Beginner's Tour

On your iPhone/iPad/iPod-Touch, you can visit this Tour any time via [Info] → {CrunchJr Tour};  This Tour provides lots of navigation opportunities to jump around as your interests dictate.

CrunchJr is a powerful computational engine covering a wide variety of topics.  This screen briefly touches on the main capabilities of the app.  Use the 5 tabs on the bottom of the screen to move around the app.  The [MiniApps] tab (Quick-mode) is best for beginners, and since it requires a minimum of typing, it's the most frequently used.  The [Crunch] tab (PowerUser-mode) provides the most powerful interface, with hundreds of general and special purpose functions and constants, user-defined functions, history recall, and general equations with variables.

Tap any of the links below (the first five correspond to the tabs in the app) to navigate around this screen, or just scroll through.

[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.
  •  3x + 5y + 2z  =  22
  •    x + 2y + 4z  =  –23
  • ½x –   y –   z  =  9
  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

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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:

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.

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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
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

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
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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