Computational Aptitude of Handheld Calculator

Computational Aptitude of Handheld Calculator

USE OF HANDHELD CALCULATORS AS SUPPORTIVE TOOLS IN
ENGINEERING EDUCATION
BY
ADEWOLE J. K . and OSUNLEKE A. S2.
Department of Chemical Engineering
1
King Fahd University of Petroleum & Minerals
2
Obafemi Awolowo University,
Ile Ife, Nigeria
1

ABSTRACT
The computational capability of a handheld non – programmable calculator as a supportive tool in effective teaching of softcomputing skill is demonstrated in this work. Seven engineering problems were solved using some of its essential in-built
scientific functions and accessories. The results obtained compared favourably well with those from sophisticated algebraic
software packages such as MATLAB and MS Excel in terms of numerical accuracy. The percentage error obtained for all the
seven problems are 0%. Acquiring skills in the use of this calculator will therefore not only enhance the learning of modern
computing software, thereby preparing students and engineers for solving real-time world problems but will also serve as an
affordable alternative to the available algebraic software packages in situations where these software are out reach. It is hoped
that this new effort will pave way for a more pragmatic approach of teaching and assessing computing skills in our higher
institutions.
Keywords: sustainable development; engineering education; computing skills; simulation software; technical competencies.
1.0

INTRODUCTION

Effective teaching in engineering education is an
important tool for sustainable industrial development. The
act of teaching the principles of engineering to produce
well baked products has been described as the most
innovative and continually evolving challenges (1). With
the emergence of many different technologies, students
need to be taught the basic knowledge required for them
to be relevant in this jet age. Globally, engineering
environment today demands both technical competencies
and excellent computing skills. Engineers and scientists
are expected to be skilful in simulation software. Gone are
the days when computer applications were consigned to
the ranks of senior staff. The emerging proliferation of
personal computers has greatly transformed application
software into common tools for problem solving.
Numerous sophisticated mathematics processing software
packages are now available. It has been observed by Foley
(2) that students in engineering and science have been
using this software but often without good results. The
author disagreed with teaching analysis in one place
(course) and computing in another place (another course),
when the two can be taught concurrently. In an attempt to

solve this problem, Hill and Rajeev et al (3, 4) wrote on
fundamentals for getting accurate simulation results.
In most schools (especially in the developing countries
where the MDGs are expected to be met by 2015), the
opportunities for hands-on practice with process
simulators may have been nonexistent or underutilised.
This is due to the fact that adequate method of teaching
computing skills has not been put in place. Students
population combined with the cost of sophisticated
software have contributed to this problem. Millions of
dollars is spent on acquiring licences for software with
little or nothing to show for it. It is quite clear that once
people are oblivious of the basics underlying the use of
this software, then it becomes difficult to use them. Also,
it has been observed that students are not interested in
learning whatever will not come out in their examinations.
The end result of this is that if a lecturer attempts to teach
them software skills, the first question they will ask is
whether it will come in the examinations or not. Of course
students know quite well that it is very difficult for them
to be asked questions that will entail real time use of
computer in the examination halls. With this in mind, the
only alternative for the lecturers is to give assignment
which majority will not do personally. All these factors
coupled with other social distractions have really

J. K. Adewole & A. S. Osunleke, 2011


contributed to lack of student’s interest and hence little or
no understanding of the basic knowledge of technical
computing. In essence, there is the need to inculcate the
use of affordable, accessible and efficient methods that
will give room for real time use of computer in the
examination halls. Accessibility in the sense that it is not
necessary to use thousands of dollars to procure the tools
needed to implement this method. We need not to have
students to queue up to practise what they have learnt.
The tool should be efficient such that moderate problems
can be solved and analysed using these tools and results
obtained are comparable with those from expensive
software packages. While the use of calculator can never
be a substitute for the available mathematical software, it
can be used, at the initial stage of learning computing
skills, to boost student morale and make computing more
interesting.
This paper is written to demonstrate the use of handheld
calculator in solving engineering problems. It discusses its
application as a supportive tool in teaching computing
skills. In justifying the use of handheld calculator,
engineering problems were solved using 1 Casio fx –
991MMS calculator and results obtained compared with
those using software like 2 Matlab and MS Excel. The
paper will present a step by step procedure of using the
available built in Functions and Modes in the handheld
calculator. The choice of this calculator is due to its
abundance and the fact that it is not programmable. It will
therefore not give room for examination malpractice.
Deep familiarization with such a calculator will give
student good background skills in using simulation
software applications.
2.1

Computer and Handheld Calculators

The history of computer can be traced back to abacus
which was developed as a calculating device in the
ancient kingdom of Babylonia in SW Asia and widely
used in early Greek and Roman times (5). The first
general purpose electronic digital calculator that was the
prototype of most computers used today was invented by
J. P. Eckert and co-invented with J. W. Mauchly in 1946.
In about four years later, Eckert and Mauchly produced a
Binary Automatic Computer (BINAC) which is capable
1

Casio is a registered trademark of the Casio Computer Co., Ltd
Matlab is a registered trademark of the Math Works Inc. and MS Excel
is a registered trademark of Microsoft Inc

2

of storing information on magnetic tape rather the than
earlier punched cards. An all transistor calculator was
introduced in 1965 by Sharp in Japan. Further research on
calculator ushered in Scientific Calculator produced by
Hewlett-Packard (HP) in 1972. Comparison between
computer and calculator can further be illustrated
graphically as shown in Fig 2.1. Details relating the
common features regarding the design and development
of the software can be found in any standard Computer
Science and Engineering Texts.

Display
Screen

Key Board

Fig. 2.1: Common Features of a Computer and
a Handheld Calculator
3.0 APPLICATIONS OF AVAILABLE FUNCTIONS
TO ENGINEERING PROBLEMS
3.1 CALC Function
Problem: One of the mathematical models proposed by
Taiwo and Adewole (6) for predicting dynamic liquid
hold up can be expressed as:
P1 = 0.0323Q – 0.0003XF + 0.0249 ed – 0.0116 (3.1)
for 0  d  0.12, where XF is the feed composition, Q
(KJ/s) is the heat flow rate and d (in m) is the distance of
the point of measurement from the top. This can be
implemented using the CALC Function
Representation: Let Q, XF, d and P1 be represented as A, B,
C and D respectively.



Algorithm: ALPHA D ALPHA = 0.0323 x ALPHA A –
0.0003 x B + 0.0249 x SHIFT ex (C) - 0.0116 CALC
For the first calculations press 0.195 = 0.1 = 0 = and the
answer will be displayed as 0.01957. The complete results
are as shown below in Table 3.1
Table 3.1: Results obtained using CALC Function
Q
XF
d
P1 (CALC) P1 (MS %
(A)
(B)
(C)
(D)
EXCEL) ERROR

 0.0001
1
2.51 
 0.86 ln 

0.
100000 f 
f
 3.7


Let

f = F.

Algorithm: (1 ÷

ALPHA F + 0.86 × ln (0.0001 ÷ 3.7

0.195

0.1

0

0.01957

0.01957

0

+ 2.51 ÷ (100000 ×

0.235

0.1

0.02

0.02136

0.02136

0

SHIFT CALC SHIFT CALC

0.195

0.2

0.04

0.02055

0.02055

0

0.2

0.06

0.02237

0.02237

0

Results: F = 0.01885.

0.235
0.195

0.4

0.08

0.02155

0.02155

0

0.235

0.4

0.1

0.02339

0.02339

0

0.195

0.6

0.12

0.02259

0.02259

0

3.2

ALPHA F))) ALPHA CALC 0

Table 3.2: Results Obtained using SOLVE Function to
Solve Colebrook Equation
f (CALCULATOR)
f (Text) % ERROR
(F)
0.0189

SOLVE Function

The SOLVE Function employs the Newton’s method to
find approximations to more complex equations. It can be
used to find the roots of non – linear equations such as

f (x) = 2x – x2

0.0189

0

The same answer was obtained as in ref 7 using a ten page
Matlab code. However the matlab program used was an
interactive one with graphical display making it more
robust. The above algorithm can also be made interactive
for various values of



D

and

N Re by defining them as

and

variables (say X and Y).

y (t )  (1  exp( t )[cos(t )   sin(t )])  0.5
where  ,  and  are constants.

Problem 2: The boiling of an equimolar mixture of
benzene and toluene at 101.3KN/m2 (760mm Hg) can also
be computed using the SOLVE Function. Given Antoine
constant for Benzene as

Problem 1: Colebrook equation relating the friction factor
( f ) for a turbulent flown of an incompressible fluid in a
pipe with the roughness ( ) and the diameter (D) of the
pipe is given by the non – linear expression


1
2.51
 0.86 ln  D 
 3.7 N Re f
f



0



Representation:

Given

that



D

Antoine constant for Toluene is
K1B=6.95334, K2B = 1343.943 K3B = 219.377

(3.2)

Representation: At the boiling point

y A  yB  1

f using the CALC

This equation can be solved for
function.

K1A= 6.90565, K2A = 1211.033 K3A = 220.79

 0.0001 and

N Re  100000 , the equation can be rewritten as

(3.3)

For equimolar mixture





xA o
PA  PBo  1
P


x A  x B  0.5
(3.4)


i.
ii.

From Antoine equation

P  10
o

k1 

k2
T  k3

(3.5)

Substituting (3.5) into (3.4), with A representing Benzene
and B Toluene, we have
k2 A
k1 B  2 B
T  k3 B
x A  k1 A  T  k3 A
10
 10
P

k


 1



Substituting for the constants and let T = X, we have
.033
6.95334 
 6.90565 1211220.7
X  219.377
X
10
 10


1343


  1520



Algorithm:

The function of the variable
The point at which the differentiation is
calculated
The change in Δx or step size

iii.

The general expression for solving such problem is
SHIFT

d
expression , a , b , Δx )
dx

Problem 1: Determine the first derivative of the
expression f ( x )  x exp( x ) at x = 0 using a step size
of h = 0.1
Representation: Let x = X
Algorithm: SHIFT

d

dx

ALPHA X x SHIFT ln ( -

ALPHA X ) , 0 , 0.1 )
Results: X = 1

( SHIFT log ( 6.90565 – (1211.033 ÷ ( ALPHA X + 220.7
) ) ) + SHIFT log ( 6.95334 – ( 1343 ÷ (ALPHA X +
219.377 ) ) ) ALPHA CALC 1520 SHIFT CALC SHIFT
CALC
The result obtained from the above is 92.1058 oC
(365.1058K). This result compares favourably with that in
ref (8) which uses trial and error to determine at which
temperature PB +PT =101.3 KN/m2 (Table 3.3).
Table 3.3: Results from Trial and Error
T (K)

PBo

PTo

PB

PT

PB  PT

373

180.006

74.152

90.003

37.076

127.079

353

100.988

38.815

50.494

77.631

128.125

3.4 Integration Calculation Function
The integration function is used to solve moderate
integration problems. To use this Function, four inputs are
required
 The function with variable x
 The boundary a and b which define the
integration range of the definite integral
 The number of partition n.
The general expression for solving such problem is

 dx expression, a , b , n )
Problem

1:

2

I ( x)  
0

sin x
1  0.25 sin 2 x

363

136.087

24.213

68.044

27.106

95.150

365

144.125

57.810

772.062

28.905

100.967

Algorithm:

365.1

144.534

57.996

72.267

28.998

101.265

(sin ALPHA X )

3.3 Differential Calculation Function
This solver can be used to obtain a numerical derivative of
explicit expressions such as f ( x )  x cos(x) . To solve
such problem, three inputs are needed

Solve

for

I(x)

given

that

dx (3.3)

 dx (( sin ALPHA X ) ÷ (

( 1 – 0.25 x

x 2 ) ) , 0 ,  ÷ 2 , 4)

Table 3.4: Results obtained using Integration Function
and Analytical Method
I (x) (CALCULATOR) I (x) (Analytical) % ERROR
1.09861


1.098612

0


The analytical solution was obtained from (9). It should
be noted that the calculator must be in radian mode to
solve this problem. The function can also be used to solve
integrals such as
150

(i)

 CpdT

D

Cp  0.235 exp[0.0473T

1

2

x 3 exp( x 2 )
(ii) I (0,1)  
dx
2
0 2  cos(ln(1  x )
1
dx (
2
0 1 x

0

1
4  x2

60,000

470,000

465,000

477,000

C  K 1 D  n( K 2  K 3 D )
n  QD



I (0,2)  

40,000

Representation: Given

1

2

20,000

C

]

1

(iv)

Table 3.5: Variation of Diameter with the Manufacturing
Costs

given that

1800

(iii) I (0,1)

(ii) Estimate the optimum value of C
(take Q = 100, 000 and use Table 3.5)

C  K1 D 

dx

  exp[sin(x)]dx

D opt 

150

U ( KJ Kg ) 

K 2Q
 K 3Q
D

(3.8)

Differentiating (3.6) and equating to zero, the optimum
diameter can be expressed as

1

(vi)

(3.7)

Substitution (3.7) into (3.6) we have,

1

(v) I (1,1)

(3.6)

 (0.855  9.42 x10

4

T )dT

20

K 2Q
K1

(3.9)

The simplified form of (3.8) is given as

C  K1 D  100000

for n  5
[ANS (i) -1731.12cal/g (ii) 0.04585 (iii) 0.785398
(iv) 0.8813736 (v) 2.532132 (vi) 121.5591 KJ/Kg]
3.5 Matrix Calculations
In MAT Mode, the calculator can be used to create
maximum of three matrices each with up to three rows
and three columns. Matrices operations such as addition,
subtraction, multiplication, transpose, inverse, and
determinant can be performed on the matrices created.
Problem: The annual manufacturing cost for a specialty
chemical is
C  K 1 D  n( K 2  K 3 D) and n  Q D

K2
 100000 K 3
D

(3.10)

Using the values from Table 3.4, a matrix structure can be
obtained as follows


 D1
 C1  
C    D
 2  2
C 3  
 
 D3




100000
100000
D1
  K1 
100000
100000  K 2 
 
D2
K3 
 
100000
100000
D3



Rearranging (3.11) gives

Where K1, K2, K3 and Q are constants
(i) Obtain an expression for optimum D


(3.11)



 D1
 K1  
K   D
 21   2
 K3  
 
 D3



1


100000
100000
D1
  C1 
100000
100000 C 2  (3.12)
  
D2
 C3 
 
100000
100000
D3



By using values from Table 3.4, K1, K2 and K3 can be
obtained as follows:
1

5 100000 470000
 K 1  20000
 K   40000 2.5 100000 465000

 
 2 
 K 3  60000 1.67 100000 477000

 
  

3.6 Regression Calculations
The REG Mode can be used to perform linear,
logarithmic, exponential, power, inverse and quadratic
regressions. This mode is very useful in data analysis,
mathematical modelling and in solving optimization
problems.
Problem: Table 3.7 shows experimental data in which the
independent variable x is the mole percentage of a
reactant and the dependent variable y is the yield (in
percent). Determine the value of x that maximises the
yield.
Table 3.7: Experimental Data on Percentage Reactant and
Yield
X

20

20

30

40

40

50

50

50

60

70

For the ease of computing K1, K2 and K3, let

Y

73

78

85

90

91

87

86

91

75

65

 K1 
 K    A1 B 
 2
K3 
 

Representation: The data is first fit with a quadratic model
of the form

Algorithm:
MODE MODE MODE 2 SHIFT 4 1 1 3 = 3 = 20000 5
100000 40000 2.5 100000 60000 1.67 100000 SHIFT 4 1
2 3 = 1 = 470000 465000 477000 SHIFT 4 3 1 X-1 x
SHIFT 4 3 2 =
The results are shown in Table 3.6.
Table 3.6:Comparison of results obtained using Excel
Link in Matlab and Matrix Function in Calculator
MS Excel
%
CALCULATOR Link/Matlab ERROR
K1

1.022

1.022

0

K2

10179.641

10179.641

0

K3

3.987

3.987

0

y  A  Bx  Cx 2

(3.13)

Algorithm: MODE MODE 2 ► 3 20,73 M+ 20,78 M+
30,85 M+ 40,90 M+ 40,91 M+ 50,87 M+ 50,86 M+
50,91 M+ 60,75 M+ 70,65 M+ SHIFT 2 ► ► 1 SHIFT 2
► ► 2 = SHIFT 2 ► ► 3
The figure that shows on the screen after pressing M+ is
the number of data that has been entered. It is strongly
recommended that the calculator memory is cleared
before initiating a new set of calculations. This can be
done by pressing SHIFT MODE 3 = =
Results:
Table 3.8: Comparison of results obtained using MS
Excel and REG Mode in Calculator
CALCULATOR MS Excel
%ERROR

 K 1   1.022   1.0 
 K   10179.641  10000
 2 
 

 K 3   3.987   4 
  
 


A

D opt  31622.78 and C opt  463245.55

The values for the MS Excel ware obtained from (10)

35.66

35.66

0

B

2.63

2.63

0

C

-0.032

-0.032

0

3.7 Equation Calculations



The EQN Mode can be used to solve equations up to three
degrees and simultaneous linear equations with up to three
unknowns. The Mode can be applied in various field of
engineering including but not limited to Thermodynamics,
Mass Transfer, Optimization and Process Control.

the ladder of their academic pursuit. With the better
understanding of the use of this important tool, the
assessment of teaching of computing skills can now easily
be done even in the examination hall so as to inject the
spirit of speed and accuracy into the students.

Problem: Consider the function

Dedication: To my mother “Obinrin rere” and other
lovely mothers around the world. “Gbogbo yin le o jere
omo o” (ameen).

f ( x)  5 x 6  36 x 5  165 x 4  60 x 3  36
2
Determine the minimum point
Representation: The first derivative of this equation is

f ' ( x)  30 x 5  180 x 4  330 x 3  180 x 2  0 (3.14)
The optimum points can be obtained from (3.14) as
follows

30 x 2 ( x 3  6 x 2  11x  6)  0
3
2
Thus x  0 and x  6 x  11x  6  0
Algorithm: MODE MODE MODE 1 ► 3 1 = -6 = 11 = 6=
Continuous pressing of the = key will display the values
of X1 = 3, X2 = 1 and X3 = 2
Other functions and Modes in this calculator are Complex
Number, Base n, Statistical Calculations, Vector
Calculations, Metric Conversions, and Scientific
Constants.
Conclusion and Recommendation
In this work, we have demonstrated the capability of using
handheld calculator to perform some seemingly difficult
scientific computations with same level of numerical
accuracy as with commonly known sophisticated
algebraic software packages. From the outcome of this
work, we have shown that the hitherto familiar handheld
calculators have so far been under-utilized because of lack
of knowledge of its functional capabilities. It can be
concluded that calculator can be used as a supportive tool
in effective teaching of soft computing skills. It is
therefore recommended that the use of calculator be
introduced in courses related to some high level
computing. Students can later build on this basic
knowledge with the use of computer as they climb higher

Acknowledgement: My profound appreciation to my
favourite secondary school maths teacher, Engr Atoyebi
and other individuals (too numerous to mention) for their
contributions to this manuscript.
REFERENCES
Global
(1) Ziemlewski, J., “Designing the New
Chemical Engineer.” Chem Eng Progress, 104 (2), pp.
6-9, (2009)
(2) Foley, H. C., “An Introduction to Chemical
Engineering
Analysis
using
Mathematica,”
Academic Press, California, (2002).
(3) Hill, D., “Process Simulation From the Ground Up,”
Chem Eng Progress, 104 (3), pp. 50 – 53, (2009)
(4) Rajeev, A., Yau-Kun, L., Oscar, S., Marco, A. S.,
and
V. Andrew, “Uncovering the Reality of
6),
Simulation,” Chem Eng Progress, 97 (5 and
pp.42 -52 and 64 – 72, (2001).
(5) Shaw, C. M., “Engineering Probelm Solving: A
Classical Perspective,” Noyes Publication, New York,
(2001).
(6) Taiwo, E. A., and Adewole, J. K., “Mathematical
Model for Predicting Dynamic Liquid Hold Up in
Packed Distillation Colum,” Nigerian Society of
Chemical Engineers, Enugu, (2007).
(7) Constantinides, A. and Mostoufi, N., “Numerical
Methods for Chemical Engineers with MATLAB
Applications,” Prentice Hall, New Jersey, (1999).
(8) Richardson, F. J., Harker, H. J. & Backhurst, R. J.,
“Particle Technology and Separation Processes,”
Butherworth Heinemann, Oxford, (2005).
(9) Osunleke, A. S., “Engineering Analysis II Solution to
Tutorial Set,” Department of Chemical Engineering,
Obafemi Awolowo University, Ile Ife, (2000).
(10) Edgar, F. T., Himmeblau, M. D., and Ladson, L.,
“Optimization of Chemical Processes,” 2nd ed.,
McGraw-Hill Chemical Engineering Series, New
York, (2001).


Computational Aptitude of Handheld Calculator

Recommended

Recommended

More Related Content

Similar to Computational Aptitude of Handheld Calculator

Similar to Computational Aptitude of Handheld Calculator (20)

Recently uploaded

Recently uploaded (20)

Computational Aptitude of Handheld Calculator