STATE ENGINEERING UNIVERSITY OF STATE ENGINEERING UNIVERSITY OF ARMENIA ( POLYTECHNIC )ARMENIA ( POLYTECHNIC )

Online teaching system

Ishkhan HovhannisyanRuben AghgashyanBeniamin Janpoladyan2007

www.seua.am

- Challenges and responds- SEUA at a Glance- Organizational model- Facilities, Software, Courseware- Instructors training - Online teaching pedagogy

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www.seua.am

State Engineering University of Armenia is challenged by the necessity to provide high quality instruction, address broader countrywide audience, and expand variety of educational services offered.

The responds of these challenges are sought on the ways of:- introduction of Web-based instruction, - usage of case-technologies, virtual labs, and electronic library,- development of faculty members and introduction of online teaching pedagogy,- partnership and cooperation with other universities.

Challenges encountered and responds sought

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www.seua.am

the main provider of training and education in technology and engineering in the Republic of Armenia,

successor institution to Yerevan Polytechnic Institute which was a leader among Soviet Polytechnics,

has three branch campuses in Gyumri, Vanadzor, and Kapan,

about 11 000 full-time students,tree degree programs: bachelor, master, and postgraduate

(Ph.D.),offers some 60 specializations in engineering, engineering

management, and social sciences, over 1 000 faculty members, most with Doctoral degrees, about 600 foreign students studying in English,plays a special role in promoting educational services and

continuing education.

SEUA at a Glance

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www.seua.am SEUA's online-teaching concept

The online-teaching project implemented at SEUA is aimed at the solving of the tasks of instruction quality and its broader accessibility, as well as at the establishing of continuous, distributed and self-studying form of education.

Online teaching project is based on the concept of free exchange of ideas, free access to the technological means and free distribution of educational technologies and products.

This concept is carried out by the creation of free Repository of teaching materials as well as by development of Open Source software free for the usage and modifications.

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www.seua.am SEUA online-teaching infrastructure

Online teaching is implemented through the following infrastructure components:

- University Intranet with connection to the Internet,

- online teaching server with installed online teaching materials, software and databases;

- lecturing classrooms, to deliver face to face lecture by usage of the presentation materials installed on the online server;

- practice classrooms, for self-studying, knowledge assessment, and virtual labs fulfillment by the usage of online server's teaching materials.

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www.seua.amOnline teaching infrastructure outline

SEUA online teaching classrooms connected to the online server

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www.seua.amOnline teaching lecturing classroom

Teacher deliver teaching materials in multimedia environment with the usage of a computer projector connected to the online teaching server.

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www.seua.amOnline teaching practice classroom

Classroom is equiped with the computers connected to the online teaching server and is aimed at the self-studying, knowledge assessment, and virtual labs implementation.

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www.seua.amOnline teaching instructor office

With the usage of an computer connected to the Internet or University Intranet instructor install and edit teaching materials at the online teaching server.

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www.seua.amPictures of online teaching lecturing classrooms

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www.seua.am Classroom opening ceremony dedicated to: Artavazd Mkhitaryan

Gayane Mkhitaryan at the classroom official opening

Mathematics dean, Vanik Zakaryan presenting Artavazd Mkhitaryan personality and chair accomplishments

Commemorating plaques, entrance and inner

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www.seua.am Classroom opening ceremony opened at: 3 March, 2006 at department of Mathematics

Rector, Yuri Sarkissyan presenting PET project, its initiators and participants Ishkhan Hovhanissyan, teacher

showcasing an online lecture on mathematics

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www.seua.am Functionality of instrumental tools /2

Instrumental means are installed at SEUA online teaching server with the access through the SEUA web-site.

Online teaching system provides functionality of the participants of teaching and learning: - students,- instructors,- teaching materials developers,- system administrators.

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www.seua.am Online teaching pedagogy

To prepare teachers for the development of teaching materials and for efficient teaching in online classes special teaching materials there are prepared: - Tutorials on management of Electronic library, Repository of case-packages, Knowledge assessment system;- Recommendation on development of lectures computer presentation;- Tutorial on formatting text materials installing in Internet;- Recommendation on teaching large classes in multimedia environment;- Tutorial on knowledge assessment tests composing based on the Bloom taxonomy.

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www.seua.am Access to online teaching system

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www.seua.am Access to the methodical materials

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www.seua.am Electronic library

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www.seua.am Case-packages

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www.seua.am Case-packages

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www.seua.am Knowledge assessment system

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www.seua.am Repository of virtual labs

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www.seua.am Repository of virtual labs

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www.seua.am

Online teaching implementation at SEUA will:

- Increase instruction general quality and efficiency,

- Provide education accessibility for broader community,

- Realize the continuous education and its open, distributed and self-studying forms.

Conclusion

STATE ENGINEERING UNIVERSITY OF ARMENIA STATE ENGINEERING UNIVERSITY OF ARMENIA ( POLYTECHNIC )( POLYTECHNIC )

Training of Foreign Students

2007

www.seua.am

- Historical reference

- Student geography

- Students Life- Admission

conditions- Study programs- Online courses

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www.seua.am

In 1958 YPI admitted the first Armenian students from the Middle East, whose number increased year by year and the geography expanded.

Beginning from 1990, the number of foreign citizens entering SEUA sharply decreased.

SEUA was the first in Armenia to amend its activities by means of a number of reforms. The stepped educational model, and trainings on some required specialties in English played a significant role. The number of foreign students increases up to 300 in 2000. At, present, about 540 students from Syria, Iran, Iraq, India, Lebanon, Egypt, Georgia, Russia and other countries are being trained at SEUA.

Historical reference

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www.seua.am Geography of Foreign Students(2006)

Country Preparat.course

bachelor program

Masterprogram

postgraduate

All programs

Syria 0 81 0 3 84

Iran 28 384 17 0 429

Georgia 0 31 2 0 33

Lebanon 0 4 0 0 4

Iraq 3 12 0 1 16

Russia 0 4 1 0 5

Other Countries 0 2 0 0 2

All Countries 31 518 20 4 573

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www.seua.am SPORT & LEISURE

THE SPORT CLUB SEUA RECREATION-

SPORT CAMPS

SEUA is multinational institution

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www.seua.am

Entrance requirements. Preparatory courses for foreign students:

- Mathematics-0 The general course of mathematics:

- Mathematics-1

- Mathematics-2

- Mathematics-3 Special courses of mathematics.

Mathematics for foreign students

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www.seua.am Course design

Syllabus.

Lectures.

Assignments.

References.

Presentations.

Exams.

Glossary.

SERIES Presentation

I. V. Hovhannisyan, A. H. Arakelyan

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www.seua.am SERIES. SUM OF A SERIES

DEFINITION 1. Suppose we have an infinite sequence of numbers ,,,,, 321 nuuuu .

The expression nuuuu 321 , (1)

or it is the same as

1inu (2)

is called a numerical series. The numbers ,,,,, 321 nuuuu are called the terms of the series. The sum of first n terms of a series is called the nth partial sum of the series:

n

iinn uuuus

121 .

DEFINITION 2. If there exists a finite limit

nn

SS

lim

it is called the sum of the series (1) and we say that the series converges. If the limit does not exist (for example, nS as n ), then we say that the series (1) diverges and has no sum

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EXAMPLE 1. Geometric progression with first term a and ratio q

12 naqaqaqa . 0a

When 1q , we have q

aq

q

a

q

aqaS

nn

n

111

.

If 1q , then q

a

q

aq

q

aS

n

nn

n

111limlim . convergent ,

sum is q

aS

1.

If 1q , nn

S

lim does not exist. divergent

If 1q , the series has the form aaa In this case naSn ,

n

nSlim divergent

If 1q , then the series has the form aaaa In this nS has no limit divergent.

SERIES. SUM OF A SERIES

33

www.seua.am

THEOREM 3. (Necessary condition for convergence) If a series

1nnu converges,

then 0lim

nn

u .

COROLLARY. If the n-th term of the series does not tend to 0 as n , then the series diverges.

EXAMPLE 2. Test for convergence .5419

1

n n

nn

SOLUTION. We have

5419

5419lim

5419limlim

nnn

nn

n

nna

nnn

n

15

41

9

65

lim5419

65lim

nn

nnnn

n

nn.

Hence, by the corollary, the series diverges.

SERIES. SUM OF A SERIES

34

www.seua.am

EXAMPLE 3. The so-called harmonic series

nnn

1

3

1

2

11

1

1

diverges, although

01

limlim n

un

nn

.

To prove this, denote the sum of the first n terms by nS and consider kS

2.

kkkkkS2

1

2

1

4

1

4

1

2

11

2

1

2

1

4

1

3

1

2

11

12

.2

1 kifk

Which means that the harmonic series diverges.

SERIES. SUM OF A SERIES

Taylor Series Presentation

By I. V. Hovhannisyan and A. H. Arakelyan

36

www.seua.am

DEFINITION 1: The power series

nn

n

n

n

xxn

xfxx

xfxxxfxf

xxn

xf

00

)(2

00

000

00

0)(

!2

!

is called the Taylor series of f at x0.

The particular case when x0 = 0 is called a Maclaurin series:

nn

n

n

n

xn

fx

fxffx

n

f

!

0

2

000

!

0 )(2

0

)(

.

Taylor series

37

www.seua.am

,,!!!2

10

2

xn

x

n

xxxe

n

nnx

0

12753

,,!12

1

!7!5!3sin

n

nn

xn

xxxxxx

0

2642

,,!2

1

!6!4!21cos

n

nn

xn

xxxxx

1,1,132

1ln1

1132

xn

x

n

xxxxx

n

nn

nn

1,1,!

11

!2

111 2

xx

n

nxxx n

Taylor series

Taylor expansions of some useful elementary functions:

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Expand the function xxf 5cos2 in powers of x .

Solution: Using the expansion of xcos :

0

2

!2

1cos

n

nn

n

xx ,

we get:

0

22

!2

101

2

1

2

110cos

2

1

2

1

2

10cos15cos

n

nn

n

xx

xx

1

2

!22

1011

n

nn

n

x.

Taylor series

Area of a Plane Figure problems

I. V. HovhannisyanA. H. Arakelyan

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www.seua.am Formulas

Area of curvilinear trapezoid in Cartesian coordinate system (see Fig.1).

Area in parametric form (see Fig.1).

Area in polar coordinate system (see Fig.2)

b

a

dxxfS )(

1

0

)()(t

t

dttxtyS a b x

y

y = f(x)

0

Fig. 1

a b x 0

Fig. 2

β α

r = r(φ)

β

α

φdφrS )(2

1 2

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www.seua.am Example 1.

Find the area of a figure bound by the parabola 2

2xy , the

lines 1x , 3x and x axis.

Solution: [ Since the figure has the form shown in figure 3, then its area can be expressed as the following integral

1 3 x

y

0

Fig. 3

y = x 2/ 2

.3

14

6

26

1

3

62

33

1

2

x

dxx

S

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www.seua.am Example 2.

Find the are of the region bounded by the curve x = 2 – y – y 2 and y-axis.

Solution: The region has the form shown if Figure 4. Here, as you see, the roles of coordinate axes are exchanged (compare with the previous example). Therefore we use the formula

i.e.

x

y

0

Fig. 4

x = 2 – y – y 21

-2

,)(d

c

dyygS

,2

14

2

1)

322(

)2(

32

1

2

2

yyy

dyyyS

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www.seua.am Example 3.

Find the area of a figure bounded by the lines:

Solution: Since the area S is bounded by two lines, (see Figure 5). then we should use the following formula:

Solving simultaneously the system of equations (*), we find the integration

limits:

Therefore,

.2 222 xyxy and

S

y

Fig. 5

O 3 x x1 x2

.)]()([2

1

12 x

x

dxxfxfS

(*)

.1;1 21 xx

1

1

353

3/2 .15

22

1

1

5

3

32)2( x

xxdxxxS

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www.seua.am Example 4.

Find the area of the region bounded by the astroid given in parametric form:

Solution: The astroid bounds the region shown in figure 6. Since S = 4 S1 and

Then

Here, integration limits t1=0 and t2=π/2 correspond to

boundary points of the region D1

.sin3)(

,cos3)(3

3

tty

ttx

y

O

Fig. 6

3

3 xD1

.sincos9)( 2 tttx

πdtttSπ

8

27cossin108

2/

0

24

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www.seua.am Example 5.

Find the area of the region bound by the curve r = a sin3φ, a > 0.

Solution: The equation r = a sin3φ, a > 0 defines a «three-leafed rose» in polar coordinate system (see Figure 7). The leaf are symmetric and each of them bound a curvilinear sector. Let us consider the first one:It is easy to see, that its area is 1/3 of the whole area bounded by the given curve; therefore, .}3sin0,3/0:),{(1 φarπφφrD

r

Fig. 7

O

π / 6

3/

0

2

6

622

3/

0

22

.4

)6sin(4

3

2

6cos1

2

3

3sin2

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1

aad

a

daSS D