The Ultimate Calculator 2.4 (UNREGISTERED version) [F1] for help Copyright (C) 1992-1994 by Daniel Corbier. All rights reserved. ucalc> ;******************************************************************* ucalc> ; This text file is a sample session which demonstrates some of the ucalc> ; features available in the Ultimate Calculator. The sections are ucalc> ; entitled: ucalc> ; ucalc> ; 1. General Calculations ucalc> ; 2. Physics for Thought ucalc> ; 3. HBO for Thought ucalc> ; 4. Are you converted yet? ucalc> ; 5. Let's use some FORCE ucalc> ; 6. How to pay ucalc> ; 7. Let's get a few FACTS straight ucalc> ;******************************************************************* ucalc> ucalc> ; *********************** ucalc> ; 1. General Calculations ucalc> ; *********************** ucalc> ucalc> 17*(5+8)^2 Answer: 2873 ucalc> cos(pi)+8/pi + sinh(14) Answer: 601303.688561062095 ucalc> test(x) = x^pi + sin(x) ; User defined function. ucalc> test(14) Answer: 3988.18506502600842 ucalc> sum(x*2+3^x,1..100) ; Summation Answer: 7.73066281098016997E+47 ucalc> ucalc> ; ********************** ucalc> ; 2. Physics for Thought ucalc> ; ********************** ucalc> ucalc> mass = 77.2 ; g ucalc> Volume = 4.0 ; cm^3 ucalc> ucalc> mass / Volume ; Density Answer: 19.3 ucalc> ucalc> mass = 13 ; Lets try a different mass ucalc> ucalc> mass / Volume ; Now lets see the new density Answer: 3.25 ucalc> ; Quantum Mechanics ucalc> ucalc> h = 6.63E-34 ; J s ucalc> m = 9.11E-31 ; kg ucalc> L = 2E-11 ; m ucalc> ucalc> E(x) = (h^2/(8*m*L^2))*x^2 ; Allowed energies for a particle in a box. ucalc> ucalc> E(1) Answer: 1.50785194840834248E-16 ucalc> ; Oops, you meant L=2E-10, no problem use the Up arrow. ucalc> L = 2E-10 ucalc> E(1) ; You didn't have to retype the eq. ! Time saver, isn't it? Answer: 1.50785194840834248E-18 ucalc> E(5) Answer: 3.7696298710208562E-17 ucalc> ucalc> ; ****************** ucalc> ; 3. HBO for Thought ucalc> ; ****************** ucalc> ucalc> mode hbo ; Results will be displayed in Hex, Binary, and Octal ucalc> ucalc> #h1E or #hAFF ; ORing two hexadecimal numbers Decimal: 2815 Hex: AFF Binary: 101011111111 Octal: 5377 ucalc> ucalc> $1E or $AFF ; Same as above (shortcut notation for hex) Decimal: 2815 Hex: AFF Binary: 101011111111 Octal: 5377 ucalc> ucalc> #b1010101 or #b111000 + 44/2 Decimal: 95 Hex: 5F Binary: 1011111 Octal: 137 ucalc> ucalc> mode hbo ; Toggle HBO mode back off ucalc> ucalc> ; ************************* ucalc> ; 4. Are you converted yet? ucalc> ; ************************* ucalc> ucalc> feet_inches(x) = x * 12 ; You can put these and more in ucalc> meters_feet(x) = 3.281 * x ; UCELC.DEF if you use them often. ucalc> celsius_fa(x) = 9/5 * x + 32 ; Celsius to Fahrenheit. ucalc> ucalc> celsius_fa(50) Answer: 122 ucalc> feet_inches(3) Answer: 36 ucalc> ucalc> ; *********************** ucalc> ; 5. Let's use some FORCE ucalc> ; *********************** ucalc> ucalc> ; FORCE = integral( pgh dA ) ucalc> ucalc> integ(6.24*(3-x)*2*sqr(9-x^2),-3..3) Answer: 529.07649351285467 ucalc> integ(3*x^2*(x+7),4..7,500) ; 500 subdivisions for higher precision Answer: 3561.75 ucalc> ucalc> ; ************* ucalc> ; 6. How to pay ucalc> ; ************* ucalc> ucalc> ; You can do all your financial calculations with Ucalc. ucalc> ucalc> ; Lets take a loan to buy a nice house ucalc> ucalc> payment(PV,i,n) = PV*i/(1-(1+i)^(-n)) ; Formula for monthly payments ucalc> ucalc> PV = 175000 ; Loan balance ucalc> i = .01 ; Interest rate (1% monthly) ucalc> n = 240 ; Number of payments (20 years) ucalc> ucalc> payment(PV,i,n) Answer: 1926.90073374681746 ucalc> n = 360 ; Maybe we can negotiate better terms ucalc> ucalc> payment(PV,i,n) Answer: 1800.07204461963275 ucalc> payment(215000,i,n) ; Can we afford a bigger loan? Answer: 2211.51708338983452 ucalc> ucalc> ; You want to become a millionaire by investing $50,000 and ucalc> ; earning 14% interest each year. How many years will it take? ucalc> ucalc> Term(FV,PV,i) = ln(FV/PV) / ln(1+i) ucalc> ucalc> FV = 1000000 ; Future investment value ucalc> PV = 50000 ; Present investment value ucalc> i = .14 ; Annual interest ucalc> ucalc> Term(FV,PV,i) Answer: 22.8632526947680305 ucalc> ; It will take around 23 years ucalc> ucalc> ; ********************************* ucalc> ; 7. Let's get a few FACTS straight ucalc> ; ********************************* ucalc> ucalc> FACT(1500)*2 Answer: 9.62399559355954973E+4114 ucalc> 1500!*2 ; version 2.4 now supports the factorial (!) symbol. Answer: 9.62399559355954973E+4114 ucalc> ; Wow, not even the US budget deficit is that big of a number. ucalc> ; Can your pocket calculator get a factorial that high? ucalc> ucalc> solve( exp(x)+3*x = 15 ) Answer: 2.14698767937181217 ucalc> ; 'last' stores the answer to the previous operation. ucalc> exp(last)+3*last ; You can use that concept for accuracy checks. Answer: 15 ucalc> solve( sin(x) = 1, 0..pi ) Answer: 1.57079632679489662 ucalc> sumtable(x^2+2*x,0..10) Count Value Cumulative 0 0 0 1 3 3 2 8 11 3 15 26 4 24 50 5 35 85 6 48 133 7 63 196 8 80 276 9 99 375 10 120 495 Answer: 495 ucalc> ucalc> ; Compound functions can be defined by using relational operators. ucalc> ucalc> ; / x^2+3, x > 0 ucalc> ; tst(x) = | 2, x = 0 ucalc> ; \ x^2-3, x < 0 ucalc> ucalc> tst(x) = (x^2+3)*(x>0) + (2)*(x=0) + (x^2-3)*(x<0) ucalc> tst(15) Answer: 228 ucalc> tst(-8) Answer: 61 ucalc> 3*tst(0)^2+pi Answer: 15.1415926535897932 ucalc> ucalc> ; These are just some of the things you can do with Ucalc. ucalc> ucalc> ; Please remember to pay the registration fee. This will allow me ucalc> ; spend the necessary amount of time in order to add some of the ucalc> ; features that you would like to see in the next version. ucalc>