Numerical Analysis

Course Code:

ES 272

Course Period:

Autumn

Course Type:

Core

Credits:

3

Theoric:

2

Practice:

2

Laboratory Hour:

0

ECTS:

6

Prerequisite Courses:

Algoritms and Computer Programming

Calculus II

Course Language:

English

Course Objectives:

This course serves as an introduction to numerical procedures that are common to engineering discipline, and their implementation using Matlab or an equivalent software.

Course Content:

Computer arithmetic, sources of error, error propagation. Approximating functions, interpolation. Solution of linear system of algebraic equations via direct methods. Roots of nonlinear algebraic equations. Numerical integration and differentiation.

Course Methodology:

1: Lecture, 3: Homework, 5: Laboratory

Course Evaluation Methods:

A: Midterm and final exams, B: Homework, C: In-class practice

Vertical Tabs

Ders Tanimlari

Course Learning Outcomes

1) Define the consequences of digital arithmetic, estimate numerical accuracy of floating-point computations, function approximation and error propagation.	1,2,3,4,5,9,10	1,2	A,B
2) Formulate an approximate solution procedure to an engineering problem, apply basic numerical techniques in this procedure and assess the accuracy and stability of the resulting solution.	1,2,3,4,5,9,10	1,2	A,B
3) Select and customize appropriate algorithms from numerical libraries, implement them as computer code files, and integrate files to construct a complete set of procedures.	1,2,3,4,5,9,10	2,3	B,C

Course Flow

Week	Topics	Study Materials
1	Introduction to numerical analysis
2	Approximate calculation of functions
3	Polynomial Evaluation, Binary Number System.
4	Computing Anomalies, Machine Numbers
5	Error and its propagation through computations
6	Rootfinding Problems, Newton's Method.
7	Secant Method, Fixed-Point Iteration.
8	Midterm Exam
9	Function Interpolation on Lagrange basis
10	Function Interpolation using divided differences
11	Tchebyshev, polynomials and a near minimax approach.
12	Numerical Integration.
13	Quadrature methods.
14	Numerical differentiation.

Recommended Sources

Textbook

Atkinson, K., Elementary Numerical Analysis, 3nd Ed, Wiley, 1993.

Additional Resources

M. Heath, Scientific Computing: An Introductory Survey, 2nd ed, McGraw Hill, 2002

Burden R.L., Douglas Faires, J., Numerical Analysis, 7th Ed., Brooks/Cole, Pacific Grove, 2001

Matthews, J.H., Numerical Methods for Mathematics, Science, and Engineering, 2nd Ed., Prentice Hall,1992

MATLAB reference manual

Material Sharing

Documents	Lecture notes, related links
Assignments	Homeworks
Exams	Exams and solutions (excluding the final)

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	60
Assignment	6	40
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		30
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		70
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.					X
2	Ability to identify, formulate, and solve Electrical and Electronics Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.			X
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.			X
4	Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.					X
5	Ability to design and conduct experiments, gather data, analyze and interpret results for investigating engineering problems				X
6	Ability to access information; For this purpose ability to perform database searching and conduct literature review.
7	Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
8	Ability to communicate effectively both orally and in writing; knowledge of a minimum of one foreign language.
9	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.		X
10	Awareness of professional and ethical responsibility.			X
11	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
12	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Including the exam week: 16x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Mid-terms	2	3	6
Homework	6	5	30
Final examination	1	3	3
Total Work Load			151
Total Work Load / 25 (h)			6.04
ECTS Credit of the Course			6

Search form

Numerical Analysis

Vertical Tabs

Ders Tanimlari