CrunchJr – Student Aid

CrunchJr is a powerful computational engine which can supply assistance for a number of assignment tasks.  It is self-contained (does not require internet access).  Several CrunchJr features can replace some of the time-consuming, error-prone drudgery of detailed computational steps needed to complete a problem or project.  More time can be spent on understanding the problem, and less on data-entry and checking.  Tabulated results show the equations being used and all the values of the variables for easy review, and results are saved for use in a later computation or session.  These capabilities are available for the full range of simple to complex computations as might be used by a high school math student, a business analyst, a physicist, an engineering graduate student,.

Clicking [Inputs] → (Functions) presents a full list of the 300+ functions available.  In addition to all the "regular suspects" that a reasonable assignment might include, there are many special-purpose functions to do unusual things, including: Two basic forms of operation are supported (Quick–mode and PowerUser–mode), and users can move back and forth at any time.  Quick–mode is well-suited to first time users, and many users end up using it as their main form of interaction.  PowerUser–mode is much more flexible and powerful.  Click Overview for a short review of Quick–mode and PowerUser–mode.

Here is a very simple example of a common homework problem (using a MiniApp in Quick–mode) – Solve 3 equations in 3 unknowns.
  1. Tap [MiniApps] → (All MiniApps), then tap the S on the right hand side alphabet to get to Screen 1 below. 
  2. Tap {Solver}.  A simple solved example is shown on Screen 2 (each MiniApp has a short discussion section).  Skip it (go to Screen 3).
  3. Scroll down, then tap 3 for N (the number of equations), and enter values (from the 3 equations above), and tap [Submit]
  4. Screen 4 shows the result



For newbies, the Beginner's Tour presents a good overview of the app with many examples and screen shots.  It describes some of the high-level capabilities, starting with the Home Screen and its five major buttons.  Tap any of these links for a quick peak.

Here is a simple PowerUser–mode example with two variables:

ρ = β + Cos(x+√x+πx²/β )

The 2 variables are beta and x.  Tap the [Crunch] tab, then enter the equation

rho = beta+cos(x+sqrt(x+pi*x^2/beta))

As you type, the bottom panel (Screen 1 below) gives you on-the-fly information about what you've typed so far.  In this case, it shows that you are in the middle of the argument for the Sqrt function, you've also used one other function (Cos) and one Constant (PI), and 3 variables (rho, beta, and x (twice)).  After entering the complete equation, hit the [Submit] button.  Oops, you left off a ")" – go back and add the ) and hit [Submit] again.  Screen 3 below appears and asks you for values.  Enter 3 values for beta (.45,  .17,  .33) and 3 values for x (.22,  .839,  1.61) and tap the [Submit] button, and your result appears on Screen 4.


The nine values for rho are automatically saved for later review or use as input.  For this example, the Show OpCount/Time toggle has been set to ON (tap [Info] → {Settings} to get to the options and toggles).  The OpCount is an approximate count of primitive operations (+, –, ×, /, shift, compare) for the computation itself (but not those for rendering the results into human-readable format).  The original equation and the values for the input variables are also saved, and may be recalled from the History later.  Equations from the History may also be redone with new values for the variables.  Tap [Inputs] → {History} to get to the history list.

CrunchJr is an expression evaluator.   It evaluates the user's input expression and tabulates the result and variable values for up to three variables (each with one or more values).  200+ Constants (e.g., PI, SQRT2) and 300+ Functions (e.g., Sqrt, Refinance, Cubic, Payoff, ComplexDiv, Ira, Integrate) are available for use.   Each Function and Constant has its own descriptive screen for further reading.  Tapping [Inputs] → {Functions} or → {Constants} leads to detailed information about the hundreds of available Functions and Constants.  Most users get the vast majority of their work done using only the basic capabilities.  However, there are several advanced features, including storing results for later use, personalizing your environment, integration, building user-defined functions, and input shortcuts.
There are several features which can make using the basic functionality of expression (and equation) evaluation easier.  When you are comfortable with the basic capabilities of the app, you may wish to tap Advanced Features to explore a variety of shortcuts, tuning parameters and computational aids, including clickable versions of this list.

1)  Equations 10)  Statistics
2)  Pre-setting variables 11)  User-defined functions
3)  Options & Toggles 12)  Nested arguments
4)  History 13)  Integration
5)  The Store 14)  Error messages
6)  Using previous values       15)  FYI messages
7)  Input shortcuts 16)  Special functions
8)  The Calc (789) Keyboard 17)  Auto expansion
9)  Cut-and-Paste





In addition to the computational capabilities, a few simple games are available, including Rock-Paper-Scissors-Lizard-Spock (from Sheldon Cooper) and the very un-intuitive Three Doors .  As you might have guessed, they have computational components.



Here again is the clickable list of the major functionalities.

[MiniApps] – 250+ quick calculations

The MiniApps are spread over 36 Domains (some MiniApps appear in multiple Domains).  Each MiniApp is a standalone computation which generates one or more values, a table, or a report, each with the input, relevant equation, and output clearly presented.  Tap the [MiniApps] tab to visit a list of the Domains, then tap any entry to see the MiniApps in that Domain.  Or, tap [MiniApps] → {All MiniApps} for a list of all the MiniApps.  MiniApps are popular because each covers a single task, and they minimize the amount of typing needed to get to the answer you want.  Among the Domains are:
  • Health & Fitness, with nine MiniApps, including Calories Burned, Body Mass Index, Aerobic Points Earned, and Heart Rate.
  • Dollars & Sense, with 12 MiniApps, including Payoff Strategies, Refinance, IRA futures, Bill Split and Present/Future Values.
  • Math, with 133 MiniApps, including a wide range of simple (to not so simple) computational tools. All the usual suspects are available, and also simple MiniApps for integration, complex arithmetic, intersecting shapes, solving quadratic, cubic and quartic equations, summations, some matrix and vector operations, ...
  • Integer Computations, with 22 MiniApps, including modulo computations, various base representations, bit count, factoring, summations, and Fibonacci and other series, ...
  • Solvers, with 44 MiniApps, including equation solvers, dot and cross products, distance computations, LCM, GCD, integration, Amdahl's Law, distance to the horizon, ...
  • Physics, with 28 MiniApps, including Ohm's Law, e = mc², Potential and Kinetic Energy, Capacitance and Resistance, Power and Work, ...
  • Toss Ups, with Coin Flip, Dice Toss, Rock-Paper-Scissors, Sheldon Cooper's Rock-Paper-Scissors-Lizard-Spock, and the very un-intuitive Three Doors.
  • And 29 other Domains

Here is a simple Solver MiniApp for a common homework problem:  Find the values of x, y, and z for these three equations:

Using Quick–mode we can quickly solve a set of equations (PowerUser–mode could be just as easily used).
  • 2x + 4y + 5.55z  =   –3
  • 5x – z  =   8
  • 0.99x + 0.6y + z  =   2.3
  • Screen 1 – tap the [MiniApps] tab, then tap the Basic Math entry, and scroll down and tap Solver to arrive here.  Note that tapping the [+Fav] button on the upper right allows quicker future navigation to this screen.
  • Screen 2 – Scroll down a little, then tap 3 for the value of N (the number of equations), and enter the terms of the 3 equations in the vals box.  The terms must be separated by commas.  Then tap [Submit].
  • Screen 3 – This screen shows the input values and the results.



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[Crunch] – PowerUser mode

The [Crunch] tab delivers the full power of the app to the user's fingertips.  Users enter expressions or equations into the box.  On-the-fly error detection catches most typos instantly.  When the first two characters of a Function or Constant are entered, a list of expansion candidates is automatically generated.  When equation entry is complete, the user taps the [Submit] button.  CrunchJr then parses the input (with full error checking and diagnostic messages).  If there are any variables, it asks for one or more values for each, then calculates the results and presents them in a tabular form for easy review.  The output generated shows the input equation and values for the variables (if any).  The result variable values are automatically saved for reference and use in this or future sessions.

There are 300+ Functions and 200+ Constants that can be used as part of the input equation.  Functions and Constants are discussed briefly in the next section, or tap [Inputs] → {Functions} or → {Constants} for full lists.  Most of the Functions return a single value and can be used anywhere in an equation that a number or a Constant can be used.  But, about 130 of the Functions are special purpose (they return text or a table of results), and thus cannot be used with other terms in an equation (e.g., MatrixInv(), EasterDate(), ComplexDiv(), PayoffBiweekly()).  Here are two samples, a simple mileage computation and a more complex, engineering-style computation.

  1)   Weekly commute is 423 miles, and a fill-up is between 13.5 and 15.5 gallons.  Tap the [Crunch] tab, then enter the simple equation mpg = 423/gals into the box and tap [Submit], then enter nine values for gals.  Here is what the output would be:



  2) A more complex example with two variables:

α = √2 (β*Sin(x/4))

The 2 variables are beta and x.  After the evaluations, all the values for alpha are kept in the Store, where they are availble for later use.
  • Screen 1 – tap the [Crunch] tab to arrive here, and enter the expression alpha = sqrt2*(beta*sin(x/4)) into the [Submit] box.  Note that as you type, CrunchJr populates the bottom panel with some useful information: one Constant (SQRT2); three Variables (alpha, beta, x); one function (Sin), along with the prototype for the Sin function.  Tap the [Submit] button.
  • Screen 2 – Enter three values: 1, 3.11, .7311 into the beta box, and five values: 2, 7, 0.45, -2, 11 into the x box.  Tap [Submit].
  • Screen 3 – This screen shows the 15 result values (scroll down to see the last value).  The 15 values for the result variable (alpha) are retained in the Store for later use.  When alpha is used in an expression, those 15 values are automatically available (the user can modify or ignore them).



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[Inputs] – Access to input capabilites

The [Inputs] tab provides eight entries which support Crunch expressions

(Favorite Functions)       User-Defined Functions
Functions     Most Recently Used
Constants     Most Frequently Used
Variables (Store)     History

  • (Favorite Functions): Users can get rapid access to a set of their favorite functions by tapping the [+Fav] button for each
  • Functions: Lists the 300+ functions.  By tapping an entry, a full description of what it does and what its arguments are, as well as buttons to automatically place the function name in the [Submit] box.
  • Constants: Lists the 200+ constants.  By tapping an entry, its value and description are displayed, as well as buttons to automatically place the constant in the [Submit] box.
  • Variables (Store): Lists all the entries retained in the Store.  By tapping an entry, the variable and its values are displayed.
  • User-Defined Functions: Provides the mechanisms to create and display user-defined functions.  These functions can be used anywhere a regular function can appear.  When an equation with a user-defined function is used, its definition is displayed above the results.  Here is a sample:

scos(a,b) → a*sin(b)+b*cos(a)

Use it like any other function, e.q., scos(.556,alpha)
  • Most Recently Used: Lists the most recently used Functions or Constants
  • Most Frequently Used: Lists the most frequently used Functions or Constants
  • History: Lists all the equations which have been entered.  Any of them can be re-executed, with the original variable values or a new set of values.


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[Search] – Find app references

The [Search] tab provides a simple, single keyword search capability over all the Functions, Constants, and Screens.  At the third character entered, it displays pointers to the keyword hits.  For example, metr generates 10 hits (5 Functions, 4 Constants, 1 Screen), and mass genrates 19 hits (9 Functions, 8 Constants, 2 Screens).  Just tap any entry to go to the information for that keyword.  Note that metr gets 10 hits, but etr gets no hits, because no keywords start with etr.  Also, the [Inputs] → {Functions} page has a Functions-only keyword search, the [Inputs] → {Constants} page has a Constants-only keyword search, and the [Info] → {All Screens} page has a Screens-only keyword search.


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[Info] – Access to 150+ screens

The [Info] tab provides access to all the internal documentation and help files (including this one), as well as an avenue to the Options & Toggles, the Contact Us page, a Reset capability, the Pasteboard contents, and a list of all the screens in alphabetical order for easy reference.  Among the tables and reports are several handy lookup tables (most very special-purpose, some unusual, some esoteric), including:
 
Greek Alphabet       ASCII Codes       Powers of 2
Morse Code  Phonetic Alphabet  Powers of 10
Metric Conversions  Keywords for C++,
C, Java, CrunchJr
English Letter
Frequency
Pythagorean Triads  Prime Numbers  Roman Numerals
HTML Symbols  Genetic Code  Chemical Symbols
Area Codes  Airport Codes  Periodic Table
URL Country Codes  Poker Distributions  Bridge Distributions
  Math Trivia

Each of these will likely have very infrequent use, but it may be handy to have them nearby when needed.  Click
 here  for a full list of the tables and reports.


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Thumbnail sketches

Solvers
Quadratic, Cubic, Quartic
Integration       LCM, GCD
Distances       Amdahl's Law
e = mc²       Pythagorean
N Equations in N Unknowns
. . .  33 more
Dollars & Sense
12 Payoff Stategies
IRA Profiles       Refinance
Bill Split, Tips       Mortgage Attrs
Mileage ($) Tracking       Price Per
Effective, Nominal Rates
Present, Future Value
Health & Fitness
Calories Burned (38 workouts)
Target HeartRates       BMI
Heat Index       Windchill
Race-Pace, -Time       Fitness Tests
Aerobic Points Earned
Math Stuff
Trig (the 21 usual suspects + 1)
Factoring       Binomial(4)
Alternate Bases (2-36)       Bit Count
Complex Arithmetic(12)       Factorials
Normalize(3), Fibonacci, Max, Min
Summations(11), Series(7), Stats(5)
Cube Root, Mod, Inverse Mod
Sqrt, Exp, Log, Random(2)
. . .  72 more
Other Categories, Etc
250+ MiniApps
150+ HelpFiles, Tables, Reports
Physics(34)       Matrix(13)
Geometry(73)       Vector(14)
Group Data(36)       Colors(4)
Statistics(5)       Roots(8)
Temperatures(10)       Dates(12)
Intersecting Shapes(14)
. . .  yada, yada, yada
Miscellaneous
Rock-Paper-Scissors-Lizard-Spock
Dice       Easter Date
Three Doors       Prime Numbers
Math Trivia       Factorials
Roman Numerals       Phonetic Alphabet
Periodic Table       Chemical Elements
CrunchJr Tour       Search
History Replay       Auto-expansion
On-the-fly error detection


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