The idea of projectour project is about creating a intell.docx

The idea of project:
our project is about creating a intelligent system that will help
the user to make decision in faster and easy way
we have an idea that is to create a new system for our college
for course register
our system is not that good as the students wants
we want the courses to be in the same sequence as the study
plan for registration - for the main courses and for the elective
also
we also want to show the courses dependence
for example you cannot take 103 course without completing 102
course
and when the course is register , we want to show the course
schedule as the picture provided.
and when the student complete his registration he can print and
save the schedule - the final out put schedule
If the student faces a class clashes it will show the clash time
and the course that have clash with
and provide them better solution such as changing the section or
report this problem to the responsible employee- provide the
student with suggestions to solve her problem
You can use the pictures below as an example .. And the logo to
put in in the interface

TASKS:
1. Read about Creativity below.
2. Do literatures review from Google or from given list of
Bibliography.
3. Design your invention into Interface Design and using any
solution models
4. Goto http://www.scoop.it/t/kaymarlyn and select ‘Tools’ tags
under ‘Search in topic’ menu. Study
and learn about “60 User Interface Design Tools A Web
Designer Must Have” and other prototyping
and mockup tools from the page.
5. Illustrate your idea into interface design using the selected
best tool for your Design Category and
provide the explanation. You might search from the Internet
using keywords to view other example of
process or models.
6. Disseminate your idea and how your system works into
proper formatted report.
7. Presentation will determined the winners ranking and will
contribute max 35/50 marks from the
total marks.
8. Shows all the workload distribution among your group
members in the given table.
9. Lastly, provide all the references and websites that you
visited and used in the report.
DESIGN CATEGORIES:

Project Requirement :
Creativity Creativity involves the generation of new ideas or the
recombination of known elements into something new,
providing valuable solutions to a problem. It also involves
motivation and emotion. Creativity “is a fundamental feature of
human intelligence in general. It is grounded in everyday
capacities such as the association of ideas, reminding,
perception, analogical thinking, searching a structured problem-
space, and reflecting self-criticism. It involves not only a
cognitive dimension (the generation of new ideas) but also
motivation and emotion, and is closely linked to cultural
context and personality factors.” (Boden 1998).
Fundamental concepts for all creative techniques are:
The suspension of premature judgment and the lack of filtering
of ideas.
Use the intermediate impossible.
Create analogies and metaphors, through symbols, etc., by
finding similarities between the situations, which we wish to
understand and another situation, which we already understand.
Build imaginative and ideal situations (invent the ideal
vision).
Find ways to make the ideal vision happen.
Relate things or ideas which were previously unrelated.
Generate multiple solutions to a problem.
AI (artificial intelligence) models of creativity AI deals with
solving non-quantified, unstructured problems. Its task is about
knowledge representation and reasoning and to build intelligent,
rational, and autonomous agents. Current AI models of
creativity involve different types and appropriate techniques of
supporting the generation of new ideas. According to Margaret

Boden (1998), in respect to the three types of creativity, there
are also three main types of computer models that involve:
1. The stimulation of the combination of ideas, mainly by using
analogies in the sense that associated ideas shares some inherent
conceptual structure.
2. The exploration of structured concepts, so that novel and
unexpected ideas result. It requires considerable domain-
expertise and analytical power to define the conceptual space
and to specify procedures that enable its potential to be
explored.
3. The transformation of a problem, so that new structures can
be generated which could not have arisen before. New solutions
to a problem can be created with transforming a problem into a
new problem, solve the new problem and then adapting the
solution back to the original problem.
AI employs symbolic approaches for creative problem solving
and includes stimulus such as heuristics, search, weak methods,
knowledge representation and reasoning to facilitate problem
structuring and idea generation. The focus of AI creativity
techniques in the form of computerized programs, is to help
users to take a fresh look at problems by guiding what may be a
user’s otherwise undisciplined intuition through a series of
problemsolving exercises, and to think in non-linear et non-
logical ways. The main advantage of computerized, guided
problem solving is that the programs prompt a user for ideas in
a thorough manner. Recent programs of AI include also
knowledge-based approaches, using large-scale databases and
narrative systems (Chen 1998). AI researches have also
developed efficient search algorithms for problem solving.
Some expected results of the creativity process are:
innovation through new product and process ideas
continuous improvement of products or services
productivity increase
efficiency
rapidity
flexibility

quality of products or services
high performance
………………………………………………………….
The idea of project:
Logo : YANBU UNIVERSITY COLLEGE
Inter Face EX:
Credit hour
Courses
5
MIS 348
5
MIS 440
5
MIS 445
3
MGT 3xx
3
MGT 418
2
LIS 101
3

XE 451
3
XE452
FINAL PROJECT, MATH 251, FALL 2015
[The project is Due Monday after the thanks giving recess]
.NAME(PRINT).________________ SHOW ALL WORK.
Explain and
SKETCH (everywhere anytime and especially as you try to
comprehend the prob-
lems below) whenever possible and/or necessary. Please
carefully recheck your
answers. Leave reasonable space between lines on your solution
sheets. Number
them and print your name.
Please sign the following. I hereby affirm that all the work in
this project was
done by myself ______________________.
1) i) Explain how to derive the representation of the Cartesian
coordinates x,y,z
in terms of the spherical coordinates ρ, θ, φ to obtain
(0.1) r =< x = ρsin(φ)cos(θ), y = ρsin(φ)sin(θ), z = ρcos(φ) > .
What are the conventional ranges of ρ, θ, φ?
ii) Conversely, explain how to express ρ, sin(θ), cos(θ), cos(φ),
sin(φ) as
functions of x,y,z.

iii) Consider the spherical coordinates ρ,θ, φ. Sketch and
describe in your own
words the set of all points x,y,z in x,y,z space such that:
a) 0 ≤ ρ ≤ 1, 0 ≤ θ < 2π, 0 ≤ φ ≤ π b) ρ = 1, 0 ≤ θ < 2π, 0 ≤ φ ≤
π,
c) 0 ≤ ρ < ∞, 0 ≤ θ < 2π, φ = π
4
, d) ρ = 1, 0 ≤ θ < 2π, φ = π
4
,
e) ρ = 1, θ = π
4
, 0 ≤ φ ≤ π. f) 1 ≤ ρ ≤ 2, 0 ≤ θ < 2π, π
6
≤ φ ≤ π
3
.
iv) In a different set of Cartesian Coordinates ρ, θ, φ sketch and
describe in your
own words the set of points (ρ, θ, φ) given above in each item
a) to f). For example
the set in a) in x,y,z space is a ball with radius 1 and center
(0,0,0). However, in
the Cartesian coordinates ρ, θ, φ the set in a) is a rectangular
box.
2) [Computation and graphing of vector fields]. Given r =<
x,y,z > and the

vector Field
(0.2) F(x,y,z) = F(r) =< 1 + z,yx,y >,
1
FINAL PROJECT, MATH 251, FALL 2015 2
i) Draw the arrows emanating from (x,y,z) and representing the
vectors F(r) =
F(x,y,z) . First draw a 2 raw table recording F(r) versus (x,y,z)
for the 4 points
(±1,±2,1) . Afterwards draw the arrows.
ii) Show that the curve
(0.3) r(t) =< x = 2cos(t), y = 4sin(t), z ≡ 0 >, 0 ≤ t < 2π,
is an ellipse. Draw the arrows emanating from (x(t),y(t),z(t))
and representing
the vector values of dr(t)
dt
, F(r(t)) = F(x(t),y(t),z(t)) . Let θ(t) be the angle
between the arrows representing dr(t)
dt
and F(r(t)) . First draw a 5 raw table
recording t, (x(t),y(t),z(t)), dr(t)
dt
, F(r(t)), cos(θ(t)) for the points (x(t),y(t),z(t))
corresponding to t = 0,π

4
, 3π
4
, 5π
4
, 7π
4
. Then draw the arrows.
iii) Given the surface
r(θ,φ) =< x = 2sin(φ)cos(θ), y = 2sin(φ)sin(θ), z = 2cos(φ) >,0 ≤
θ < 2π, 0 ≤ φ ≤ π,
in parametric form. Use trigonometric formulas to show that the
following iden-
tity holds
x2(θ,φ) + y2(θ,φ) + z2(θ,φ) ≡ 22.
iv) Draw the arrows emanating from (x(θ,φ),y(θ,φ),z(θ,φ)) and
representing the
vectors ∂r(θ,φ)
∂θ
× ∂r(θ,φ)
∂φ
, F(r(θ,φ)) = F(x(θ,φ),y(θ,φ),z(θ,φ)) . Let α(θ,φ) be
the angle between the arrows representing ∂r(θ,φ)
∂θ
× ∂r(θ,φ)

∂φ
and F(r(θ,φ)) . First
draw a table with raws and columns recording
(θ,φ),(x(θ,φ),y(θ,φ),z(θ,φ)),
∂r(θ,φ)
∂θ
×∂r(θ,φ)
∂φ
and F(r(θ,φ)), cos(α(θ,φ)) for the points (x(θ,φ),y(θ,φ),z(θ,φ))
corresponding
to (θ,φ) =(π
4
, π
6
),(3π
4
, π
6
),(5π
4
, π
6
),(7π
4
, π
6
),(3π

4
, 5π
6
),(5π
4
, 5π
6
),(7π
4
, 5π
6
). Then draw
the arrows in (x,y,z) space.
Repeat iv) with
F(x,y,z) = F(r) =< 1,x,0 > .
3) Given the integral
(0.4) DI =
∫ 8
0
∫ 2
3
√
y
f(x,y)dxdy.

a) Sketch the domain of integration D in (0.4) . What are the 4
curves that
enclose D in the x,y plane?
b) Determine the missing upper and lower limits in the integral
below such that
(0.5) DI =
∫ ∫
f(x,y)dydx =
∫ 8
0
∫ 2
3
√
y
f(x,y)dxdy.
c) If f(x,y) is the density of a drum of shape D, what could be
the meaning of
the number DI? If f(x,y) ≡ 1 in DI, what could be the geometric
meaning of the
number DI? If z = f(x,y) ≥ 0 is interpreted as the length of the
line segment with
end points (x,y,0) (in D) and (x,y,f(x,y)) , what could be the
geometric meaning
of the number DI?

d) Given
(0.6) TI =
∫ 8
0
∫ 2
3
√
y
∫ f(x,y)
0
dzdxdy.
Show that TI = DI. What geometric meaning could be attributed
to the number
TI?
e) Determine the value of DI in (0.5) with f(x,y) = ex
4
.
f) Subdivide the square with vertices at (0,0),(1,0),(1,1),(0,1) in
the x,y plane
by a partition generated by the lines x = 0,0.25,0.5,0.75,1 and
by the lines y =
0,0.25,0.5,0.75,1 and obtain 16 sub squares. With the function
f(x,y) = xy
calculate the Riemann Sum ,RS, where in each sub square you
choose the value of
xy at the “left lower vertex” . Evaluate
DI =

∫ 1
0
∫ 1
0
(xy)dydx.
and determine [DI −RS].
4) a) The function z = f(x,y) = 2x2−2xy+y2 in defined for all
−∞ < x,y < ∞
. Determine the critical points and the values of f(x,y) at these
critical points.
Determine wether the function attains a local minimum a local
maximum or a
saddle point at these critical points.
b) Determine all the critical points of the function z = f(x,y) =
(xy)
1
3 that is
defined for all −∞ < x,y < ∞ and mark these critical points in
the x,y plane .
c) Use the method of traces to determine the shape of the
surface z = f(x,y) =
xy defined for all −∞ < x,y < ∞ . Determine the traces of z =
f(x,y) in the
planes z = 0,1,−1,3,−3,5,−5,7,−7. (you may add more traces) .
Sketch first the
level curves. Determine a parametric representation r(t) =<
x(t),y(t),z(t) > for
the trace z = −3 . Determine a parametric representation r(t) =<

x(t),y(t),z(t) >
for the projection of the trace z = −3 on thex,y plane.
d) Determine the value of the absolute minimum and absolute
maximum of the
function z = f(x,y) = xy defined in the domain D given by −1 ≤
x,y ≤ 1.
5) a) Determine the 6 upper and lower limits to
(0.7) TI =
∫ ∫ ∫
E
dzdydx
where E is the half hemisphere enclosed by the xy plane and the
surface (that is
the set of all x,y,z, such that)
(0.8) x2 + y2 + z2 = 42, z ≥ 0.
Evidently the solid E can also be described by inequalities as
the set
of all x,y,z such that
(0.9) x2 + y2 + z2 ≤ 42, z ≥ 0.
Do not evaluate TI in (0.7) yet.
b) Look up in a high school text book or on the internet the
volume of a ball
with radius R. What would you expect TI to be? Why?

c) What is the set of the spherical coordinates ρ,θ, φ that
matches the set
of all x,y,z such that x2 + y2 + z2 ≤ 42, z ≥
0? Sketch this new set of
points (ρ,θ, φ) in a new system of Cartesian coordinates ρ,θ, φ.
What is the shape of this new set in the new system of
coordinates ρ,θ, φ?
What are the 6 surfaces that bound this new set? Denote this
new set by B.
d) It is known that
(0.10) TI =
∫ ∫ ∫
E
dzdydx =
∫ ∫ ∫
B
ρ2sinφdρdθdφ.
Determine the 6 limits in the triple integral
TI =
∫ ∫ ∫
B
ρ2sinφdρdθdφ
then evaluate TI. Is the value TI consistent with your

expectations in b)? Why?
e) Given the triple integral
TI =
3∫
−3
√
9−x2∫
−
√
9−x2
x+y+10∫
x+y−10
f(x,y,z)dzdydx.
Describe the solid V over which the integration is carried out.
Describe; the upper and lower surfaces, their common domain D
on
which they are projected in the x,y plane and the “walls”.
Provide a parametric representation r(t,s) for each of these
surfaces,
for the “walls” and for the common domain.
f) Evaluate
DI =
3∫
−3

√
9−x2∫
−
√
9−x2
(x2 + y2)dydx
by converting to polar coordinates.
6) Given the function H(x,y,z) =
z3 −x3y9 , the temporarily fixed point P0 =
(1,1,1) and the vector V =< 1,2,3 >.
a) Determine at P0 the directional derivative of H in the
direction of V .
b) Let
(0.11) r(t) =< 1,1,1 > +
1
√
14
< 1,2,3 > t, 0 ≤ t < ∞,
be the equation of the ray emanating from P0 and containing the
vector <1,2,3>.
What are r(0), r(2)?

Determine cos(θ) where θ is the angle between ∇ H(P0) and V .
Is the angle θ acute or obtuse?
Calculate the function
(0.12) N(t) = H(r(t)).
What is the value of N(0) ? Is the function N(t) increasing or
decreasing along
the ray (0.11) at t = 0 in the direction of V =<
1,2,3 >? Repeat the same
calculation however with V =< −1,2,−1 >.
In which direction=θ and for which vectors V will the
directional derivative
be maximal at P0? Determine the value of this maximum.
In which direction=θ and for which vectors V will the
directional derivative be minimal at P0? Determine the value of
this minimum.
Determine an equation of the plane containing P0 such that the
directional derivative
of H along every arrow in this plane emanating from P0 is 0.
c) Show that the surface that is given implicitly by the equation
(0.13) H(x,y,z) = z3 −x3y9 = 0.
contains the point P0 =
(1,1,1). Determine an equation for the tangent plane and an
equation for the
normal line to this surface that contains the point P0 =
(1,1,1).
d) Solve (0.13) for z and determine explicitly the function z =
f(x,y). Consider
the following parametric representation of the surface
determined by z = f(x,y)

r(t,s) =< x = t, y = s, z = f(t,s) >, −∞ < t,s < ∞.
Evaluate the following quantities for t = 1,s =
1; r(1,1), ∂r(1,1)
∂t
, ∂r(1,1)
∂s
,∂r(1,1)
∂t
× ∂r(1,1)
∂s
. Then show that
i) r(1,1) is the position vector of the point P0 =
(1,1,1) and ii)that ∂r(1,1)
∂t
×
∂r(1,1)
∂s
and ∇ H(P0) are collinear.
7) a) Determine an equation of the surface z =
f(x,y) obtained by revolving the curve
z = f(x) = cos(x),0≤ x ≤ π

2
(that lies in the plane y =
0 ) about the z axis. Sketch the shape of this surface.
b) Determine an equation of the surface z =
f(x,y) obtained
by revolving the curve z = f(x) = x2,x ≥
0 (that lies in the plane y = 0) about the z axis.
Sketch the shape of this surface.
c) Given the parabola y = f(x) = x2, −∞ < x <
∞ that lies in the x,y plane.
At each point (x = t, y = t2, z = 0 ), −∞ < t <
∞ ,that is temporarily fixed on the parabola,
erect a perpendicular line given by r(t,s) =< t, t2, 0 >
+s < 0,0,1 >=< t, t2, s >,−∞ < s <
∞. By definition this
is a cylindrical surface.
d) What is the shape of the curve r(t,1) =< t, t2, 1 >
,−∞ < t < ∞ ? What is the shape of the
curve r(t,−2) =< t, t2, −2 >,−∞ < t <
∞. Sketch these 2 curves.
e) A particle moves along the curve r(t,1) as −∞ < t <
∞. What is the direction of motion along the curve?
Determine the coordinates of the points on this curve that
correspond to t =
−2,−1,0,1,2.
Sketch a the arrow tangent to the curve at times t =
−2,−1,0,1,2 that represent the vector ∂r(t,1)
∂t
.

Have the tails of these arrows emanate from the head of the
position arrow r(t,1).
f) The differential ∂r(t0,1)
∂t
dt represents a SIMPLE APPROXIMATION to the directed
“curvy” segment of the curve at t0 and
∣ ∣ ∣ ∂r(t0,1)∂t ∣ ∣ ∣ dt represents a SIMPLE
APPROXIMATION
to the length of this “curvy” segment. Therefore,the arc length
traversed
by a particle from time t = 0 to t = π
2
is given by
(0.14) legth =
∫ π
2
0
∣ ∣ ∣ ∣ ∂r(u,1)∂u
∣ ∣ ∣ ∣ du.
Determine the integrand in (0.14).You don’t have to calculate
the integral.

g) Calculate; i) the coordinates of the point P0 on the surface
r(t,s) =<
t, t2, s > that
correspond to t = 1,s = 2.
ii) The normal
∂r(1,2)
∂t
×
∂r(1,2)
∂s
to the surface at P0. iii) The two unit normals ±n at P0 that are
collinear
with ∂r(1,2)
∂t
×
∂r(1,2)
∂s
iv) the SIMPLE APPROXIMATION
∣ ∣ ∣ ∂r(1,2)∂t × ∂r(1,2)∂s ∣ ∣ ∣ dtds to the AREA OF a
“curvy” quadrangle (having P0 as a vertex) in the mesh created
on the surface of
r(t,s) =< t, t2, s > by two families of curves.
Determine an equation for the tangent plane and an equation for
the normal
line to this surface that contain the point P0.
8) Given a vector field F(x,y,z) =< F1(x,y,z), F2(x,y,z),
F3(x,y,z) > .

a) Define
(0.15)
∇ ×F =
i j k
∂
∂x
∂
∂y
∂
∂z
F1 F2 F3
∂F1∂y )k.
Utilize the right hand side of (0.15) to determine ∇ ×F for F =<
x2,y2,z2 >
and F =< x2 + yz,y2 + 2zx,z2 + 5x >.
b) Define
(0.16) ∇ ·F =
∂F1
∂x
+

∂F2
∂y
+
∂F3
∂z
and determine ∇ ·F for F =< x2,y2,z2 > and F =< x2 +yz,y2
+2zx,z2 +5x >.
Denote by w = φ(x,y,z) a scalar function. For φ(x,y,z) = exy+2z
determine
∂2φ
∂y∂x
and ∂
2φ
∂x∂y
.
c) Prove or demonstrate that for any vector field F(x,y,z) and
scalar function
φ the following holds; i) ∇ · (∇ ×F) = 0 and ii) ∇ × (∇ φ) =< 0,0,0
>.
—————————-
Useful formulas.
An element of area dA in polar coordinates is given by
dA = rdrdθ.

An element of volume dV in cylindrical coordinates is given by
dV = rdzdrdθ.
An element of volume dV in spherical coordinates is given by
dV = ρ2sinφdρdθdφ.

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