torpedo manual

7/31/2019 Torpedo Manual

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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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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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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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Chaper 2 Lists

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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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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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Chaper 3 Matrix

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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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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Chaper 4 Functions

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

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