LeoCalculator.

Version 3.4

Free download: zip file or selfextract winzip file

LeoCalculator performs calculation of mathematical expressions that could include not only basic operations but also elementary and basic statistics functions  and brackets. Flexible user interface permits typing expressions at keyboard as well usage only mouse intact with virtual keyboard at the application window.

Edit box at the top contains a string of mathematical expression to calculate. It can contain:

• numbers in with or without decimal point and with or without a power of 10 like: 7, 3.21, 1.2e-2 or 3.E3;
• pi in this application is equal to 3.141592653;
• basic mathematical operations + , - ,* , / ;
• power of grade operation ^ used like 2^3 = 8;
• brackets define order of execution of operations;
• elementary mathematical functions: sin,cos,tan,asin,acos,atan,ln,log10,exp,pow10,abs,sqrt,int,min,max,sum,!.
• random functions: rand, gauss
• basic statistical functions like mean, sigma, student, trust.
• user defined variables.

• variables can be any combinations of letters and numbers except spaces and reserved words e, E, pi and function names.
• value expressions as usual are numbers but in most cases it could be mathematical expressions too. Tip: variable expression that contains other variables should contain more letters than included variables.

Functions:

Behavior most of functions are standard and self-explanatory.

It worth to make some clarification about some of them:

pow10(x) is equal to 10^x

int(5.6) will give 5

!(n) - factorial n

rand(x) will give random value in interval from 0 to x

gauss(x) will give random values that will demonstrate normal distribution around 0 with standard deviation x

min(x1,x2,....,xi) returns minimal value among all arguments

max(x1,x2,....,xi) returns maximum value among all arguments

sum(x1,x2,....,xi) returns sum of all arguments

mean(x1,x2,....,xi) returns average of all arguments

sigma(x1,x2,....,xi) returns standard deviation of all arguments

student(sigma,N,delta) returns probability that next value after series N measurements will be inside interval from mean-delta to mean+delta where sigma is standard deviation.

trust(sigma,N,prob) returns delta that defined interval from mean-delta to mean+delta in witch with probability prob next value after series N measurements will be inside where sigma is standard deviation.

Examples:

1) Distance between points.

Let there are two points with coordinates first: x=2.3 and y=4.2 and second: x=5.1 and y=2.42

Execution of the expression: sqrt((2.3-5.1)^2+(4.2-2.42)^2) (you can just copy/paste in LeoCalculator) will give result: 3.31789

2) Area of the ellipse:

  pi*a*b in expression field and  a=4.6; b=1.27 in definition will give 18.3532

Later to experiment with other possible values of width and height of ellipse is enough just to change definition of coefficients.

3) Compound interest.

If one put  $124.618 in saving account with fixed interest 4.5% and will reinvest it in 5 years there will be:

money*(1+0.01*interest)^years =  124.618
money=100
interest=4.5
years=5

Not too big deal comparable the same situation without reinvestment:

money+money*(0.01*interest)*years = 122.5
money=100
interest=4.5
years=5

But on the really long run compound scheme will beat eat it all situation big. In century $100 compound account became  $8158.85 comparable only $550 when no reinvestment involved. There is always inflation to remember about.

4) Mortgage.

To calculate mortgage monthly payment put in LeoCalculator expression:

price*monthlyinterest/(1-(1+monthlyinterest)^(-12*years)) =1935.87
monthlyinterest =annualinterest/(12*100)
annualinterest=6.7
years=30
price=300000
if to change number of years to 40 - monthly payment will be 1799.31. Not too much difference by the way. What happened if interest jump up to 12%? For 30 years mortgage monthly payment will be 3085.84. Really hurt. Compare to beautiful 0.5% interest -  896.906. Never happen of course.

5) Molecular weight.

To calculate molecular weight of the compound with known formula one has to use formula like (ethanol):

C*2+H*5+O+H = 46.0688

C=12.011
O=15.994
H=1.0079
 

As one can see LeoCalculator permits to use pretty close to standard chemical notation formula to calculate molecular weight.

6) Statistics of experiment.

Presume that one made series of measurements of some experimental value like free fall acceleration or velocity of sound. Presume that there are several values collected. There could be several questions to answer to make best predictions about what to expect if series of measurements will be continued.

At first what is the most possible real value of the parameter. It is the average or the mean.

Let presume for argument sake that one makes six measurements of times of stone free fall from his balcony and calculated g. Using mean function at LeoCalculator one can get average:

mean(9.5,9.9,10.2,9.3,11.0,9.4) = 9.88333

Interesting question could be what probability that next measurement will give the result of g more then 12.5?

Using LeoCalculator one can easy answer this:

1-student(sigma(9.5,9.9,10.2,9.3,11.0,9.4),6,abs(mean(9.5,9.9,10.2,9.3,11.0,9.4)-12.5)) = 0.006473 or 0.6%

Very unlikely but possible. If you doing bet on it the stake better be no less then 1/150.

Contact us for negotiation about including custom functions into LeoCalculator.