam
1
35
    Total
230

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have adequate knowledge in Mathematics, Science, Computer Science and Software Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

X
2

To be able to identify, define, formulate, and solve complex Software Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

X
3

To be able to design, implement, verify, validate, document, measure and maintain a complex software system, process, or product under realistic constraints and conditions, in such a way as to meet the requirements; ability to apply modern methods for this purpose.

X
4

To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in software engineering applications; to be able to use information technologies effectively.

X
5

To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex Software Engineering problems.

X
6

To be able to work effectively in Software Engineering disciplinary and multi-disciplinary teams; to be able to work individually.

7

To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to be able to present effectively, to be able to give and receive clear and comprehensible instructions.

X
8

To have knowledge about global and social impact of engineering practices and software applications on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of Engineering and Software Engineering solutions.

9

To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications.

10

To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

11

To be able to collect data in the area of Software Engineering, and to be able to communicate with colleagues in a foreign language.

X
12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Software Engineering.

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