torpedo manual
TRANSCRIPT
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Torpedo v1.0Graphing Calculator
User Guide
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Blackscreen Apps Chapter 1
Torpedo Graphing Calculator User Guide 1
GraphingIntroduction to Graphing capabilities of the Torpedo calculator.
Select the Graphing Mode
Push the menu button in the upper left of the first keyboard page to
bring up the settings menu then select Graphing Mode. From here youcan switch the calculator into the desired mode.
Window Setup
Before graphing a function you will want to set the viewing extents of
the window by pushing the dark green Wnd button at the top of thekeyboard. From here the window extents can be set using any valid
equation. For Polar and Parametric graphs you will also need to setthe start, stop, and step values. I.e. For polar graphs it is often
desireable to use 0 to 2 for the start and stop and /180 for the step.The Scale values determine the placement of the hash marks on the x
and y axis.
Entering Equations
To enter equations to be graphed you use the dark green key at the topleft of the keyboard labelled f(x)= to bring up the Functions menu.
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Torpedo Graphing Calculator User Guide 3
Here we show an example of a simple equation graphed alongside its
derivative.
Polar Examples
Polar equations are of the form r=f() where r is the radius and theta is
the angle. An angle of zero extends outwards to the right of the originand a circle is comprised of 2 or 360 depending if the calculator is in
radians mode or degrees. This setting can be controlled from theorange button labelled menu.
Graph of r = 2sin 4 from 0 to 2
Graph of r = /2 from -6 to 6
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Chaper 1 Graphing
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Parametric ExampleParametric equations are of the form x = f1(t), y=f2(t) and are graphed
with x increasing to the right and y increasing upwards. The startingvalue, ending value, and increment value are controlled from the Wnd
screen.
Graph of Baseball hit at 25m/s at 55 Degrees Elevation
This graph shows the elevation of the ball above the ground at zero tthe ball was at 0.8 meters above the ground
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Torpedo Graphing Calculator User Guide 5
ListsIntroduction to List capabilities of the Torpedo calculator.
Creating A List of Values
Torpedo supports two methods of entering a list. They can be entered
using the List Editor or using the curly brace keys in the calculator.There are also functions that create lists (see functions chapter)
{ V, V, } with V being any equation that results in a value.
e.g.
List Editor
The list editor allows easy entry and editing of a list. Select the orange
List key and choose the Edit List option.
The letter at the top indicates the variable the is being stored in. Bypressing the letter at the top a menu will come up that lets you select a
new location. If a variable without a list in it is selected it will beoverwritten when the user enters the first value in the list.
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Math Operations on Lists
Most math operations work on lists in the same way they work on
values. If a single value is used for the second operation then that
value is used on each element. If a list is provided it must match insize. The Functions chapter explains the use of the other operators andshows which ones work with lists.
+, -, *, /
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Torpedo Graphing Calculator User Guide 7
MatrixIntroduction to Matrix capabilities of the Torpedo calculator.
Creating A Matrix
Matrices can be entered via the bracket keys and stored into variables
for use in math operatoions. There are also functions that creatematrices (see Functions chapter)
matrix = [row,row,] all rows must have same number of values
row = [V,V,]
e.g.
Math Operations on Matrices
Most math operations work on lists in the same way they work on
values. If a single value is used for the second operation then thatvalue is used on each element. If a list is provided it must match in
size. The Functions chapter explains the use of the other operators and
shows which ones work with matrices.
+, -, *, /
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Matrix times Matrix
Scale a Matrix
Addition
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Key and Menu FunctionsThis chapter describes the format of the function inputs and the
content and use of the menu buttons and the operations available withthem.
Table: Format specifiers and their meaning
Format Meaning
{EQ} Equation (any valid sequence)
{VAR} Variable [A-Z] from the var menu
{V} Single value
{L} Value List{LV} Variable with a list stored
{M} Matrix
{V|L} Value or List
{V|L|M} Value, List, or Matrix
{L|M} List or Matrix
{TOL} Tolerence (Always Optional)*
[ ] Brackets denote optional fields
*The tolerence value specifies the accuracy of the iterative functions todetermine how close to the true answer to get. If not provided the
default will always be .00001.
Keyboard
This section will describe the use of the functions found on thekeyboard.
, Square and Square Root
Format: {V|L} {V|L}
The square and square root functions return a single value whenoperating on a value or return a new list of the same size as the input
with each value set to the square or square root of the input list.
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^ Power
Format: {V|L|M}^{V}
Raises the value to the left of the operator to the power of the value tothe right of the operator. For lists and matrices each element is raised
to the power.
ln log Logarithmic
Format: ln {V|L}
Calculates the log and natural log of the input value or list.
e Constant values
Format: e
The e and keys contain constant commonly used values.
e Constant values
Format: e
The e and keys contain constant commonly used values.
x,t, System variable used in Graphing
These variables can be used in the same manner as the capital lettervariables but may be changed by the system during graphing
operations. Only one variable exists and its symbol is changed basedon the current graphing mode (Function, Parabolic, or Polar).
Note: Ans contains the last
calculated answer and can
be accessed from thesecond keyboard page.
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Store Value
Format: {V|L|M}{VAR} or {V}{VAR}[{V}][{V}]
This key is used to store the results of an equation into a variablelocation. To store a value into a cell of a list or matrix use brackets to
not the cell number values. The answer can be a value, list, or matrixexcept when storing into a cell of a list or matrix.
EE exponent
The EE character is used to denote the exponent portion of a number.Note that the negate key (-) and not the minus is used to signal
negative exponents.
Calc Menu
The Calc menu has three pages. Slide over the menu from right to leftto see the other pages.
abs Absolute Value
Format: abs {V|L|M}
abs returns the absolute value(s) of a value, list or matrix. Lists and
matrices return the absolute value of each element.
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Format output as Fractions
Format: {EQ}
Changes the display of the answer to be in terms of numerator /denominator where possible for value(s) of a value, list or matrix.
CubeFormat: {V|L|M}
Returns the Value, List, or Matrix with value(s) cubed.
Cube Root
Format: {V|L|M}
Returns the Value, List, or Matrix with cube root of value(s). For listsand matrices each element is replaced with the cube root of the input
value.
n nth Root
Format: {V}n{V|L|M}
Returns the Value, List, or Matrix with nth root with n determined by
the preceding value. For lists and matrices each element is replacedwith the nth root of the input value.
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fMin( fMax( Function Minimum and Maximum
Format: fMin(1{EQ},2{VAR},3{V},4{V}[,5{TOL}])
This function will evaluate the equation(1) with the variable(2)changing for values between the minimum(3) and the maximum(4)
and find the point in the equation where a local minimum or maximumoccurs. The value returned will be the value of the variable (x value)
and not the equation value at the min/max. A bound error will occur ifminimum(3) evaluates to be greater than or equal to maximum(4).
The tolerence is optional and precision is limited to ~6 placesregardless of precision specified. i.e. you can lower precision but it
will only go so high.
The variable used to evaluate the expression will contain the answer
after the function returns.
d/dx( Function Derivative
Format: d/dx(1{EQ},2{VAR},3{V}[,4{TOL}])
This will evaluate the derivative (rate of change) with an equation(1)
for a variable(2) at a value(3). The answer will also be stored into thevariable used to evaluate the equation.
( Integrate Function
Format: (1{EQ},2{VAR},3{V},4{V}[,5{TOL}])
This will integrate the equation(1) for the variable(2) between thelower value(3) and the upper value(4) within the specified tolerence.
Note: The the answer is
also stored in the
evaluation variable
Note: To graph the
derivative of some
function Y1 use the
equation d/dx(Y1,x,x)
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solve( Find Solution for f(x)=0
Format: solve(1{EQ},2{VAR},3{V},4{V}[,5{TOL}])
This will find a value for variable(2) that is between minimum(3) andmaximum(4) that solves equation(1) to be zero within the specified
tolerance.
~( Aproximate Value
Format: ~(1{V|L|M},2{V})
This will round the values of each element of parameter 1 to thenumber of fractional places as determined by the integer value ofparameter 2.
int Integer Part of Value
Format: int {V|L|M}
Truncates the displayed value to just the integer portion of the answerfor values, lists, and matrices. This function added to frac of the same
value will always result in the original value.
frac Fractional Part of Value
Format: frac {V|L|M}
Note: To find the
intersection of two
functions Y1 and Y2 use
the equation solve(Y1-Y2,x,lower,upper)
Note: This function starts
at the top of the next page.
Swipe from right to left on
the menu to move to the
next page.
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Truncates the displayed value to just the fraction portion of the answer.This value added with the value of the int function for the same value
will always result in the original value.
intM Integer Part of Value (Modified)
Format: intM {V|L|M}
Truncates the displayed value to just the integer portion of the answer
but for values less than zero the number is one less than the int
function.
min( max( Find the minimum or maximum value(s)
Format: min(1{V},2{V}) max(3{L}[,4{L}])
Returns the minimum or maximum value for the two values(1&2)passed or in the case of a single list(3) the maximum value from the
list is returned. When two lists are given(3&4), each element in (3) iscompared with the corresponding element in (4) and a new list with
the minimum or maximum for each element is returned.
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! Factorial
Format: {V}!
The factorial function returns the value of n*(n-1)*2*1 where n isthe integer portion of the given value. Values higher than or equal to
171 will return infinity(inf).
rand# Random Number Generator
Format: rand# and {V}rand#
The rand# function computes a sequence of pseudo-random values inthe range of 0 to 1. The random number generator can be seeded by
assigning a value to rand#. When seeding only the integer portion ofthe value is used so seeding with 0 and 0.1 will result in the same
sequence of random numbers. Only 32bits are used in the generator soseed values greater than or equal to 2^32 are invalid and 0 is used
instead. The generator is seeded with zero upon startup or reset.When seeding the input value is returned.
nCr nPr Combinations and Permutations
Format: 1{V} nCr 2{V}
The integer portion of the first value(1) is the number of items in theset and the integer portion of the second value(2) is the number of
items drawn from the set. The input values are also capped at 2^32nCr evaluates the number of combinations and assumes each item in
the set is unique and can be drawn only once. nPr evaluates the
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number of permutations and assumes each item in the set has the samechance of being picked for each draw. The function will return
infinity(inf) once the calculated value exceeds the precisioncapabilities.
Trig Menu
The Trig menu has two pages. The first page contains the standard
trigonometry functions with the hyperbolic variants on the second.Slide over the menu from right to left to see the other page.
Answer in terms of
Format: {EQ}
Changes the display of the answer to be in terms of numerator /denominator where the inut value(s) of a value, elements of a list or
elements of a matrix can be evenly divided by . The function uses atolerance of 1e-5 so it should only be used when the answer isexpected to be in terms of. i.e. The number 5 evaluates as 113/71as that value is very close to 5.
sin cos tan Standard Trigonometry Functions
Format: sin {V|L}
Returns the sine, cosine, or tangent for the input. The return valuedepends on the Trig Mode in the settings menu. The input will be
treated as either radians or degree depending on that setting. The inputvalue can also be specified as specifically degrees or radians with the
degree and radian operators found in the angle menu.
Note: The nCr function
can be used to calculate
the probability of winning
the lottery. Here the
probability is about 1 in
1.5 million.
Note: The solve function
finds the value of x where
the function equals zero
within the range of low to
high.
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sin cos tan Inverse Trigonometry Functions
Format: tan {V|L}
Inverse operations of the sin, cos, and tan operators.
sinh cosh tanh Hyperbolic Trigonometry Functions
Format: tanh {V|L}
Returns the hyperbolic sine, hyperbolic cosine, or hyperbolic tangentfor the input.
sinh cosh tanh Inverse Hyperbolic Functions
Format: cosh {V|L}
Inverse operations of the sinh, cosh, and tanh operators.
List Menu
Note: The degree operator
has a higher priority than
the sin function and
converts the numbers toradians when in radian
mode or does nothing
when in degree mode.
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The List menu has two pages. The first page contains the standardtrigonometry functions with the hyperbolic variants on the second.
Slide over the menu from right to left to see the other page.
Lists can be entered from the calc screen using the curly braces todenote the beginning and ending of the list with commas separatingthe values.
SortA( SortD( Sort a list Ascending or Descending
Format: SortA({L}[,{LV}]*})
SortA will sort a list from low value to high value and SortD high tolow. The functions will take additional lists that will have the same
element swaps performed on it as the first list. All list variables mustcontain lists with the same number of elements as the one being sorted.
size Size of a list or matrix
Format: size {L|M}
The dim operator returns a value with the number of elements of a list
or it returns a list with two values for the number of rows and columnsrespectively.
Note: The SortA sorted the
list 3,2,1 and returned1,2,3 the same swaps were
performed on the list
stored in A and made it
3,2,1.
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Fill( List Filled with Value
Format: Fill(1{V},2{V})
The Fill( function creates and returns a new list filled with values fromparameter 1 and with the size set to the integer value of parameter 2.
seq( List from Sequence
Format: seq(1{EQ},2{VAR},3{V},4{V},5{V})
The seq( function creates a new list with the values set by evaluating
an equation. An error will occur if the number of elements will begreater than 100.
1{EQ} The Equation to evaluate
2{VAR} Variable used to evaluate equation
3{V} Starting Value of Variable
4{V} Ending Value of Variable
5{V} Increment Amount
min( max( Min or Max Value
Format: max({L}) max({V},{V}) max({L},{L})
Returns the larger/smaller of two values, the largest/smallest elementin a list or a new list comprised of the larger/smaller values from two
lists.
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mean( median Mean/Median value from List elements
Format: median({L}) median({L},{L})
Returns the mean or median value for a list of values. If two lists are
given the second list is taken to be the frequency of the values in thefirst list. The list sizes must match.
Summation of List elements
Format: {L}
Returns the sum of a list of values.
Product of List elements
Format: {L}
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Returns the product of a list of values.
Matrix Menu
Matrices can be entered from the calc screen using the bracket keys [
and ]. Matrices that are larger than the screen can display can beviewed by sliding up/down left/right on the matrix itself to expose thehidden portions.
[ row row ]
[ {V} , {V} , ] (rows)
This example shows a matrix with three rows and two columns.
det determinant of Matrix
Format: det {M}
Calculates the determinant of a square matrix. If the matrix is notsquare an error will be returned.
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T Transpose of Matrix
Format: {M}T
Swaps rows and columns of given matrix.
size Row and Column Sizes
Format: size {M|L}
The dim operator returns a value with the number of elements of a listor it returns a list with two values for the number of rows and columns
respectively.
ident Identity Matrix
Format: ident {V}
The ident function will return a square matrix with zeros in the cellsnot on the diagonal and ones in the diagonal cells. The integer value
of the parameter will determine the number of rows and colums.Values greater than 100 will produce an error.
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lud( Lower Upper Permutation Decomposition
Format: lud(1{M},2{VAR},3{VAR},4{VAR})
The lud( function decomposes a matrix into a lower matrix L, an uppermatrix U, and a permutation matrix P such that P*L*U results in the
original input matrix. L will be all zeros above the diagonal with oneson the diagonal. U will be all zeros below the diagonal and P will be a
identity matrix with rows swapped based on the row interchangestaken during the decomposition. Only works for square matrices.
1{M} The Square Matrix to decompose
2{VAR} Variable where L is stored after execution
3{VAR} Variable where U is stored after execution
4{VAR} Variable where P is stored after execution
1 Create the matrix and save to a variable.
2 Call the lud( function with our matrix and variables that willcontain the L, U, and P matrices when done. L is returned and
here we have sent the output to the fractions formatter for L and U.
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3 Here we show that P*L*U returns the original matrix.
Angle Menu
The Angle menu has functions for converting to radians or degrees,degree minute second format, and polar coordinate systems.
Degrees
Format: {V|L}
Changes the given value or list of values to radians when the calculator
is in radian mode and does nothing when in degree mode. Used tospecify a number as being in degrees for Trig functions without
needing to know which mode the calculator is in.
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r Radians
Format: {V|L}r
Changes the given value or list of values to degree when the calculatoris in degree mode and does nothing when in radian mode.
DMS Degree, Minute, Seconds Formatter
Format: {EQ}DMS
Display the input equations answer formatted as degrees, minutes, andseconds.
Degree, Minute, Seconds Input
Format: {V}[{V}][{V}]
Converts the input from degrees, minute, seconds to decimal. The
minute and second inputs are optional.
RPr Rect Coordinate to Polar Radius
Format: RPR({V},{V})
Converts from a Cartesian X,Y coordinate to a Polar Radius
Component. This equates to the length from the origin to the X,Yvalues.
RP Rect Coordinate to Polar Theta Angle
Format: RP({V},{V})
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Converts from a Cartesian X,Y coordinate to a polar system thetaangle component.
PRx Polar Coordinate to Cartesian x
Format: PRx({V},{V})
Converts from a Polar coordinate to a Cartesian system x component.
PRy Polar Coordinate to Cartesian y
Format: PRy({V},{V})
Converts from a Polar coordinate to a cartesian system y component.
Test Menu
The test menu contains Boolean logic, equality, and relational
operators.
=,,,, Equality, Relational
Format: {V|L|M}={V|L|M}
Returns 1 if the test evaluates to true otherwise 0. The compared
values must match in both type and dimension. Comparing a listresults in a list with element by element comparison values while amatrix is only valid for equality or inequality and results in 1 or 0.
Draw Menu
This menu is still experimental but will allow the user to augment the3D graph.
ClearScrn Clears All Overlays
Format: ClearScrn
Removes any overlays added to the graph.
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Shade( ShadeA( Shade an Area of the graph
Format: Shade(1{EQ},2{EQ},3{V},4{V},5{V},6{V})
Fill in an area of the graph. The area is bounded by the space betweenequation 1 and 2 and from lower x 3 to upper x 4. Parameters 5 and 6
are optional with 5 specifying the color and 6 the amount oftransparency (0..1). Functions are evaluated using the x variable.
This only works for Function Equations.
Color Value Associated Color
0 Dark Gray
1 Red
2 Blue3 Green
4 Orange
5 Light Blue