COURSE INFORMATION Course Title: ADVANCED NUMERICAL METHODS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
CEN 545	A	2	3	2	0	4	7.5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Erind Bedalli
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Elective
Classroom and Meeting Time:
Course Description:	This course will help student understand advanced numerical methods for graduate level studies.
Course Objectives:	To equip the students with the mathematical tools and skills that are needed in different areas of Computer Engineering. Introduction to complexity theory. Statistical analysis of data, moments of data distribution. Fourier series, Fourier Transforms and its application in data analysis. Wavelet Theory. Application of Fourier Transforms in Image Processing. Eigenvalue and eigenvector problems. Diagonalization by Eigenvector Matrix, Diagonalization by Singular Value Decomposition. Introduction to Principal Component Analysis (PCA) and to Independent Component Analysis (ICA).

COURSE OUTLINE

Week	Topics
1	General overview of the fundamental numerical methods.
2	General introduction to MATLAB.
3	Numerical Differentiation.
4	Numerical Integration.
5	Differential Equations and Initial Value Problems.
6	Finite difference methods.
7	Two-Point Boundary Value Problems.
8	Midterm exam
9	Systems of Linear Algebraic Equations.
10	Eigenvalues, eigenvectors and solvability.
11	Diagonalization of covariance matrix, by Eigenvector matrix, diagonalization by SVD (Singular Value Decomposition)
12	Introduction of Principal Component Analysis and Independent Component Analysis
13	Basics of Optimization.
14	Review

Prerequisite(s):
Textbook:	Numerical Methods in Engineering with MATLAB®, by Jaan Kiusalaas
Other References:	Numerical Recipes - The Art of Scientific Computing (3rd Edition) by W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery Data-Driven Modeling and Scientific Computation J. N. Kutz.
Laboratory Work:	2 hours per week
Computer Usage:	Yes
Others:	No

COURSE LEARNING OUTCOMES

1	To learn and be able to implement advanced numerical methods on numerical differentiation and integration.
2	To learn and be able to implement advanced numerical methods on differential equations, initial value problems and boundary value problems.
3	To learn and be able to implement advanced numerical methods on systems of linear algebra equations, eigenvalues and eigenvectors,
4	To learn and be able to implement Singular Value Decomposition.
5	To learn and be able to implement Principal Component Analysis.
6	A very good proficiency in Matlab and Octave.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Professional Master in Computer Engineering Program
1	Engineering graduates with sufficient theoretical and practical background for a successful profession and with application skills of fundamental scientific knowledge in the engineering practice.	5
2	Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations	5
3	Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.	4
4	Engineering graduates with the practice of selecting and using appropriate technical and engineering tools in engineering problems, and ability of effective usage of information science technologies.	4
5	Ability of designing and conducting experiments, conduction data acquisition and analysis and making conclusions.	4
6	Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.	4
7	The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.	4
8	Ability for effective oral and official communication skills in foreign language.	4
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	4
10	Engineering graduates with well-structured responsibilities in profession and ethics.	3
11	Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.	3
12	Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.	3

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	7.5
Midterm Exam(s)	1	25
Project	1	15
Final Exam	1	40
Attendance		5
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	5	80
Hours for off-the-classroom study (Pre-study, practice)	16	2	32
Mid-terms	1	15	15
Assignments	3	12	36
Final examination	1	24.5	24.5
Other			0
Total Work Load:			187.5
Total Work Load/25(h):			7.5
ECTS Credit of the Course:			7.5