
Numerical Methods 
Anul I, semestrul II 

Course presentation
Course structure
Remarks
Curriculum
Course materials
Seminars
Test subjects 


Course presentation 

The course of Numerical Methods is given for the students of the English stream of the
Electrical Engineering and Computer Science branch of the Faculty of Engineering
Taught in Modern Languages.
The aim of this course is to introduce the students to the specific of numerical computation,
especially in basic linear algebra problems.
The topics discussed will be matrix multiplication, solution of linear systems of equations,
iterative methods for linear systems, linear least squares problems, the computation of eigenvalues
and eigenvectors.


Computation with real numbers represented in the floating point format has some
particularities that makes it a nontrivial task.
In addition to the efficiency (in terms of execution time and used memory) of an algorithm,
the programmer should be concerned also with the limitation of the inherent errors
in numerical computation.
The Numerical Methods course presents, for each algorithm discussed, the reasons that lie
behind its reliability and efficiency.
Thus, the student will accumulate the knowhow of designing and evaluating numerical algorithms.


The students are expected to have followed and understood the course of Linear Algebra.
They should also be familiar with a programming language.


Course structure 

 Faculty of Engineering Taught in Modern Languages
 Branch: Electrical Engineering and Computer Science
 1st year, 2nd semester
 Credit points: 4 (?)
 Activities:

course: 
28 hours 
(2 hours/week) 

seminar: 
28 hours 
(2 hours/week) 


total: 
56 hours 


conf.dr.ing. Bogdan Dumitrescu 
 Required previous courses: Linear Algebra, Programming
 How the final marks are computed:

start bonus: 
10 points 

seminar attendance: 
10 points 

seminar activity: 
20 points 

homeworks: 
10 points 

final test: 
50 points 


total: 
100 points 


The seminar attendance will be appreciated as follows: for 10 or more seminars attended,
the student receives 10 points; for 9 seminars attended, 9 points etc.


The activity at the seminar will be appreciated upon the number of problems solved
at the blackboard. Also, there will be small tests in each all students will receive
the task of solving independently a problem.


The homeworks consist of solving problems given at the seminars and not solved there.


The final test will take 100 minutes and will consist of solving 34 problems.
The students will be allowed to use any written material.
However, the use of any computing device is forbidden.
The minimum number of points required to pass the test is 15.


The final mark will be computed by summing the points for the above activities,
dividing by 10 and rounding.


Remarks 

During the final test, the exchange of any oral or written information between students
is forbidden.
The instructor reserves the right of punishing both the provider and the
receiver of information.
The punishment consists of cancellation of the test for the students involved in the exchange
and may come during or after the test.


Curriculum 


1. 
Introduction. The floating point format. Conditioning of numerical problems.
Stability of numerical algorithms.

4 hours 

2. 
Direct methods for solving linear systems. Gaussian elimination.
The LU factorization. The Cholesky factorization.
The determinant and the inverse of a matrix.

8 hours 

3. 
Iterative methods for solving linear systems.

2 hours 

4. 
The linear least squares problem. Orthogonal transformations, reflectors and rotations.
Orthogonal triangularization. The QR factorization.
Solution of over and underdetermined linear systems.

6 hours 

5. 
Eigenvalues and eigenvectors. The power and inverse power methods.
The QR method.

4 hours 

6. 
The singular value decomposition and its applications.

2 hours 


Seminars 

The purpose of seminars is to solve problems that review and complete the information
given at the course.
The problems will be solved mainly by the students.
(The instructor has no intention of transforming the seminars into courses.)
The students are free to propose any correct solutions to the given problems and are encouraged
to volunteer for presenting their solutions at the blackboard.
Also, the students are welcome to propose problems related to the course topic.


Test subjects 

Exemples of problems given at the final test are given
in the
download
section of this site. 

