COURSE INFORMATION Course Title: NUMERICAL ANALYSIS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 206	B	4	4	0	0	4	6

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:	Arban Uka
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:	Compulsory
Classroom and Meeting Time:	B010
Course Description:	Overview of binary Numbers. Error analysis. Solving systems of linear equations: Gaussian Elimination, modification Gaussian Elimination and L-U decomposition. Solutions of nonlinear equations and systems: Bisection, Newton’s, secant and fixed-point iteration methods. Interpolation: Lagrange Approximation, Newton’s Polynomials and Polynomial Approximation. Curve Fitting. Numerical Differentiation. Numerical Integration. Numerical Optimization. Numerical Solutions of the initial value and boundary value problems: Euler’s, Heun’s, Taylor’s, Runge-Kutta Methods
Course Objectives:	The students will develop an understanding of the numerical methods applied in solving equations of one variable, interpolation, differentiation, integration, differential equations and systems of linear equations.

COURSE OUTLINE

Week	Topics
1	Solving one-variable equations: the bisection and false position methods.
2	Solving one-variable equations: Newton-Raphson, secant and fixed-point iteration methods.
3	Implementation and comparison of methods for solving one-variable equations.
4	Interpolation. The Lagrange polynomial and the Neville's method.
5	Newton's divided differences. Cubic spline interpolation.
6	Implementation and comparison of the interpolation techniques.
7	Numerical differentiation techniques.
8	Midterm exam.
9	Numerical integration: trapezoidal rule, Simpson's rule.
10	Composite numerical integration. Gaussian quadrature.
11	Numerical methods for solving differential equations and initial value problems: Euler method.
12	Higher order Taylor and Runge-Kutta methods.
13	Iterative techniques in matrix algebra. Jacobi and Gauss-Siedel techniques.
14	Approximating eigenvalues.

Prerequisite(s):	MTH 101, MTH 102
Textbook:	"Numerical Methods for Engineers", Steven Chapra. “Numerical analysis”, 9th edition, Richard Burden, Douglas Faires
Other References:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	To learn and be able to implement the numerical methods for solving equations of one variable: bisection method, Newton-Raphson, secant etc.
2	To learn and be able to implement numerical methods for interpolation problems: Lagrange problem, Newton's divided differences, splines etc.
3	To learn and be able to implement numerical methods for differentiation.
4	To learn and be able to implement numerical methods for integration: trapezoidal rule, Simpson's rule, composite integration, Gaussian quadrature etc.
5	To learn and be able to implement numerical methods for differential equations: Euler and Runge-Kutta methods.
6	To learn and be able to implement numerical methods for matrix algebra.

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

No	Program Competencies	Cont.
Bachelor in Computer Engineering (3 years) 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.	5
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.	3
8	Ability for effective oral and official communication skills in foreign language.	3
9	Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.	3
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.	2
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
Quiz	2	7.5
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	4	64
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	10	10
Assignments	2	8	16
Final examination	1	18	18
Other			0
Total Work Load:			150
Total Work Load/25(h):			6
ECTS Credit of the Course:			6