Friden_1155_Program_Abstracts_Apr74 Friden 1155 Program Abstracts Apr74

Friden_1155_Program_Abstracts_Apr74 Friden_1155_Program_Abstracts_Apr74

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PROGRAM
ABSTRACTS
FRIDEN MODEL
1155
ADVANCED
PROGRAMMABLE
CALCULATOR
SINGER
BUSINESS
MACHINES
Copyright © 1972, The Singer Company
All
rights reserved throughout
the
world.
PROGRAM
ABSTRACTS
FRID-EN
MODEL 1155
ADVANCED PROGRAMMABLE
CALCULATOR
Publication
No.
52-0002-01
April
1974
SINGER
BUSINESS
MACHINES
2350
WASHINGTON
AVE
SAN
LEANDRO
CALI
F
94571
PRINTED
IN
USA,
BUSINESS
Amortization
of
a
Loan
Annual
Percentage
Rate
Compound
Interest
Budgeting
.....
.
Life
Annuities
. . . .
Automobile
Dealer
Calculations
Job
Cost
Computations
Rebar
Weight
Summary
...
Automobile
Financing.
. . .
Several
Financial
Calculations
Short
Term
Discount
Note.
.
Bond
Price
or
Yield
. . . .
Bond
Price
with
Concessions
Tax
Exempt
Bond
-
General
Program
Bonds
-
General
Program
(48%
Tax
Rate,
Par
Only)
Bonds
-
General
Program
(48%
Tax
Rate) .
Insurance
Rebate:
Short
Rate
or
Prorate)
Interest
on
Loan
for
Tax
Deduction
.
Installment
Loan
-
Payment
Known
BIOCHEMISTRY
Quality
Control
Chart.
CHEMISTRY
Decay
Constant
and
Half
Life
Relative
Elemental
Percentages
Output
Concentration
-
Varigrad
ELECTRICAL
ENGINEERING
Flux
Density
-
Circular
Loop
Circuit
Analysis
. . . . .
Fourier
Transform.
. . . .
Fourier
Transform
-
Pulse
.
Euler-Fourier
Formulas
-
Periodic
Functions
Euler-Fourier
Formulas
-f(t) =
Constant.
Current
-
Resonant
RLC
Circuit
Power
Supply
Design
. . . . . . . . . .
CONTENTS
I
I
I
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
5
6
6
6
7
7
7
7
7
8
8
8
4/74
Friden
1155
Calculator
-
Program
Abstracts
iii
Contents
MECHANICAL ENGINEERING
Cam
Design
............
.
Compression
Spring
Design
-Round
Wire
Cam
Design
-Modified
Cycloid.
. . . .
Extension
Spring
Design
-
Stress
Concentration
Torsion
Spring
Calculations
Flat
Spring
Calculations
. . . . . . . . . . . .
STRUCTURAL
ENGINEERING
Cantilever
Bean
-
Partial
Uniform
Load.
Stress
and
Strain
-
Elastic
Bodies
Weibull
Distribution
Function.
. . . . .
SURVEYING
Traverse
Closure
(revised
program)
Traverse
Calculations.
. . . . . .
Coordinates
of
an
Observer's
Position
Area
by
Helon'
s
Formula
Cut
and
Fill
Calculations
.....
.
Manning's
Equation
. . . . . . . . .
Conversion
between
Azimuth
and
Bearing
Intersection
of
Two
Lines
. . . .
Intersection
of
a
Line
and a
Circle
Intersection
of
Two
Circles
Grade
Elevations
. . . . . . . .
Computation
of
Curve
Data.
. . .
Long
Chord
Data
for
Traverse
Closure
Coordinate
Geometry
for
a
Traverse
Area
of
a
Traverse
. . . . .
Vertical
Curve
Equation
. . . . . . •
Deflection
Angle
Calculations
Traverse
Closure
using
Interior
Angles
Curve
Staking
Calculation
. . . . . .
CIVIL ENGINEERING
Hardy
Cross
Network
Analysis
NUMERICAL ANALYSIS
Solution
to
Three
Linear
Equations
Solution
of
a
Quadratic
Equation
Simpson's
Rule
of
Integration.
. .
Calculation
of
Coefficients
of
a
Polynomial
Evaluation
of a
Polynomial
and
its
Derivatives
Inversion
of
a 3 x 3
Matrix.
. . . . . . . .
iv
Program
Abstracts
-
Friden
1155
Calculator
9
9
9
9
9
10
11
11
11
12
12
12
12
12
12
13
13
13
13
13
13
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14
14
14
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15
15
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17
17
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4/74
Multiplication
of Two 3 x 3
Matrices
Determinant
of
a
.3
x 3
Matrix
. .
+,
-,
Product
for
Vectors
. . .
X,-7-'
l/x
for
Complex
Numbers
Newton-Raphson Method
....
3 x 3
Matrix
Multiplied
by a Column
Vector.
Evaluate
y = f(xl,
x2'
...
xn
).
. . . . •
Root
of
a
Non-linear
Equation
. . . . . .
Factorization
into
Primes
. . . . . . . . . .
Evaluation
of a
Polynomial
-
Complex
Value .
Root
of
a
Polynomial
-
Real
or
Complex.
Division
of
Polynomials
. . . . .
Solution
of
a
Differential
Equation
Binary
-
Decimal
Conversions
Harmonic
Analysis
. . . . . .
Product
of Two n x n
Matrices
Solution of n
Linear
Equations
n x n
Matrix
Inverter
. . . .
STATISTICS
Mean,
S.D.,
S.E.,
T-Values
.....
Covariance,
Correlation,
and
Regression
Fitting
of a
Quadratic
to
Data
Pairs.
• .
Linear
Regression
. . . . . . •
Fitting
of y = Ae
Bx
to
Data
Pairs.
x2
for
a 2 x 2 Contingency
Table
x2
for
n x m Contingency
Table
Paired
-T
Test
. . .
Binomial
Distribution
. . . .
Poisson
Distribution
. . . .
Mean, S.
D.,
S.
E.,
Range
for
Data.
•
Significance
between
Two
Proportions
Likelihood
Ratio
. . . . . . . .
Combinations,
Permutations.
. .
Multiple
Correlation
Coefficients.
.
Normal
Distribution
Ordinates
. .
Least
Squares
Fit
to y =
ax
b . . .
One-way
Analysis
of
Variance
. . .
Anova
Table
- 2 x 2
Factorial
Design
x2
Distribution
Ordinates
. . • . . .
F
Distribution
Ordinates.
. . . . .
Integrals
for
the
Normal
Distribution
Integral
for
the
x2
Distribution.
. .
Reliability
Testing
-
Test
Period
Reliability
Testing
-Confidence
Limits
.
Reliability
Testing
-Confidence
Level.
.
Random
Permutations
of
Sequenced
Integer
Values
Pseudo-random
Number
Table
. . . . . . . • .
18
18
18
18
18
18
18
19
19
19
19
19
19
19
20
20
20
20
Contents
21
21
21
21
21
21
21
22
22
22
22
22
22
22
23
23
23
23
23
23
23
23
23
24
24
24
24
24
4/74
Friden
1155
Calculator
-
Program
Abstracts
v
Contents
vi
Check
for
Randomness
of
Digits
in a
Table
. . . . .
Generation
of
a
Set
of
Pseudo-random
Integer
Values.
Statistics
of a
Set
of
Groups
. . . . . . . .
Multiple
Linear
Regression
. , , ,
Least
Square
Fit
with a
Polynomial.
REAL
ESTATE
Real
Estate
Investment
Projection
Analysis
Depreciation
Calculations
Mortgage
Yield.
. . , , , , , . . , . . ,
EDUCATION
Test
Correction:
Less
than
40 fq!uestions .
Test
Correction:
40 -50 fq!uestions, ,
Determination
of
Grades
. , . . , , ,
SUBROUTINE PROGRAMS
Pack
Values
. , .
Unpack
Values
. .
Round a
Decimal
Value
Vector
Sorting
Routines.
MrSCELLANEOUS
Navigational
Course
Calculation
Six
Geometric
Problems
Manual Mode
Diagnostic
...,
Program
Abstracts-
Friden
1155
Calculator
",
.
24
24
24
25
25
26
26
26
27
27
27
28
28
28
28
29
29
29
4/74
INTRODUCTION
INTRODUCTION TO ABSTRACTS
4/74
This
publication
contains
abstracts
of
all
programs
prepared
by
Singer
Business
Machines
for
use
with
the
1155
Programmable
Calculator.
Programs
may
be
ordered
from
the
local
Singer
Business
Mar-hines
Office.
Publication
numbers
have
been
changed
to
reflect
a new
numbering
system
for
documents.
When
ordering,
please
specify
the
publication
number
in
this
manual
for
the
program
wanted.
Friden
1155
Calculator
-
Program
Abstracts
BUSINESS
ABSTRACTS
52-8003-001
52-8003-002
52-8003-003
4/74
AMORTIZATION
OF
A LOAN
There
are
several
options
available:
(1)
(2)
(3)
Calculation
of
payment/period,
X,
necessary
to
amortize
a
loan
if
the
principal,
P,
annual
interest
rate,
i,
and
number
of
periods,
n,
with
m
periods
per
year
are
known.
Determination
of
n,
the
number
of
full
payments
of x
dollars
given
P,
i,
m
and
x.
Also
calculate
the
amount
of
the
last
payment.
For
a
given
n 1 < n
or
n 5 n1 5 nb,
determine
the
interest
payment
for
n 1 ,
payment
on
the
principJl,
total
principal
paid
to
date,
total
interest
paid
to
date,
total
amount
paid
to
date,
and
the
principal
remaining.
ANNUAL
PERCENTAGE
RATE
This
program
uses
the
Muller
iterative
method
to
determine
i
such
that
i(1 +
i)n
R = P
.--;'--~-
where
(1 +
i)n-l
R =
payment/period
P =
principal
n =
number
of
payments
i =
interest
rate/period
The
process
stops
when
the
difference
between
two
successive
i
values
510-
4•
To
determine
the
APR,
it
is
necessary
to
multiply
i by-
the
number
of
periods
per
year.
COMPOUND
INTEREST
Evaluates
the
formula
A =
P(1
+
i)n
p
where
P =
principal,
i =
annual
interest
rate,
p =
number
of
periods
per
year,
n =
number
of
periods.
For
each
period,
the
interest
is
printed,
the
total
interest
to
date,
and
the
total
amount
to
date.
Friden
1155
Calculator
-
Program
Abstracts
1
Business
52-8003-004
52-8003-005
52-8003-006
52-8003-007
52-8003-008
52-8003-009
BUDGETING
The
distribution
of
payments
on a
principal
is
determined
meeting
specific
requirements.
The
year
is
divided
into
quarters.
The
payment
during
the
first
month
of
each
quarter
is
approximately
equal
to
1.25
times
the
latter
2
months.
Monthly
totals
and
the
grand
total
are
printed.
LIFE
ANNUITIES
The
program
performs
calculations
for
the
values
of
whole
life
annuities
and
temporary
life
annuities.
AUTOMOBILE
DEALER
CALCULATIONS
Given
the
amount
to
be
financed,
the
number
of
months,
the
number
of
extra
days
and
the
add-on
rate,
the
program
calculates
APR,
the
amount
of
life
insurance
premium,
the
amount
of
accident
and
health
insurance
premium,
the
total
to
be
financed
including
insurance,
the
amount
of
the
finance
charge
and
the
monthly
payment
for
each
of
five
insurance
options.
It
is
easily
tailored
to
individual
needs.
JOB
COST COMPUTATIONS
Consider
a
table
consisting
of
fewer
than
26
items,
each
having
two
associated
cost
values
-
for
example,
price/item
and
labor
(hr)/item.
The
user
simply
keys
in
a
quantity
for
each
item
and
the
machine
will
print
total
material
cost
and
total
labor
cost
for
that
item.
At
the
same
time,
it
keeps
running
totals.
After
all
items
have
been
entered,
it
will
compute
total
job
cost
based
on a
sales
tax
rate
and
an
hourly
labor
rate.
REBAR
WEIGHT SUMMARY
The
program
accepts
three
input
values:
number
of
bars,
size
of
bar,
and
length
per
bar.
Given
the
pound/foot
for
each
size
as
a
part
of
the
program,
the
machine
determines
total
length
and
poundage
for
each
size
bar
as
well
as
the
grand
weight
total.
AUTOMOBILE FINANCING
This
program
is
set
up
to
be
tailored
to
the
user's
needs.
The
input
includes
principal,
number
of
months,
odd
days.
add-on
rate.
There
is
an
opportunity
to
input
other
charges
such
as
title
or
recording
fee.
Various
rates
for
credit
life,
AIH
insurance,
taxes,
etc.
are
incorporated
into
the
program
by
the
user.
Included
in
the
output
are
the
total
note
value,
the
amount
financed,
the
finance
charge,
insurance
charges,
total
other
charges,
monthly
payment,
and
APR.
2
Program
Abstracts
-
Friden
1155
Calculator
4/74
52-8003-010
52-8003-011
52-8003-012
52-8003-013
52-8003-014
52-8003-015
52-8003-016
4/74
Business
SEVERAL
FINANCIAL CALCULATIONS
Amortization
Schedule
Discounting
a
Note
Status
of
a
Loan
Number
of
Payments
to
Pay
Off a
Loan
SHORT
TERM
DISCOUNT NOTE
Given
the
face
value,
maturity
and
transaction
dates,
and
one
of
the
three
values
discount
rate,
effective
yield,
or
price,
the
program
will
determine
the
other
two
values.
BOND
PRICE
OR YIELD
Given
the
date
of
maturity,
settlement
date,
bond
rate,
and
gross
yield,
the
pro-
gram
will
calculate
dollar
price.
If
the
former
three
values
and
dollar
price
are
known,
it
will
determine
the
gross
yield.
BOND
PRICE
WITH CONCESSIONS
This
program
determines
the
bond
price
when
given
either
the
expected
yield
or
the
straight
price.
TAX
EXEMPT
BOND -
GENERAL
PROGRAM
This
program
will
determine
the
following.
1.
Dollar
price
required
for
a
specified
gross
or
true
yield
2.
Gross
yield
for
a
specified
dollar
price
or
true
yield
3.
True
yield
(after
capital
gains
tax.
if
any)
for
a
specified
dollar
price
or
gross
yield
4.
Any of
the
above
for
a
call
date
(with
possibly
a
different
redemption
value)
5.
Any
of
the
above
for
a
different
tax
rate
6.
The
dollar
price
and
actual
price
after
concessions
7.
The
accrued
interest
for
the
present
coupon
period
8.
The
total
price
BONDS -
GENERAL
PROGRAM (48C
{
Tax
Rate,
Par
Only)
The
program
determines
1
through
4
and
6
through
8
as
for
Business
Program
014
above.
It
assumes
a
489c;
tax
rate
and
that
all
bonds
are
redeemable
at
par
even
on
call
dates.
BONDS -
GENERAL
PROGRAM (48%
Tax
Rate)
This
program
is
the
same
as
Business
Program
015
except
that
bonds
redeemable
at
premium
are
allowed.
Friden
1155
Calculator
-
Program
Abstracts
3
Business
52-8003 -017
52-8003-018
52-8003-019
4
INSURANCE REBATE: SHORT RATE OR PRORATE
This
program
will
determine
the
rebate
factor
commonly
found on
an
insurance
rebate
'wheel'.
This
may
be
either
the
short
rate
factor
or·
the
prorate
factor.
It
then
multiplies
this
factor
by
the
annual
premium
to
determine
the
actual
amount
of
the
rebate.
INTEREST
ON
LOAN
FOR
TAX DEDUCTION
This
program
will
compute
the
amount
of
interest
paid on a
loan
during
one
tax
year.
If
the
loan
was
not
prepaid
during
the
year,
the
finance
charge
is
prorated
by
month.
If
it
was
prepaid,
the
amount
of
tax-deductrule
interest
is
the
finance
charge
minus
the
rebate
on the
finance
charge
minus
the
interest
paid
in
previous
years.
INSTALLMENT LOAN -PAYMENT
KNOWN
Given a
principal
balance,
add-on
rate,
payment
per
period,
number
of
periods
per
year
(52, 26, 24, 12), and
an
insurance\Qption,
the
program
will
determine
term,
amount
financed,
finance
charges,
last
payment,
APR.
Program
Abstracts
-
Friden
1155
Caclulator
4/74
BIOCHEMISTRY
ABSTRACTS
52-8004-001
4/74
QUALITY CONTROL CHART
This
program
prepares
a
quality
control
chart
for
a
given
set
of
data
for
a
particular
parameter
(preferably
greater
than
30
observations).
It
determines
the
number
of
observations
(N),
the
mean
(x),
standard
deviation
(S. D.),
x ± 2 S.
D.,
and
the
coefficient
of
variation
(v).
It
includes
an
error
routine
for
incorrectly
entered
data.
Friden
1155
Calculator
-
Program
Abstracts
5
CHEMISTRY
ABSTRACTS
52-8005-001
52-8005-002
52-8005-003
DECAY CONSTANT AND HALF
LIFE
This
program
calculates
the
decay
constant
and
half-life
given
a
number
of
activity
readings
at
various
times.
There
is
an
option
available
to
calculate
1
::
(
for
ta';;
t
"tb
where
M,
is
initial
mass
and Mt
~
mass
at
time
t.
There
is
an
error
routine
for
incorrectly
entered
data.
RELATIVE
ELEMENTAL
PERCENTAGES
The
program
determines
the
% of
an
element
in a
particular
compound.
The
atomic
weights
of
twelve
common
el~ments
are
already
incorporated
into
the
program
(the
user
may
elect
to
add
others).
An
element
number
and
the
number
of
atoms
of
that
particular
element
present
are
entered
for
each
element.
An
error
routine
is
available
for
incorrectly
entered
data.
OUTPUT
CONCENTRATION -VARIGRAb
This
program
calculates
the
output
concentration
of a
variable
gradient
device
consisting
of a
number
of
identical
chambers
(not
more
than
12)
connected
in
series
in
hydrostatic
equilibrium.
6
Program
Abstracts
-
Friden
1155
Calculator
4/74
ELECTRICAL
ENGINEERING
ABSTRACTS
52-800S-00l
52-8009-002
52-8009-003
!
52-8009-004
52-8009-005
4/74
FLUX
DENSITY -
CmCULAR
LOOP
The
program
calculates
the
flux
denSity
along
the
axis
of a
circular
loop.
cmCUIT
ANALYSIS
Given
a
circuit
containing
two
nodes
and
five
branches,
the
program
determines
the
voltages
at
the
two
nodes.
The
user
inputs
a topology
matrix
which
describes
the
circuit;
resistances,
and
voltages.
FOURIER
TRANSFORM
The
program
evaluates:
00 00
g(
w)
= f
F(t)
cos
w t dt -j f
F(t)
sin
w t
dt
= Af -j
Bf
-00
-00
for
frequency,
f
~
0
(w
= 23t'f) in
increments
of M (f
may
increment
arithmetically,
geometrically
or
logarithmically).
FOURIER
TRANSFORM
-
PULSE
This
program
performs
the
same
function
as
003
except
that
it
is
especially
written
for
a
pulse
and
is
faster
in
execution.
EULER-FOURIER
FORMULAS -
PERIODIC
FUNCTIONS
The
program
determines
an
(n=O,
1,
2
...
),
btl
(n=l,
2,
...
)
such
that
(t=time)
00
f(t) = a2
0 +
n~l
(an
cos
2
3t'
nt
+ bn
sin
2
3t'
nt)
where
.5
an
=
21
f(t)
cos
23t'nt
dt
(n =
0,1,2
...
)
-.5
.5
bn = 2 f f(t)
sin
23t'
nt
dt
(n =
1,
2,
3
...
)
-.5
Friden
1155
Calculator
-Program
Abstracts
7
Electrical
Engineering
52-8009-006
52-8009-007
52-8009-008
8
then
cn
(amplitude)
=
~
an2 + bn2
'l'n
(phase)
=
tan
-1
(:~)
itt)
is
defined
by
the
user
and
each
of
the
integrals
may
be
a
sum
of
integrals
of
functions
defined
on
sub-intervals.
EULER-FOURIER
FORMULAS -f(t) = CONSTANT
This
program
performs
the
same
function
as
005
except
that
f(t) = a
constant
value
for
an
interval
of t
and
thus
the
execution
time
is
faster.
CURRENT -RESONANT
RLC
CIRCUIT
Given
voltage
(V).
resistance
(R),
inductance
(L),
capacitance
(C),
the
program
calculates
i
(current)
for
time
t
between
a
and
b in
increments
of
t:,
t.
when
i 2Ve
-Rt/(2L)
~4L/C
-
R2
L
~
+
Ri
+
~
J i dt = 0
and
i = 0,
L.di/dt
=V
at
t = 0
POWER
SUPPLY
DESIGN
This
program
is
an
aid
to
the
designing
of
power
supplies
-
series
or
shunt.
The
user
supplies
the
voltage
and
current
values.
The
suggested
values
for
capacitor,
resistor,
and
transformer
ac
may
be
accepted
or
replaced.
The
machine
prints
out
the
appropriate
values
for
low,
nominal,
and
high
for
either
series
or
shunt
or
both
if
so
desired.
Program
Abstracts
-
Friden
1155
Calculator
4/74
MECHANICAL
ENGINEERING
ABSTRACTS
52-8012-001
52-8012-002
52-8012-003
52-8012-004
52-8012-005
4/74
CAM
DESIGN
This
program
determines
the
displacement,
velocity.
and
acceleration
for
the
following
types
of
curves
for
cams
with (1) a
radial
translating
roller
follower,
or
(2)
an
offset
translating
roller
follower:
a.
parabolic
b.
harmonic
c.
cycloidal
COMPRESSION
SPRING
DESIGN
-ROUND
WIRE
Find
various
spring
parameters
given
the
values
of
other
parameters.
8PD
P Gd 4
S =
-;or
; F =
8D31\l
H (N+1)d +
2(D-d)
CAM
DESIGN -
MODIFIED
CYCLOID
The
program
determines
the
velocity
and
acceleration
of
various
points
(values
of 8).
EXTENSION
SPRING
DESIGN -
STRESS
CONCENTRATION
Find
anyone
of
the
parameters
given
the
values
of
the
others.
SB=
32PR
!.1
--;d3
•
r3
ST=
16PR
(~)
--
•
rod
3 4c - 4 c =
TORSION
SPRING
CALCULATIONS
Given
all
but
one
of
the
parameter
values,
find
the
remaining
one:
S =
32PR
--;(iT
Ed
4T
M =
10.8
DN
Friden
1155
Calculator
-
Program
Abstracts
9
Mechanical
Engineering
52-8012-006
FLAT
SPRING
CALCULATIONS
Given
all
but
one
of
the
parameter
values,
find
the
remaining
one
for
either
(1) a
cantilever
type
(rectangular
section).
or
(2)
an
elliptical
type
(rectangular
section).
s =
6PL
bh 2
(1)
10
Program
Abstracts
-
Friden
1155
Calculator
S 3
PL
2"
bh
2
(2)
4/74
STRUCTURAL
ENGINEERING
ABSTRACTS
52-8008-001
CANTILEVER
BEAM
-
PARTIAL
UNIFORM LOAD
Given
the
following
parameters:
the
modulus
of
elasticity
of
the
material
(E);
the
moment
of
inertia
(I);
the
load
(W);
and
L,
a,
b
(refer
to
diagram),
the
program
calculates
V AB
(shear
A
to
B), MAB
(bending
moment
A
to
B),
Y
AB
(deflection
A
to
B),
V
BC
' MBC ' YBC ' V
CD'
MCD' YCD' M
max
' Y
max
'
e (end
slope)
for
any
x
value.
It
contains
an
error
routine
for
incorrectly
entered
data.
Y
b
----I~
a
O~--~========~--~~D~X
~------L
-------I~
A
52-8008-002
STRESS AND STRAIN -ELASTIC BODIES
Given
Rl
and
R1'
(max
and
min
radii
of
curvature
for
body
1;
R2
and
R2'
for
body
2;
modulus
of
elasticity
for
each
body;
Poisson's
ratio
for
each
body;
total
pressure;
and
the
angle
between
the
planes
containing
1/R
1
and
1/R
2,
the
program
calculates
the
maximum
unit
compressive
stress,
the
major
and
minor
semi-axes
of
elliptical
contact
area
and
the
combined
deformation
of
both
bodies
at
each
contact
along
the
axis
of
load.
52-8008-003
WEIBULL
DISTRIBUTION FUNCTION
4/74
This
program
may
be
used
for
anal~'sis
of
failure
data.
It
performs
a
regression
analysis
on
the
number
pairs
(x,
F(x»,
where
x
is
the
time
to
failure
and
F(x)
==
median
rank
c:: i -
.3
[i
==
the
failure
order
number
n
+.4
(1,
2,
3,
- -
-);
n=
size
of
the
samples].
Friden
1155
Calculator
-
Program
Abstracts
11
SURVEYING
52-8007
-001 TRAVERSE CLOSURE
(revised)
This
is
a S€t of
17
programs
designed
to
solve
the
general
problem
of
determin-
ing
the
successive
coordinates
of
the
points
as
well
as
the
amount
of
error
of
closure,
and
then
of
balancing
the
traverse
using
compass,
transit,
or
Crandalls
Rule
if
the
error
is
too
large.
The
data
may
be
in
the
form
of
bearings,
azi-
muths,
or
field
deflection
angles
along
with
a
distance.
The
traverse
may
be
either
'closed'
or
'open'
and
may
contain
curved
legs.
Up
to
39
(if
all
straight)
legs
may
be
accepted
as
input.
The
area
will
be
printed
in
square
feet
and
acres.
Surveying
programs
013, 014,
and
015
are
designed
to
be
used
in
con-
junction
with
this
program
to
perform
various
coordinate
geometry
functions.
52-8007-002
TRAVERSE CALCULATIONS
Given
the
coordinates
of two
successive
points
of a
traverse,
the
program
determines
the
bearing,
the
changes
in
latitude
and
departure
and
the
distance
between
them.
52-8007-003
COORDINATES
OF
AN
OBSERVER'S
POSITION
Finds
the
coordinates
of
an
observer's
position
by
measuring
two
angles
and
the
coordinates
of
three
points.
52-8007-004
AREA
BY
HELON'S FORMULA
Find
the
area
of a
triangle
given
the
lengths
of
its
three
sides,
using
the
formula:
S =
YI
(l-a)(l-b)(l-c)
52-8007-005
CUT
AND
FILL
CALCULATIONS
This
program
will
calculate
cross-sectional
areas,
volume
of
earth
between
two
cross-sectional
areas
separated
by a
length
L,
I
volume,
and
I
L.
The
input
is
series
of
number
pairs
describing
the
contour.
52-8007-004
MANNING'S EQUATION
This
program
calculates
Q;
volume
of
water
flow
not
under
pressure,
where
12
Program
Abstracts
-
Friden
1155
Calculator
4/74
Q:;:::1.49
A'R2/3'Sl/2
n
A:;:::
end
area
R
:;:::
hydraulic
radius
n
:;:::
roughness
factor
S
:;:::
drop
per
foot.
Surveying
52-8007-007
CONVERSION
BETWEEN
AZIMUTH
AND
BEAmNG
This
program
will
convert
the
azimuth
of a
line,
measured
from
the
north
merid-
ian
in
a
clockwise
direction,
to
a
bearing
and
vice
versa.
52-8007-008
INTERSECTION
OF
TWO
LINES
This
program
will
determine
the
coordinates
(N. ,
E.)
of
the
point
of
intersection
of two
lines,
each
defined
by
a
point
and a
bearing
or
azimuth.
52-8007-009
INTERSECTION OF A LINE
AND
A CIRCLE
Given a
line
described
by a
point
(N.,
E.)
and a
bearing
or
azimuth
and
a
circle
defined
by
the
coordinates
of
its
center
and a
radius,
the
program
will
calculate
the
coordinates
of
the
point(s) of
intersection.
52-8007-010 INTERSECTION
OF
TWO
CIRCLES
Given
two
circles
described
by
the
coordinates
of
their
centers
and
the
lengths
of
their
respective
radii,
the
program
will
determine
the
points
of
intersection.
52-8007-011 GRADE ELEVATIONS .
Given a
starting
stake
number
and
elevation,
the
program
will
determine
the
grade
%
change
and
the
elevations
at
all
50-foot
stakes
in
between.
52-8007-012 COMPUTATION
OF
CURVE DATA
4/74
Consider
the
following
diagram:
Given
a
value
for
A
or
R
and
one
of
the
other
five
values,
the
program
will
determine
the
four
remaining
values
as
well
as
the
area
of
the
segment.
Friden
1155
Calculator
-
Program
Abstracts
13
Surveying
52-8007-013 LONG CHORD DATA
FOR
TRAVERSE CLOSURE
This
program
can
be
used
to
prepare
for
option (-1) of
Surveying
Program
001;
i.
e.,
it
finds the
bearing
and
length
of
the
long
chord
of
an
arc.
The
following
values
must
he
known:
the
radius
of
the
arc,
either
the
delta
angle
or
length
of
the
arc,
either
a
tangent
to
one of
the
ends
of
the
arc
or
the
tangent
to
an
arc
that
eventually
connects
tangentially
to
the
arc.
52-8007-014 COORDINATE GEOMETRY
FOR
A TRAVERSE
Using
the
information
stored
by
one of
the
Surveying
Program
001
programs,
the
following
coordinate
geometry
functions
may
be
performed.
1.
Find
the
bearing
and
distance
between
any two
points.
2.
Given
a
point
and a
bearing
of a
straight
line
from
that
point
determine
either
a.
the
point
of
intersection
of
that
line
with
a
straight
line
or
with
a
circular
arc
defined
by
two
other
points,
or
b.
the
coordinates
of a
point
at
a gi ven
distance
along
that
straight
line.
3.
Determine
the
intersection
of two
lines
each
defined
by two
point
numbers.
4.
Add a
point
to
the
set
of
points
already
defined.
5.
Calculate
the
area
of a
portion
or
all
of
the
traverse,
accumulating
areas
if
so
desired.
52-8007
-015 AREA
OF
A TRAVERSE
This
program
may
be
used
in
conjunction
with
Surveying
Program
001
or
inde-
pendently.
The
user
may
find
the
complete
area
of a
traverse
defined
in
the
aforementioned
program
where
the
data
represents
the
balanced
or
unbalanced
state,
or
he
may
key
in
the
coordinates
himself.
The
area
of
portions
of
the
traverse
may
be
determined
by
referencing
individual
point
numbers
or
a
num-
ber
of
consecutive
points.
A
routine
for
finding
the
area
of a
segment
of a
circle
is
included.
52-8007-016 VERTICAL CURVE
E~UATION
Given
two
grades,
the
length
of
the
curve,
and
the
station
and
elevation
of
the
point
of
intersection
of
the
grades,
the
program
will
determine
the
station
and
elevation
of
the
high
point
and
the
elevations
at
desired
station
increments
along
52-8007-017
the
curve.
14
DEFLECTION
ANGLE CALCULATIONS
Given
the
radius,
beginning
and ending
stations,
and
station
increment,
the
pro-
gram
will
determine
deflection
angles
as
well
as
the
chord
lengths
for
the
suc-
cessi
ve
stations
beginning
with
the
first
even
station
after
the
initial
one.
Program
Abstracts
-
Friden
1155
Calculator
4/74
Surveying
52-8007-018 TRAVERSE CLOSURE
USING
INTERIOR ANGLES
Given
the
interior
angle
measurements
for
a
traverse,
the
program
finds
the
sum,
compares
it
against
the
theoretical
sum,
distributes
the
error,
and
deter-
mines
azimuths
and
bearing
given
the
first
known
azimuth
or
bearing.
52-8007-019 CURVE STAKING CALCULATION
4/74
This
program
determines
the
total
deflection
angle
from
initial
stake
point
and
the
chordal
distance
between
successive
stakes
when
the
radius
of
the
staked
curve,
the
radius
of
the
stationing
curve,
and
the
station
numbers
are
given.
Friden
1155
Calculator
-
Program
Abstracts
15
CIVIL ENGINEERING
52-S013-001 HARDY CROSS NETWORK ANALYSIS
16
This
program
performs
a
standard
hydraulic
network
analysis
using
the
Hardy
Cross
method.
The
total
number
of
loops
and
pipes
handled
by
the
machine
can
be
calculated
from
the
following
formula.
n
[2 .
(total
no. of
pipes
in
a
system
of
n loops) +
1/4
.I
(Pi + 2)]
<S7
·e=l
where
Pi
==
number
of
pipes
in
loop
i.
Program
Abstracts
-
Friden
1155
Calculator
4/74
NUMERICAL ANALYSIS
ABSTRACTS
52-8001-001 SOLUTION TO
THREE
LINEAR EQUATIONS
Given
the
coefficients
for
three
simultaneous
linear
equations,
the
program
determines
the
values
of
the
three
unknowns.
52-8001-002
SOLUTION
OF
A QUADRATIC EQUATION
If
A,
B,
and
C
are
given
such
that
AX2
+ BX + C =
0,
the
program
determines
X
by
the
formula
-B
±
'JB
2 -4AC
X = 2A ' X
may
be
real
or
complex.
52-8001-003
SIMPSON'S
RULE
FOR
INTEGRATION
This
program
uses
Simpson's
one-third
rule
to
evaluate
the
definite
integral
b
f f(x)
dx
given
'n'
number
of
intervals.
The
user
inserts
a
routine
to
calculate
a '
f(x).
There
is
an
option
available
to
combine
two
approximations
to
yield
a
third
and
better
one.
52-8001-004
CALCULATION
OF
COEFFICIENTS
OF
A POLYNOMIAL
Given
two
or
three
real
roots,
the
program
will
calculate
the
coefficients
of
the
corresponding
quadratic
or
cubic.
52-8001-005
EVALUATION
OF
A POLYNOMIAL AND
ITS
DERIVATIVES
For
a
particular
value
of
x,
evaluate
a
polynomial
of
degree
n;
also
its
first
and
second
derivatives.
Option
1
does
not
save
the
coefficients,
i.e.,
for
each
value
of
x
the
coefficients
must
be
re-entered.
Option
2
saves
the
coefficients
(n
~
10)
so
that
multiple
values
of
x
may
be
entered.
52-8001-006
INVERSION
OF
A 3x3 MATRIX
4/74
Given
the
elements
of a 3x3
matrix,
A,
determine
the
elements
of a 3x3
matrix,
'E,
such
that
B = A
-1
•
Friden
1155
Calculator
-
Program
Abstracts
17
Numerical
Analysis
52-8001-007
52-8001-008
52-8001-009
52-8001-010
52-8001-011
52-8001-012
52-8001-013
18
MULTIPLICATION
OF
TW03x3
MATRICES
If
the
elements
of
two 3x3
matrices
are
keyed
in,
the
program
will
determine
the
elements
of
the
matrix
C which
is
the
product,
C = AB. An
error
routine
is
included
for
data
which
is
incorrectly
entered.
DETERMINANT
OF
A 3x3 MATRIX
Given
the
elements
of a 3x3
matrix,
the
program
will
calculate
the
value
of
the
determinant.
+,
-,
PRODUCT FOR VECTORS
Given
two
three
dimensional
vectors
determine
the
vector
obtained
by
addition.
and
subtraction;
also
the
dot
product
and
cross
product.
X,
-:-,
l/X
FOR
COMPLEX
NUMBERS
This
program
finds:
(a)
the
reCiprocal
of a
complex
number
(b)
the
product
of
two
or
more
complex
numbers
(c)
the
quotient
of two
or
more
complex
numbers.
NEWTON -RAPHSON METHOD
Given
the
coefficients
of a
polynomial
P(x) of
degree
n (n
~
12),
the
program
will
find
the
real
roots
using
the
Newton-Raphson
method.
For
each
root
a
starting
value,
xo'
and
an
accuracy
E:
is
input.
The
iterative
process
stops
when
IXi+l
-xii
< E:.
3x3 MATRIX
MULTIPLIED
BY A COLUMN VECTOR
This
program
multiplies
a 3x3
matrix
A by a
3-element
column
vector
b
to
yield
a
3-element
vector
x.
x =
A'b.
EVALUATE Y
::;:
f(x l, x 2
••••
Xn)
Evaluates
a
function
of n
variables
(n
~
4)
for
all
values
of
ai
~
Xi
~
bi
at
incre-
ments
of
11
xi'
The
user
must
insert
the
necessary
instructions
for
the
evalua-
tion
of
the
function
(assuming
Register
01 -
Register
n
contain
xl'
x2'
•••
xn
respectively)
.
Program
Abstracts
-
Friden
1155
Calculator
4/74
52-8001-014
52-8001-015
52-8001-016
52-8001-017
52 -8001-018
52-8001-019
Numerical
Analysis
ROOT
OF
A NON-LINEAR EQUATION
This
program
uses
the
Muller
method
to
determine
a
root
of a
non-linear
algebraic
equation
in
the
variable
x,
represented
by f(x) =
O.
This
method
uses
a
quadratic
equation
as
an
approximation
through
three
points.
FACTORIZATION INTO
PRIMES
Given
an
integral
value,
x,
factor
it
into
prime
numbers
such
that
their
product
equals
x.
EVALUATION
OF
A POLYNOMIAL -
COMPLEX
VALUE
If
the
real
coefficients
of a
polynomial
of
degree
n (n
~
10)
are
input
to
the
program,
the
function
f(x)
and
its
first
derivative
are
evaluated
for
any
complex
values
x = a +
bi.Naturally,
if b = 0,
then
the
evaluations
are
made
us ing
the
real
value
of
x.
ROOT
OF
A POLYNOMIAL -
REAL
OR
COMPLEX
Finds
the
roots
(real,
complex)
of a
polynomial
of
degree
n(n £ 8),
using
Newton's
method.
It
prints
the
answer
if
IXi+l -
Xi
1<
10-
7.
Each
root
requires
an
initial
guess
for
the
components
a
and
b of a +
bi.
DIVISION
OF
POLYNOMIALS
This
program
divides
a
polynomial
of
degree
n
by
a
polynomial
of
degree
m
where
m $ n.
The
value
of
n
ranges
from
2
to
13
and
m
ranges
from
1
to
6
de-
pending
upon
the
value
of
n.
There
is
an
error
routine
for
incorrectly
entered
data.
SOLUTION
OF
A
DIFFERENTIAL
EQUATION
This
program
solves
a
1st,
2nd
or
3rd
order
differential
equation
f(x,
y,
y'
...
y(n».
The
Runge-Kutta
method
is
used
to
solve
a
system
of
first
order
equations
to
which
the
2nd
or
3rd
order
equation
has
been
reduced.
The
input
values
are:
the
degree,
n;
the
corresponding
initial
conditions;
h,
the
constant
increment
in
x;
N,
the
number
of
values
to
be
calculated.
52-8001-020
BINARY-DECIMAL CONVERSIONS
4/74
Converts
a
decimal
integer
< 4096
to
a
binary
number
or
converts
a
binary
integer
to
a
decimal
integer.
Friden
1155
Calculator
-
Program
Abstracts
19
Numerical
Analysis
52-8001-021 HARMONIC ANALYSIS
Ao'
AI'
...
,An'
B1, B2
••••
, Bn-1
are
determined
such
that
n
n-l
y = Ao +
~
A
cos
Kx
+
~
BK
sin
Kx
K=1
K
K=1
give
2n
observed
values
(xi, Yi), (i =
0,1,2,
...
,
2n-l)
assuming
(a)
repetition
of
values
starting
with
Y
2n
(b)
equal
spacing
of
the
xi
where
x 0 = 0
and
x2n =
211"
(c)
2n
~
120 -7
(number
of
sig.
digits
+
1).
52-8001-022
PRODUCT
OF
TWO n x n MATRICES ( n L 6 )
Given
two n x n
matrices,
A
and
B,
the
program
will
find
their
matrix
product.
One
of
the
matrices
is
replaced
by
the
product
while
the
other
is
retained.
The
program
can
easily
be
used
to
find
the
product
of
a
chain
of n x n
matrices.
52-8001-023
SOLUTION OF N LINEAR EQUATIONS
This
program
uses
a
modified
Gauss
elimination
method
to
solve
a
system
of
N
nonhomogeneous
linear
equations
in
N unknowns
with
N L
9.
52-8001-024
n x n MATRIX
INVERTER
(
nL
9)
(Restricted)
20
Given
an
n x n
matrix
A,
the
program
will
find A
-1
and
the
determinant
of
A.
It
may
be
necessary
to
exchange
rows
in
the
original
A
matrix
in
order
to
find A -1.
The
algorithm
used
replaces
A
by
A
-1
in
the
memory.
Program
Abstracts
-
Friden
1155
Calculator
4/74
STATISTICS
ABSTRACTS
52-8002-001 MEAN,
S.
D.,
S.
E.,
T-VALUES
Calculates
X,
s.
d.
and
s.
e.
for
up
to
four
groups
of
observations.
Then
it
determines
the
T-val
ue
comparing
each
group
mean
against
the
other
means.
It
includes
a
correction
routine.
52-8003-002
COVARIANCE, CORRELATION,
AND
REGRESSION
Option 1:
For
a
given
set
of N
observations
(x.,
y.),
the
program
determines
1 1
the
measure
of
covariance,
the
correlation
coefficient.
the
regression
coeffi-
cient
and
the
standard
error.
It
includes
a
correction
routine.
Option
2:
The
above
statistics
are
calculated
from
the
input
data
-N,
X,
UX'
y,
uy,
LXY.
52-8002-003
FITTING
OF
A QUADRATIC
TO
DATA PAIRS
It
uses
the
least
squares
approximation
method
to
fit
N
data
pairs
(xi'
y i)
to
a
second
degree
polynomial
with
real
coefficients
Aj.
It
includes
an
error
correction
routine.
An
option
permits
the
calculation
of
SF
-"
A, + A2x + A3x2
for
a
given
(x, y)
pair,
also
y -
y,
L (y_y)2.
52-8002-004
LINEAR REGRESSION
The
program
uses
the
least
squares
method
to
fit
the
equation
y =
mx
+ b
to
{(xi,Yi)}'
There
is
an
optional
routine
to
determine
y,
y-yand
L(y_y)2
to
check
the
goodness
of
fit.
An
error
routine
is
incorporated
into
the
program.
52-8002-005
FITTING
OF
Y =
Ae
Bx
TO DATA PAIRS
This
program
determ
ines
Band
C
such
that
In y = Bx + C.
Then
A = e C.
Calculation
of
SF,
y-y,
and
L (y_y)2
is
optional.
An
error
correction
routine
is
included.
52-8002-006
x2 FOR A 2x2 CONTINGENCY TABLE
It
determines
X2
for
a 2x2
contingency
table
using
Yate's
correction.
52-8002-007
l FOR n
by
m CONTINGENCY
TABLE
2
~
This
program
evaluates
X
for
an
nxm
contingency
table
where
n
~
10
and
m
is
unbounded.
It
includes
an
error
correction
routine.
4/74
Friden
1155
Calculator
-
Program
Abstracts
21
Statistics
52-8002-008
PAIRED-T
TEST
A t
-value
is
determined
for
n
paired
values
(Xi,
yO.
It
has
an
error
correction
routine.
52-8002-008
BINOMIAL DISTRIBUTION
52-8002-010
52-8002-011
52-8002-012
52-8002-013
52-8002-014
22
For
a
given
nand
p,
it
finds
P(r)
for
r =
0,
1,
2,
---,
n
which
equals
the
probability
of
exactly
r
occurrences
in
n
independent
trials.
POISSON DISTRIBUTION
For
a
given
m
==
expected
value
of
x,
it
determines
the
Poisson
distribution
P(x).
MEAN,
S.D.,
S.E.,
RANGE FOR DATA
For
a
set
of
data,
either
grouped
or
ungrouped,
the
following
statistics
are
der
ived
-
number
of
observations,
range,
standard
deviation,
standard
error,
arithmetic
and
geometric
means.
An
error
routine
is
included
for
incorrectly
entered
data.
SIGNIFICANCE BETWEEN
TWO
PROPORTIONS
It
computes
the
level
of
significance
for
the
difference
between
two
sample
proportions.
LIKELIHOOD RATIO
The
program
determines
the
likelihood
ratio
for
K
sample
variances
of
the
same
sample
size.
L = 1
indicates
maximum
uniformity
and
= 0
indicates
maximum
non-uniformity.
COMBINATIONS, PERMUTATIONS
It
calculates
the
number
of
permutations
of n
different
items
takenr
at
a
time.
OR
It
calculates
the
number
of
combinations
of
n
different
items
taken
r
at
a
time.
OR
It
calculates
the
number
of
permutations
of n
items
of which
q,
r,
s
---
z
are
alike.
Program
Abstracts
-
Friden
1155
Calculator
4/74
Statistics
52-8002-015
MULTIPLE
CORRELATION
COEFFICIENTS
It
determines
the
multiple
correlation
coefficients
among
three
variables,
given
the
simple
correlation
coefficients
between
two
of
the
variables.
52-8002-016
NORMAL DISTRIBUTION OR DINA
TES
Given
IL
,
U,
and
x,
it
computes
the
ordinate
of
the
normal
distribution.
52-8002-017
LEAST
SQUARES
FIT
TO
y =
ax
b
The
program
finds
C
and
D
such
that
In y =
C'ln
x + D
is
a
least
squares
fit
to
{(Xi,
Yi)}.
Then
a = eD
and
b
-=
C.
There
is
an
error
correction
routine.
52-8002-018
ONE-WAY
ANALYSIS
OF
VARIANCE
It
performs
a
standard
one-way
analysis
of
variance
between
,K
groups
of
data
producing
for
each
group
- n
and
X;
then
it
finds
degrees
of
freedom,
sum
of
squares
for
'between',
'within'
and
'total'
sources
of
variation,
mean
square
for
'between'
and
'within'
and
finally
the
F-ratio.
An
error
routine
is
included.
52-8002-019
ANOVA
TABLE
-2x2
FACTORIAL
DESIGN
52-8002-020
52-8002-021
It
computes
a
standard
analysis
of
variance
table
for
a 2x2
factorial
design
with
n
observations
in
each
cell.
x2 DISTRIBUTION ORDINATES
2
The
program
finds
various
pOi.r1ts
on
the
X
distribution
curve,
given
the
pegrees
of
freedom,
limits
a
and
b,
I1X
(for
which
a
~
X2
< b
in
increments
of
I1X
).
F DISTRIBUTION ORDINATES
This
determines
values
on
the
F
distribution
given
f 1
and
f 2
degrees
of
freedom
for
a
'5.
F < b
in
increments
of
11
F.
52-8002-022
INTEGRALS
FOR
THE NORMAL DISTRIBUTION
The
machine
will
calculate
either
the
area
under
the
curve
between
-00
and
Z
or
between
-Z
and
Z
using
Simpson's
Rule.
52-8002-023
INTEGRAL
FOR
THE
x2 DISTRIBUTION
2
The
program
finds
the
area
under
the
curve
for
the
limits
X
and
00
and
degrees
of
freedom,
f,
using
a
modified
Simpson's
Rule.
4/74
Friden
1155
Calculator
-
Program
Abstracts
23
Statistics
52-8002-024
RELIABILITY
TESTING -
TEST
PERIOD
In
machine
reliability
testing,
given
a
target
MTBF
(MTBSC
or
MCBSC),
m,
a
confidence
limit,
1 -
a,
and
a
number
of
failures
r,
it
determines
the
mini-
mum
length
of
the
test
period
needed
to
reject
the
hypothesis
ill
< m
and
to
accept
the
alternative
ill
~
m
with
confidence
1 -
a.
Termination
of
the
test
may
either
occur
at
the
time
of
the
rth
failure
or
sometime
after
the
rth
failure.
52-8002-025
RELIABILITY
TESTING -CONFIDENCE LIMITS
Given
a
testing
time
t
during
which r
failures
(or
service
calls)
were
observed,
the
program
determines
confidence
limits
for
m
(MTBF,
MTBSC,
or
MCBSC)
given
a.
52-8002-026
RELIABILITY TESTING -CONFIDENCE
LEVEL
Given
a
testing
time
t
during
which r
failures
occurred
and
a
traget
m(MTBF,
MCBSC
or
MTBSC),
it
determines
the
level
1 - a
at
which
you
can
accept
A
m
>m.
52-8002-027
RANDOM PERMUTATIONS
OF
SEQUENCED INTEGER VALUES
Given two
integers
a
and
b,
the
program
finds
a
pseudo-random
permutation
of
all
the
integers
between
a
and
b,
inclusive.
52-8002-028
PSEUDO-RANDOM NUMBER TABLE .
This
program
generates
a
table
of
ten-digit
integral
numbers,
printing
them
in
groups
of
ten.
A
different
starting
value
produces
a
different
table.
52-8002-029
CHECK
FOR
RANDOMNESS OF DIGITS IN A
TABLE
This
program
provides
a
frequency
distribution
of
the
occurrence
of
the
digits
0,
1,
2,
...
, 9
in
the
table
generated
by
Statistics
Program
028.
52-8002-030
GENERATION
OF
A
SET
OF
PSEUDO-RANDOM
INTEGER
VALUES
This
program
will
generate
n
pseudo-random
integer
values
between
two
li~its.
52-8002-031
STATISTICS
OF
A
SET
OF
GROUPS
This
program
will
determine
the
mean
and
standard
deviation
for
n
values
in
a
group.
It
will
them
compute
the
overall
mean
and
SD
for
a
set
of
up
to
five
groups.
Each
time
that
a new
groups
is
added,
the
lowest
numbered
group
will
be
dropped
from
the
statistics
for
the
next
set
of
groups.
24v
Program
Abstracts
-
Friden
1155
Calculator
4/74
Statistics
52-8002-032
MULTIPLE
LINEAR REGRESSION
This
program
will
determine
the
values
for
Bl,
B2,
B3,
and
A
such
that
1 =
Blxl
+ B2x2 + B3x3 + A
will
be
the
best
fit
for
n
data
points
(xt>x2,x3'y).
It
will
also
determine
the
standard
error
of
the
estimate.
If
the
data
points
con-
sist
of
(xl'
x2'
y),
then
the
regression
equation
will
be
~
=
Blxl
+ B2x2 + A.
The
program
will
save
up
to
18
data
points
for
three
independent
variables
or
24
data
points
for
two
independent
variables.
Any
points
above
these
limits
will
be
used
in
the
calculation
of
the
regression
coefficients
but
then
are
destroyed.
After
the
regression
coefficients
have
been
determined,
the
user
may
elect
to
have
the
machine
automatically
print
Xl'
x2' x3'
y,
9,
(y -
y)
for
each
data
point
stored.
Then
additional
data
points
may
be
entered
to
be
included
in the
standard
error.
52-8002-033
(Not
written)
52-8002-034
LEAST SQUARE
FIT
WITH A POLYNOMIAL
4/74
This
program
will
fit
a
polynomial
to
data
pairs
(x, y):
that
is,
determine
A
AO'
AI,
...
,An
such
that
y = An
A n
n-l
y = Anx + An_Ix +
...
+Alxl +
AO
is
a
least
squares
fit.
The
value
of n
may
be
between
2 and
11,
inclusive.
The
number
of
data
pOints
stored
depends
upon the
order
of
the
polynomial
to
be
fitted.
The
standard
error
of
the
estimate
is
determined.
Friden
1155
Calculator
-
Program
Abstracts
25
REAL ESTATE
52-8014-001
REAL
ESTATE INVESTMENT
PROJECTION
ANALYSIS
This
program
accepts
such
input
values
as
purchase
price,
down
payment,
con-
ditions
of up to
ten
mortgages,
itemized
income,
itemized
expenses,
tax
bracket,
vacancy
factor,
depreciation
method
and
percent,
and will
print
for
whatever
number
of
years
selected
the
following
information
among
others.
1.
Net
operating
income
2.
Equity
and
interest
on
all
loans
as
well
as
total
3.
Net
spendable
before
taxes
4.
Net
income
after
interest
5.
Depreciation
6.
Taxable
net
income
and
taxes
7.
Net
spendable
after
taxes
8.
Capitalization
rate
9.
Return
on equity
Grand
totals
and
averages
per
year
are
printed
at
the
end.
52-8014-002 DEPRECIATION CALCULATIONS
This
program
calculates
depreciation
by any of
three
methods:
Straight
line
Declining
balance
Sum
of
integers
52-8014-003 MORTGAGE YIELD
26
Given
the
value
of the note,
the
interest
rate,
the
time
due
(years),
monthly
payment,
and
the.
yield
or
discount
rate,
the
machine
will
determine
either
of
the
latter
two
rates
not
given.
If
the
time
= 0,
the
machine
will
use
that
time
that
will
completely
amortize
the
loan.
Program
Abstracts
-
Friden
1155
Calculator
4/74
EDUCATION
ABSTRACTS
52-8010-001
TEST
CORRECTION: LESS THAN 40 QUESTIONS
Given a
test
of
less
than
40
multiple
choice
questions
each
having
9
or
less
choices
(numbered
1-9),
the
program
screens
student
responses
for
wrong
answers,
assigns
a
score,
determines
the
group
mean,
the
number
of
students,
the
standard
deviation
and
a
frequency
distribution
for
all
questions
of
the
number
of
incorrect
answers
per
question.
There
is
an
error
routine
for
incorrectly
entered
data.
52-8010-002
TEST
CORRECTION: 40 -
50
QUESTIONS
Performs
the
same
functions
as
001 but
the
corrections
are
made
on 13
questions
at
a
time
rather
than
the
entire
test.
There
is
an
error
routine
for
incorrectly
entered
data.
52-8010-003
DETERMINATION
OF
GRADES
4/74
This
program
will
average
the
test
scores
for
a
student
[eliminating
the
x
lowest
scores
(x<7)].
It
will
find
his
standard
deviation:
also,
the
over-all
class
average
and
standard
deviation.
Error
routines
are
included.
Friden
1155
Calculator
-'
Program
Abstracts
27
SUBROUTINE PROGRAMS
ABSTRACTS
52-8006-001
52-8006-002
52-8006-003
52-8006-004
28
PACK
VALUES
This
subroutine
accepts
values
through
the
keyboard
and
packs
them
beginning
with
Register
01.
The
number
of
values
packed
per
register
depends
upon
the
number
of
significant
digits
per
value
(x)
and
=
12/(x
+ 1).
Each
value
has
a
sign
digit
= 1
for
negative
or
= 0
for
positive.
The
subroutine
uses
Register
00,
16-19.
It
is
usually
used
with
subroutine
002.
UNPACK VALUES
Given
up
to
15
packed
registers
(Register
01-15),
containing
from
1-6
values
(depending
upon
the
number
of
significant
digits)
the
subroutine
will
return
a
particular
value
from
the
register
to
which
Register
00
is
pointing.
It
is
usually
used
in
conjunction
with
subroutine
001.
ROUND A DECIMAL VALUE
This
is
a
small
routine
to
round
a
decimal
value
to x
decimal
places.
VECTOR
SORTING ROUTINES
It
arranges
a
vector
of
up to 18
elements
in
ascending
or
descending
order,
storing
the
results
in
Register
01-N.
Program
Abstracts
-
Friden
1155
Calculator
4/74
MISCELLANEOUS
ABSTRACTS
52-8011-001
52-8011-002
52-8011-003
4/74
NAVIGA TIONAL COURSE CALCULATION
The
program
calculates
a
navigational
course
consisting
of
one
or
more
adjoining
legs.
Output
variables
include:
compass
heading;
ground
speed;
distance
of
the
leg;
cumulative
distance;
flying
time;
cumulative
flying
time;
fuel
consumption;
cumulative
fuel
consumption,
given
input
variables:
initial
latitude
and
longitude;
destination
latitude
and
longitude;
magnetic
variation;
wind
direction
and
speed;
air
speed;
fuel
consumption
rate.
SIX GEOMETRIC PROBLEMS
(a)
Given
distance
d
and
6..
9
from
a known
point
K(x,
y)
find
the
coordinates
of
the
unknown
point
U.
(b)
Points
on a
line
from
Po
to
Pn in
increments
of
D.
x.
(c)
Points
on a
Circle,
given
a
starting
angle,
stopping
4
and
D.
4
(d)
Point
of
intersection
of 2
lines.
(e)
An
angle
in
degrees,
minutes
and
seconds
converted
to
decimal
degrees.
(f)
Distance
between
2
points
and
the
-4
made
by a
line
connecting
them
and
the
x
axis.
MANUAL MODE DIAGNOSTIC
This
procedure
is
designed
to
test
the
operability
of
the
machine.
It
should
be
used
in
conjunction
with
001
to
make
sure
that
the
machine
is
functioning
in
the
manner
it
should
be.
Friden
1155
Calculator
-
Program
Abstracts
29
SINGER
BUSINESS
MACHINES
Publication
No.
52-0002-01

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