Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
9
, No
.
1
,
J
an
ua
ry
201
8
,
pp.
1
31
~
13
8
IS
S
N:
25
02
-
4752
,
DOI: 10
.11
591/
ijeecs
.
v9.i
1
.
pp
1
31
-
13
8
131
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Develop
ment of
Learnin
g Tools
usin
g Maples fo
r En
ginee
ring
Math
ematics Sub
jec
t
No
rl
en
da M
ohd
Noor
*
,
Hani
fa
h
Su
l
aima
n,
Z
uraid
a
Al
w
ad
ood
,
S
uh
ai
la
Abd
H
alim
,
Nu
rul
Fil
z
ah
Syamimi
W
ahi
d,
N
or
Ad
il
ah
A
b
H
alim
Cent
er
for
Ma
th
emati
c
al Studie
s
,
Facu
lty
of
Com
pute
r and
Ma
them
at
ic
a
l
Sci
ences
Univer
siti
Te
kno
logi
MA
RA
,
Ma
lay
s
ia
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
J
ul
9
,
201
7
Re
vised
N
ov
2
6
, 2
01
7
Accepte
d
Dec
11
, 201
7
Mathe
m
at
i
cs
is
one
of
the
basic
and
cor
e
subje
ct
for
eng
ine
er
i
ng
student
s
.
Le
arn
ing
m
at
he
m
at
ic
s
hel
ps
in
deve
lopi
ng
pro
ble
m
solving
s
kil
ls
as
the
subjec
t
r
equi
r
e
s
cri
tical
thi
n
king.
How
eve
r
,
m
an
y
studen
t
s
per
ce
iv
e
m
at
hemati
cs
as
a
diffi
cu
lt
subj
ec
t
and
eve
n
tuall
y
get
poor
r
esult
for
th
e
subjec
t
.
In
the
in
stit
uti
on
under
st
ud
y
,
the
re
wer
e
inc
re
ase
s
in
fa
ilure
ra
te
fo
r
the
subje
ct
for
t
he
past
f
ew
sem
este
rs.
B
ase
d
on
a
pre
li
m
ina
r
y
st
ud
y
,
it
was
found
tha
t
55
p
erc
en
t
of
engi
n
e
eri
ng
studen
t
claimed
that
they
enc
ount
ered
diffi
cu
lt
i
es
in
visual
i
zi
ng
fun
ct
ion
s
in
3
-
dimension
al
spa
ce,
whi
ch
i
s
the
m
a
i
n
cont
en
t
for
enginee
ring
ca
l
cul
us
subjec
t
.
Thi
s
fa
ct
is
ver
y
unsat
i
sfac
tor
y
as
engi
ne
eri
ng
stud
ent
s
are
exp
ec
t
e
d
to
poss
ess
strong
m
at
hemati
c
al
proble
m
solving
skill
s.
In
li
ght
of
th
is,
th
e
obj
ec
t
ive
of
th
is
re
sea
r
ch
is
to
deve
lop
an
int
er
ac
t
ive
t
each
ing
and
learni
ng
tool
s,
so
as
to
a
ss
ist
student
s
in
visual
izing
3
-
dimensional
s
pac
e
func
t
ions.
The
too
l
is
int
e
nded
to
b
e
used
in
t
ea
ch
ing
and
le
arn
ing
proc
ess
in
cl
assro
om
s
and
it
is
e
xpec
t
ed
tha
t
th
e
student
s
’
under
standi
ng
in
the subject coul
d
be im
prove
d.
Ke
yw
or
d
s
:
En
gin
eeri
ng C
al
culus
Learn
i
ng T
oo
ls
Ma
ple
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
Norlen
da
M
ohd Noor
,
Ce
nter fo
r
Ma
t
hem
atical
Studie
s,
Fac
ulty
o
f C
om
pu
te
r
an
d M
at
hem
a
ti
cal
Scie
nces
,
Un
i
ver
sit
i Te
knol
og
i M
ARA
,
4045
0
S
ha
h A
lam
Selangor
,
Ma
la
ysi
a (+6
03
-
5543
5356)
.
Em
a
il
:
e
-
m
ail:
norlen
da@sa
la
m
.u
itm
.ed
u.
m
y
1.
INTROD
U
CTION
Desp
it
e
of
be
ing
t
he
prere
qu
isi
te
fo
r
en
gine
erin
g
co
ur
s
es
,
a
pr
el
im
inary
research
has
found
that
m
any
stud
e
nts
per
cei
ved
cal
culus
as
a
hi
gh
le
vel
of
dif
ficult
ie
s
a
m
on
g
any
ot
her
m
ath
em
atics
cours
es.
An
analy
sis
of
m
a
them
a
ti
cs
resu
lt
s
ov
er
a
nu
m
ber
of
sem
e
ste
rs
in
the
in
sti
tuti
on
unde
r
stud
y
has
s
how
n
a
n
al
arm
ing
rate
of
fail
ure
i
n
th
e
sub
j
ect
.
T
he
r
e
are
va
riet
ie
s
of
fact
or
s
that
con
t
rib
ute
to
this
fail
ur
e
rate
.
Cl
ass
abse
nteei
s
m
is
on
e
of
the
m
ai
n
factor
that
le
ads
to
la
ck
of
thoro
ugh
knowle
dge
of
the
sub
j
e
ct
[1]
.
Fu
rt
her
m
or
e,
insuffici
e
nt
pra
ct
ic
es
in
w
ork
ing
out
the
prob
le
m
-
so
lvin
g
exer
ci
se
s
al
s
o
c
on
tri
bute
d
to
this
pro
blem
.
Ba
se
d
on o
bs
e
r
vation,
stu
de
nts
easi
ly
distract
ed
by
surr
oun
ding
act
ivit
ie
s
and
this
m
ay
con
tribu
te
t
o
loss
of
fo
c
us
a
nd
at
te
ntio
n.
A
s
a
resu
lt
,
the
ba
sic
m
at
he
m
a
tics
sk
il
ls
and
knowle
dge
are
no
t
ab
sorbe
d
e
ntirel
y
in
cl
assroom
s
[2]
.
In
a
dd
it
io
n
to
this,
stud
e
nt
s
per
cei
ve
d
m
a
them
a
ti
cs
as
a
diff
ic
ult
su
bjec
t.
The
dif
ficult
ie
s
in
acqu
i
rin
g
the
m
at
he
m
at
ic
sk
il
ls
and
c
once
pts
m
ay
deterior
at
e
i
f
the
te
achin
g
a
nd
le
a
rn
i
ng
proce
ss
rem
ai
n
ineff
ect
i
ve
f
or
the stu
de
nts.
Learn
i
ng
cal
c
ul
us
can
be
su
c
h
a
dr
y
s
ubj
ect
with
the
tradit
ion
al
m
et
ho
d
of
te
achin
g,
wh
i
ch
in
vo
l
ved
te
xt
book,
the
bo
a
r
d
wr
it
in
g
a
nd
e
xer
ci
se
ha
ndouts.
Re
cords
showe
d
that
the
fail
ur
e
rate
fo
r
an
e
ng
i
ne
erin
g
cal
culus
i
n
one
of
the
public
un
i
ver
sit
y
inc
r
eases
f
ro
m
25
to
45
pe
rce
nt
f
or
the
past
fe
w
sem
est
ers.
Thi
s
rate
is
hig
h
since
e
ng
i
neer
i
ng
stu
den
ts
are
e
xp
e
ct
ed
to
posses
s
strong
m
at
hem
at
ic
al
sk
il
ls
and
thi
nk
i
ng.
Fr
om
a
pr
el
im
inary
survey
par
ti
ci
pat
ed
by
over
80
0
en
gin
ee
rin
g
st
ud
e
nts,
facto
rs
that
ha
ve
c
ontrib
uted
t
o
this
fig
ur
e
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
47
52
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
1
,
Jan
ua
ry
201
8
:
1
31
–
13
8
132
include
po
or
m
at
he
m
at
ic
s
back
gr
ound,
prob
le
m
s
in
m
e
m
or
iz
ing
f
or
m
ulas,
m
isun
de
r
stood
c
oncept
an
d
m
at
he
m
at
ic
s
a
nx
ie
ti
es.
Ne
ver
t
heless,
with
the
a
dvan
ce
m
ent
of
te
ch
no
l
og
y,
le
a
rn
i
ng
m
at
hem
a
ti
c
s
can
be
m
ade
interest
in
g
and
joyf
ul.
Sin
ce
the
re
vo
l
ution
of
com
pu
te
r
te
ch
no
l
og
y,
m
any
researc
he
rs
ha
ve
fou
nd
ways
to
cat
ch
stud
e
nt
interest
in
le
ar
ning
cal
culu
s.
Ma
ny
com
pu
te
r
softwa
re
an
d
app
li
cat
io
ns
ha
ve
bee
n
dev
el
oped
t
o
hel
p
im
pro
ve
stud
e
nt
un
derst
and
i
ng
i
n
m
any
su
bject
s
.
A
bulk
of
m
a
the
m
at
ic
s
ap
plica
ti
on
s
software
on
le
arn
i
ng
m
at
he
m
at
ic
s
is
avail
able
in
the
m
ark
et
,
su
ch
as
Ma
ple,
MATLAB,
Ma
the
m
at
ic
a
and
othe
rs.
Th
ese
softwar
e
s
are
co
ntinuo
usl
y
up
grade
d
i
n
orde
r
to
m
a
ke
them
m
or
e
eff
ect
ive
an
d
us
er
-
f
rien
dly.
These
syst
em
s
hav
e
ben
e
fite
d
unde
rgraduate
s
a
nd
po
st
gr
a
duat
es
in
m
a
the
m
at
i
cs,
en
gin
ee
rin
g
an
d
ph
ysi
cs
courses
by
ke
epin
g
track
of the
det
ai
ls i
n
com
plica
te
d
m
anipu
la
ti
on
s
[
3]
.
Ther
e
a
re
m
a
n
y
chall
eng
es
th
at
te
achers
or
l
ect
ur
er
s
ha
ve
to
face
to
en
sur
e
the
underst
an
ding
of
the
stud
e
nts
in
t
he
su
bject
m
at
te
r.
Am
on
g
t
he
c
ha
ll
eng
es
is
t
he
diff
ic
ulty
in
te
achin
g
diff
e
re
nt
ty
pes
of
stu
de
nts
in
a
cl
assroom
.
In
gen
e
ral,
the
re
are
two
ty
pe
s
of
stu
d
e
nt
in
cl
assr
oo
m
a
nd
the
se
two
gro
up
s
hav
e
diff
e
ren
t
perform
ance
ou
tc
om
es
[4]
.
The
first
ty
pe
is
the
m
ixed
-
a
bili
ty
gr
oup
w
ho
te
nd
to
at
trib
ut
e
their
m
at
hem
at
ic
s
perform
ance
to
thei
r
te
ache
r
.
T
he
sec
ond
ty
pe
is
the
vo
cat
ion
al
-
a
nd
a
cadem
ic
-
track
gro
up
w
ho
are
m
or
e
li
kely
to
bla
m
e
them
se
lves
wh
e
n
they
fail
ed
to
pe
rfor
m
well
.
Other
c
halle
ng
e
i
nclu
de
the
exam
a
nx
ie
ty
,
wh
ic
h
is
al
so
a
causati
ve
f
act
or
that
ans
wer
s
wh
y
stu
den
ts
are
no
t
able
to
su
cc
essfu
ll
y
com
plete
the
course
[
5]
.
Nowa
days,
st
ud
e
nts
are
m
or
e
at
tract
ed
t
o
stu
dy
us
in
g
m
od
er
n
te
ch
no
l
og
y.
Stu
de
nts
can
us
e
m
at
he
m
at
ic
s
s
of
t
war
e
or
a
pp
li
cat
ion
s
to
he
l
p
them
under
st
and
t
he
s
ubj
ec
t
bette
r
.
I
n
a
r
ecent
survey
,
it
was
repor
te
d
t
hat
a
bout
55
per
ce
nt
of
e
nginee
ring
stu
de
nts
ha
ve
a
dm
itted
th
at
they
enc
ount
ered
dif
ficult
ie
s
in
visu
al
iz
in
g
3
-
dim
ension
al
s
pa
ce
f
un
ct
io
n.
T
his
prob
le
m
is
cl
os
el
y
relat
e
d
to
s
patia
l
ab
il
ity.
By
def
i
ni
ti
on
,
sp
at
ia
l
abili
ty
i
s
a
capaci
ty
f
or
m
ental
ly
gen
erati
ng,
r
otati
ng,
a
nd
tra
ns
f
orm
ing
vis
ual
im
ages
.
This
a
bili
ty
is
i
m
po
rtant
f
or
de
velo
ping
ex
pe
rtise
in
le
arn
in
g
an
d
w
ork
set
ti
ng
s
since
it
is
on
e
of
the
th
re
e
sp
eci
fic
co
gnit
ive
abil
it
ie
s.
Un
f
ort
unat
el
y,
no
t
al
l
stud
ents
ha
ve
this
pa
rtic
ul
ar
abili
ty
and
this
weaknes
s
has
f
or
ce
th
e
m
to
struggle
in
un
de
rstan
ding
the
top
ic
of
3
-
dim
ensio
nal
functi
on
s
.
They
are
no
t
able
to
s
olv
e
the
give
n
prob
le
m
s
if
they
fail
ed
to
visu
al
iz
e
the
physi
cal
s
ha
pe
of
the
s
olids
involve
d
i
n
th
e
quest
ion.
T
he
se
f
un
ct
io
ns
i
nclu
de
sp
he
re,
co
ne,
par
a
boloid
or
oth
e
r
qua
dr
ic
su
r
faces.
I
n
vi
ew
to
this
,
it
is
the
intenti
on
of
t
his
resea
rch
t
o
introd
uce
a
cus
tom
iz
ed
com
pu
te
r
a
ppli
cat
ion
t
o
assist
t
heir
le
ar
ning
proc
ess
in
vis
ualiz
ing
the
3
-
dim
en
siona
l
sp
ace
functi
on
s.
In
t
his
m
od
ern
era,
the
re
are
ways
to
help
s
tud
e
nt
to
im
pr
ov
e
t
he
un
der
s
ta
nd
in
g
of
m
ath
em
atics
by
m
eans
of
i
nter
act
ive
le
arn
in
g
te
chnolo
gy.
Ma
them
a
ti
cal
so
ft
war
e
ca
n
help
st
ud
e
nts
i
n
s
olv
in
g
a
prob
le
m
wh
e
n
deali
ng
with
com
plex
qu
e
sti
on
s
[6]
.
It
m
ay
help
st
ud
e
nts
to
im
pr
ov
e
th
ei
r
pro
gram
m
ing
sk
il
ls
an
d
pr
e
par
e
t
hem
for
f
uture,
s
pecifica
ll
y
when
their
fu
t
ure
work
i
ng
en
vir
on
m
ent
requires
them
to
use
pro
gr
am
m
ing
l
angua
ges.
I
n
a
dd
it
io
n,
t
hese
l
earn
i
ng
to
ols
c
an
al
s
o
help
t
he
stu
den
t
i
n
a
si
m
ple
ta
sk
,
s
uc
h
as
plo
tt
ing 2
-
dim
ensio
nal o
r
3
-
dim
ension
al
f
un
ct
ion
s b
y usin
g
the
c
om
pu
te
r.
A
s
a
n
e
xam
ple,
by only
cha
ngin
g
a
functi
on
pa
ra
m
et
er,
diff
e
rent
cur
ve
or
grap
hs
can
ea
sil
y
be
plo
tt
ed.
Whe
n
this
pract
ic
al
par
t
ha
s
bee
n
m
ade
easi
er
f
or
t
he
m
,
stud
ents
w
il
l
hav
e
m
or
e
tim
e
to
fo
c
us
on
the
f
undam
ental
knowle
dg
e
of
the
s
ubj
ect
.
Fu
rt
her
m
or
e,
m
any
research
hav
e
s
how
n
that
the
us
e
of
so
ftwa
re
or
any
interact
ive
too
ls
ha
ve
de
f
init
el
y
increases
the
st
ud
e
nts’ i
nterest
and
unde
rstan
ding
on the
sub
j
ect
m
at
te
r
[7
,
8]
.
As
a
w
hole
,
w
it
h
these
m
at
h
e
m
at
ic
al
interact
ive
to
ols,
t
he
le
arn
i
ng
proce
ss
ca
n
be
m
ad
e
interest
ing
and
e
njo
ya
ble,
besides
im
pr
oving
the student
s’
unde
rstan
di
ng
in
the s
ubj
e
ct
m
a
tt
er.
Despi
te
these ad
vant
ages,
so
m
e
of
the
do
w
ns
id
es
of
th
ese
le
arn
in
g
to
ols
are
due
to
the
cost
factor
and
the
co
nnect
ivit
y
to
the
cl
oud
serv
e
r.
The
ob
j
e
ct
ive
of
this r
e
searc
h i
s to
dev
el
op a
n
interact
ive te
achin
g
an
d
le
ar
ning to
ols f
or e
ng
i
neer
i
ng
cal
culus
s
ub
to
pic.
T
he
sc
op
e
of
t
he
s
ub
t
opic
includes
,
ve
ct
or
fiel
d,
c
ur
l,
div
e
rg
e
nce
a
nd
ba
sic
li
ne
int
egr
al
,
unde
r
the
sect
ion o
f vect
or ca
lc
ulu
s.
Th
is t
ool
is u
plo
a
de
d
i
nto
a
clo
ud w
e
bs
it
e to m
ake it easi
ly
accessi
ble for
any stu
de
nts takin
g
the
s
ubj
ec
t.
The
pa
per
is
orga
nized
as
fo
l
lows
:
Sect
ion
2
pr
ese
nts
t
he
Re
search
Me
th
od,
Sect
io
n
3
di
scusses
t
he
Re
su
lt
s and
A
na
ly
sis;
an
d
th
e
la
st sect
ion
pr
e
sents the
c
oncl
us
io
n of t
he pa
per.
2.
RESEA
R
CH MET
HO
D
This
researc
h
is
div
i
ded
int
o
fou
r
ph
a
ses,
as
de
picte
d
i
n
Ta
ble
1.
T
he
first
phase
involve
d
a
pr
el
im
inary
su
rv
ey
to
gat
her
inf
or
m
at
ion
on
the
stud
e
nts
ta
king
the
sub
je
ct
.
The
seco
nd
phase
in
vo
l
ve
d
the
dev
el
op
m
ent
of
the
a
ppli
cat
ion
on
th
ree
diff
e
re
nt
top
ic
s.
O
nce
the
a
pp
li
cat
io
n
is
f
ully
dev
el
ope
d
an
d
integrate
d,
it
will
be
util
iz
e
d
in
cl
assr
oo
m
te
aching
a
nd
l
earn
i
ng
proces
s
and
stu
de
nt
will
be
giv
e
n
a
su
r
vey
qu
e
sti
on to
e
va
luate
the e
ff
ect
iveness
.
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Develo
pm
e
nt
of
Lea
r
ning
Too
ls usin
g Ma
ple
s for En
gin
eeri
ng M
ath
e
ma
ti
c
s
…
(
Norlen
da
Mo
hd No
or
)
133
Table
1.
Su
m
m
ary o
f
the
r
esea
rch flo
w
Ph
ase
Activ
ities
Ph
ase I
:
Preli
m
in
ary su
rvey
Ph
ase II
:
Dev
elo
p
m
en
t of
the ap
p
licatio
n
on
eac
h
top
ic of
the su
b
j
ect
Ph
ase III
:
a.
Pre
-
test
b.
Test r
u
n
the ap
p
lic
atio
n
c.
Po
st
-
test
Ph
ase IV
:
An
aly
sis
2.1. Ph
as
e I
A
pr
el
im
inary
su
r
vey
was
c
onduct
ed
in
Ju
l
y
2016,
i
n
wh
i
ch
800
e
ngine
erin
g
stu
de
nts
took
par
t
i
n
answerin
g
a
set
of
qu
est
i
onna
ires.
These
stu
den
ts
we
re
sel
ect
ed
from
fo
ur
eng
i
neer
i
ng
fa
culti
es,
nam
ely
ci
vil
,
m
echan
ic
al
,
an
d
el
ect
rical
an
d
chem
ic
al
eng
inee
ri
ng.
T
he
y
hav
e
diff
e
re
nt
bac
kgr
ound
edu
cat
io
n,
i
n
wh
ic
h
they
cam
e
fr
om
eng
ineerin
g
dip
l
om
a
pr
ogr
a
m
s,
m
a
tric
ulati
on
st
ud
ie
s
a
nd
sci
e
nce
dip
l
om
a
pr
ogram
s.
The
re
are
al
m
os
t
80
per
ce
nt
of
the
m
m
anag
ed
to
ob
ta
in
at
le
ast
A
grade
for
their
m
at
he
m
ati
cs
subj
ect
in
di
plo
m
a
pro
gr
am
.
2.2. Ph
as
e II
The
en
gin
ee
ri
ng
cal
cul
us
s
ubj
ect
co
ntain
s
three
m
a
in
top
ic
s,
seq
ue
nce
an
d
seri
es,
m
ult
iple
integrati
on
a
nd
vector
cal
c
ulus.
The
m
ai
n
idea
is
to
dev
el
op
the
com
pu
te
r
app
li
cat
ion
for
these
th
ree
to
pics
.
In
this
pap
e
r
how
e
ver,
we
fo
c
us
e
d
on
th
e
third
c
hap
te
r,
that
is,
vec
tor
cal
cul
us
.
The
ap
plica
ti
on
was
dev
el
op
e
d by
usi
ng Mat
hlet from
Maple 201
6.
As
f
or
the
be
gi
nn
in
g,
the
c
hosen
s
ub
to
pics
for
the
de
velo
pm
ent
under
ve
ct
or
cal
cul
us
are
the
li
ne
integral,
the
gradie
nt
of
a
f
unct
ion,
di
verg
ence
an
d
cu
rl.
Figure
1
s
hows
the
f
ront
pa
ge
of
MAPL
E
2016
so
ft
war
e
.
T
he
Text
a
nd
Ma
th
m
od
e
butt
on,
Com
bo
Bo
x,
Ma
them
a
ti
cal
Ex
pr
essi
on,
Pl
ot
co
ntaine
r
a
nd
s
om
e
of o
t
her
m
enu
s
are use
d
to
cre
at
e this Ma
thle
t t
oo
l.
Fig
ur
e
1.
F
ron
t Page
of Mapl
e 2016
First,
the
ta
ble
s
f
or
Ma
thlet
a
re
create
d.
The
n
the
butt
on,
te
xt,
m
at
he
m
at
ical
expressi
on
box
an
d
al
s
o
the
plo
t
bo
x
w
ere
ad
ded
us
in
g
com
po
ne
nt
pa
le
tt
e
.
Fo
r
the
dev
el
op
m
ent
of
the
eq
uation,
Do
c
omm
and
i
s
us
ed
to
ge
ner
at
e
t
he
so
luti
on.
Othe
rs
com
m
and
use
s
the
Ma
ple
com
m
and
a
nd
the
Edi
t
Clic
k
Act
i
on
is
cl
ic
ked
t
o
insert the s
ourc
e cod
e
of the s
ub
-
to
pic. T
he
n, the f
il
e is save
d
in a
ny prefe
r
red
fo
l
der. Fig
ur
e
2a
a
nd
Fig
ur
e
2b
sh
ows
t
he
c
ompone
nt
pro
pe
rtie
s
f
or
the
crea
te
d
butt
on.
If
a
butt
on
c
onsist
s
of
certai
n
co
nd
it
io
ns
that
ne
ed
t
o
be
sat
isfie
d,
Do
c
omm
and
is
require
d.
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52
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
1
,
Jan
ua
ry
201
8
:
1
31
–
13
8
134
Figure
2a. C
om
po
nen
t P
r
op
e
rtie
s
Figure
2a.
W
i
ndows
f
or
c
reati
ng Butto
ns
Figure
3a
a
nd
Figure
3b
dep
i
ct
ed
the
proce
s
s
for
de
velo
ping
the
e
qu
at
io
ns.
Do
com
m
and
are
bein
g
us
e
d
to
gen
e
ra
te
the
so
luti
on.
Other
s
c
ommand
us
ed
the
Ma
ple
com
m
a
nd.
W
e
cl
ic
ked
Edi
t
Clic
k
Act
ion
t
o
insert the
s
ourc
e co
de of
the s
ub
-
to
pic.
Figure
3a. Edit
Cl
ic
k
Acti
on
Figure
3b. Wi
ndow
for
e
diti
ng
the
s
ource c
ode
The
inter
face
of
t
he
ap
p
is
di
scusse
d
in
Re
su
lt
an
d
A
naly
sis.
O
nce
the
oth
e
r
tw
o
to
pics
ha
ve
be
e
n
fu
ll
y
dev
el
op
e
d,
it
will
be
integrated
to
one
sing
le
ap
plica
ti
on
to
cat
er
the
stude
nts
ta
king
this
en
gin
eeri
ng
cal
culus
s
ubje
c
t.
2.3. Ph
as
e III
an
d
Ph
as
e I
V
In
t
his
phase,
stud
e
nts
will
b
e
giv
e
n
a
set
of
sur
vey
quest
ion
s
re
gardin
g
the
sub
j
ect
.
T
he
y
will
be
aske
d
to
s
ha
re
the
e
xp
e
rienc
e
in
le
ar
ning
and
un
der
sta
ndin
g
the
sub
j
e
ct
with
a
nd
w
it
ho
ut
t
he
us
e
of
the
dev
el
op
e
d
to
ol
.
A
sur
v
ey
will
be
carried
out
to
evalu
at
e
the
eff
ect
ive
ne
ss
of
t
he
ne
w
ap
plica
ti
on
.
The
analy
sis
from
t
he
s
urvey
will
b
e
discusse
d i
n t
he fut
ur
e
rese
arch pa
per.
3.
RES
ULT A
ND AN
ALYSIS
The
f
ollow
i
ng
fig
ur
es
de
picte
d
the
interface
for
so
lvi
ng
gr
a
dient,
di
verge
nc
e
,
cur
l,
li
ne
in
te
gr
al
an
d
the
gr
a
ph
of
th
e
vector
fiel
d
that
are
desi
gn
e
d
in
this
to
ol
.
Figure
4
s
how
s
the
interface
for
so
l
ving
gra
dient
.
A
stu
den
t
is
r
e
qu
i
red
t
o
enter
a
scal
ar
f
un
ct
i
on
i
n
tw
o
or
th
ree
va
riables
i
n
the
em
pty
box
on
the
le
ft
co
lum
n.
The
s
olu
ti
on wi
ll
ap
pear
in
t
he
r
ig
ht co
lum
n
on
ce t
hey cli
ck
ed
the
S
olve
fo
r Gra
dien
t
bu
t
ton
. T
he
pur
pose of
the
sec
ond
r
ow
is
t
o
e
valuat
e
the
gradie
nt
at
any
par
ti
cul
ar
po
i
nt
z
y
x
,
,
.
T
o
e
valuate
a
diff
e
ren
t
gradie
nt,
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c Eng &
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02
-
4752
Develo
pm
e
nt
of
Lea
r
ning
Too
ls usin
g Ma
ple
s for En
gin
eeri
ng M
ath
e
ma
ti
c
s
…
(
Norlen
da
Mo
hd No
or
)
135
stud
e
nt
can
cl
ic
k
the
Rese
t
A
ll
bu
tt
on.
Fig
ure
5
on
t
he
oth
e
r
ha
nd,
show
s
ano
t
her
sam
ple
fo
r
s
olv
i
ng
gradien
t
of any
functi
on
of
3 variables
.
Figure
4. Re
su
l
t for
2
-
var
ia
ble
G
r
adie
nt
Figure
5. Re
su
l
t for
3
-
var
ia
ble
G
r
adie
nt
Fo
r
so
l
ving
Di
verge
nce
an
d
Curl,
C
om
bo
Box
is
us
e
d
to
choose
ei
the
r
2
-
s
pace
or
3
-
s
pace.
T
he
2
-
sp
ace wil
l disp
la
y a zero
valu
e at R
b
ox
and
value
z bo
x.
T
he
Dive
r
gen
ce
value wil
l disp
la
y i
nco
m
pr
essible
if
the
res
ult
val
ue
is
zer
o.
If
t
he
Diverge
nc
e
disp
la
y
s
a
po
sit
ive
value
,
it
is
com
pr
essib
le
and
sour
ce
wh
il
e
neg
at
ive
value
m
eans
that
the
vector
fiel
d
is
com
pr
essible
and
sin
k.
F
or
Curl,
it
will
s
how
irr
otati
onal
an
d
conser
vative
if
the
res
ult
ap
pe
ars
as
ze
ro
va
lue.
Else
,
it
will
be
r
otati
on
al
.
Fig
ur
e
6
a
nd
7
s
hows
sam
ple
of
so
lvi
ng for di
ve
rg
e
nce a
nd c
url
in 2
-
sp
ace
3
-
sp
ace,
r
es
pecti
vely
.
The
gr
a
ph
i
n
F
igure
8
disp
la
y
s
the
directi
on
that
is
disp
e
rse
d
f
or
vecto
r
fie
ld
2
2
,
xy
y
x
y
x
f
.
The ran
ge o
f
th
e grap
h for
x
-
pl
ane,
y
-
plane
a
nd z
-
p
la
ne
are
-
1 t
o 1, res
pect
ivel
y.
The
la
st
i
nterf
a
ce
sho
wn
in
Figure
9
e
na
bles
the
stu
de
nt
to
s
olv
e
t
he
li
ne
in
te
gr
al
,
i
n
wh
ic
h
the
c
urve
that
a
par
ti
cl
e
m
ov
es
from
po
int
a
to p
oi
nt
b
is
a
strai
gh
t
li
ne.
St
ud
e
nts
ar
e
require
d
to
e
nter
the
c
om
ponen
t o
f
the
vect
or
fiel
d,
the
sta
rting
a
nd
en
ding
poin
t.
The
n,
so
l
utio
n
will
app
ea
r
a
t
the
seco
nd
r
ow
on
t
he
rig
ht
box.
As
sho
wn
i
n
Fi
gure 9, s
tu
den
t
w
il
l find
that e
valuati
ng a lin
e integral or work do
ne
by any
v
ect
or
f
ie
l
d
is ver
y
easy
,
as
lo
ng
a
s
they
ha
ve
th
e
basic
knowle
dg
e
ab
out
the
li
ne
integ
ral
it
sel
f.
And,
it
is
the
intenti
on
of
t
his
researc
h
t
o upg
rad
e
the a
ppli
cat
ion
to
d
i
ff
e
re
nt ty
pes of cu
r
ves, suc
h
a
s cir
cl
e, p
a
raboli
c a
nd o
t
her
s
.
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Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
1
,
Jan
ua
ry
201
8
:
1
31
–
13
8
136
Figure
6. S
olv
i
ng D
i
verge
nce
and Cu
rl for
2
-
sp
ace
Figure
7. S
olv
i
ng D
i
verge
nce
and Cu
rl for
3
-
sp
ace
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Develo
pm
e
nt
of
Lea
r
ning
Too
ls usin
g Ma
ple
s for En
gin
eeri
ng M
ath
e
ma
ti
c
s
…
(
Norlen
da
Mo
hd No
or
)
137
Figure
8. Plott
ing g
ra
ph for ve
ct
or
fiel
d
Figure
9. I
nterfac
e f
or
So
l
ving
Line
In
te
gr
al
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
47
52
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
1
,
Jan
ua
ry
201
8
:
1
31
–
13
8
138
This
ap
plica
ti
on
was
uploa
de
d
to
the
Ma
ple
Cl
ou
d.
Stu
de
nt
s
fr
om
any
pa
rt
of
t
he
w
or
l
d
are
abl
e
to
acce
ss
the
a
ppli
cat
ion
at
any
tim
e,
as
lon
g
as
they
are
c
onnecte
d
to
a
ne
twork
.
I
n
a
ddit
ion
,
the
st
ude
nts
ar
e
al
so
a
ble to use
this f
aci
li
ty
at any tim
e conve
nient to
them
.
The
ap
plica
ti
on
nee
ds
m
any
m
or
e
enh
a
ncem
ent
and
i
m
pr
ovem
ents
series,
as
it
is
on
ly
an
introd
uctor
y
pa
rt
of
a
gr
a
ph
i
cal
us
er
inter
fa
ce
(GUI)
de
vel
op
m
ent.
The
re
are
al
so
m
any
oth
er
s
ub
to
pics
can
to
be
a
dd
e
d
in
the
ap
plica
ti
on
,
am
on
g
t
he
m
are
Su
r
face
integral,
Dive
r
gen
ce
t
heorem
and
Sto
kes
th
eor
em
.
Diff
e
re
nt
ty
pes
of
s
urfaces
a
nd
cu
r
ves
will
a
lso
be
a
dded
t
o
cat
er
var
ie
ty
form
s
of
vect
or
cal
culu
s
pro
bl
e
m
s.
Be
sides
that,
the
c
on
te
nt
on
the
ot
her
tw
o
top
ic
s
will
be
dev
el
op
e
d
a
nd
these
will
the
n
be
inte
gr
at
e
d
as
a
sing
le
teac
hing
and lear
ning t
oo
ls
for st
uden
t as well
as t
he l
ect
ur
ers
.
In
the
f
uture
pro
j
ect
,
the
ap
pl
ic
at
ion
will
be
te
ste
d
by
us
ers
,
the
stud
e
nt,
tog
et
her
with
the
le
ct
ur
er
s.
It
is
a
ntici
pated
t
hat
this
a
pp
li
cat
ion
is
a
ble
to
help
the
st
ud
e
nt
i
n
thei
r
cl
ass
assig
nm
e
nt,
t
uto
rial
a
nd
th
us
deep
e
n
t
heir u
nd
e
rstan
ding
of the
s
ub
j
ect
c
onte
nt.
4.
CON
CLUSION
In
c
on
cl
us
io
n,
the
te
achin
g
and
le
ar
ning
to
ol
us
in
g
Ma
thl
et
was
su
ccess
fu
ll
y
dev
el
op
e
d
f
or
ve
ct
or
cal
culus
s
ub
t
op
ic
s
wh
ic
h
are
gr
a
die
nt,
di
verge
nce,
cu
rl
s
and
li
ne
int
egr
al
s.
T
he
to
ol
can
be
us
e
d
in
a
cl
assroom
le
arn
in
g
pr
ocess
a
nd
it
is
e
xp
ect
ed
t
hat
it
is
a
bl
e
to
im
pr
ove
the
stu
de
nts’
unde
rstan
ding
on
t
he
su
bject
co
ntent
.
Fu
rthe
rm
or
e,
this
too
l
can
al
so
help
them
with
their
tuto
r
ia
ls
and
assignm
ents.
Fu
rt
her
stud
y
will
be
lo
ok
i
ng
at
the
a
naly
sis
of
t
he
st
udents
’
perfor
m
a
nce
after
t
he
intera
ct
ive
too
l
is
int
rod
uced
in
cl
assroom
and
this
will
be
f
ollow
e
d
by
t
he
ne
xt
dev
el
opm
ent
of
le
ar
ning
t
oo
ls
co
ve
rin
g
oth
e
r
to
pics
in
eng
i
neer
i
ng calc
ulu
s
.
ACKN
O
WLE
DGE
MENT
This
resea
rch
is
fund
e
d
by
th
e
In
sti
tute
of
Re
search
Ma
na
gem
ent
&
In
novatio
n
(I
RM
I)
,
Un
i
ver
sit
i
Tek
no
l
og
i
MA
RA
Ma
la
ysi
a
(U
iTM
)
under
the
AR
AS
Gr
a
nt
(
600
-
IRMI/
DAN
A5
/
3/AR
AS
(01
84
/
2016
)
).
T
he
auth
or
s
w
ould
li
ke
to
t
hank
the
IRMI,
U
iTM
and
al
l
le
ct
ur
er
s,
st
ud
e
nts,
researc
h
assist
ants
an
d
othe
r
ind
ivi
du
al
s
wh
o
a
re eit
he
r dir
ect
ly
o
r
in
direc
tl
y i
nv
olv
e
d i
n t
his project.
REFERE
NCE
S
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Praka
sh
AP
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Jerl
in
JE,
Fern
ande
s
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stud
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ause
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il
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Fulle
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ple
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m
at
i
cs
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c
it
e
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[6]
Form
ane
ck
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Math
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n
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assroom
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Pros
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nd
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ple
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ent
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11
–
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Baha
ri
B,
Kart
iwi
M.
Deve
lopment
of
educ
at
ion
a
l
game
for
prim
ar
y
school
m
at
h
emati
cs
using
m
ic
rosoft
kinect
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lectr
Eng
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[8]
Abdulamee
r
A,
S
ula
iman
M,
Ar
as
MSM,
et
al
.
GU
I
Based
Con
trol
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y
stem
Anal
y
sis
using
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Control
le
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for
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a
ti
on.
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nes
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ec
tr
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