Reformatted for gjots from engmath.s5 from http://3lib.ukonline.co.uk/pocketinfo/index.html by Bob Hepple, bhepple @freeshell.org, Nov 2002 \NewEntry An Engineering Maths Database for the Psion Series 5 By Kevin Millican ... and edited by Bob Hepple (removing engineering stuff, adding more maths & astronomy) If there are any errors or if you would like to submit additional records for inclusion, please contact me at :- Email: kevin.millican@altavista.net \NewEntry astro \NewFolder \NewEntry Earth Polar radius 6356.8km Equatorial radius 6378.2km Mean radius 6371km Surface area 5.101*10**14 m² Volume 1.083*10**21 m² Mass 5.977*10**27 g Mean distance to Sun (1AU) 1.496*10**11 m Escape velocity at surface 11.2 km/s Rotational velocity at equator 465 m/s Mean velocity about sun 29.78 km/s \NewEntry Moon radius 1738km Surface area 3.796*10**m² Sideral period of moon about earth 27.32 solar days Mean synodical or lunar month 29.531 mean solar days Mean distance from the earth 3.844*10**8 m Escape velocity at surface 2.38 km/s Angle subtended in the sky ½ degree approx \NewEntry Sun Radius 6.960*10**8 m Surface area 6.087*10**m² Mass 1.99*10**30 kg \NewEntry Time Mean solar day 86400 mean solar seconds Sidereal day 86164.090 mean solar seconds tropical (civil) year 365.242 mean solar days 31556925.9747 s sidereal year 365.256 mean solar days \NewEntry Distance 1AU 1.495985*10**11 m 1 Parsec 3.0856*10**16 m 1 Parsec 2.062648*10**5 AU 1 Parsec 3.2615 ly ly 9.45605*10**15 m 6.324*10**4 AU 0.3066 pc \EndFolder \NewEntry General \NewFolder \NewEntry Decimal Prefixes T tera 10**12 G giga 10**9 M mega 10**6 k kilo 10**3 h hecto 10**2 da deca 10 d deci 10**-1 c centi 10**-2 m milli 10**-3 µ micro 10**-6 n nano 10**-9 p pico 10**-12 \EndFolder \NewEntry Maths \NewFolder \NewEntry Circle Equation x²+y²=a² A = pi*r² = (pi/4)D² \NewEntry Ellipse Equation x²/a² + y²/b² = 1 A = pi*r1*r2 = pi*D1*D2 / 4 \NewEntry Hyperbola Equation x²/a² - y²/b² = 1 \NewEntry Parabola Equation y² = ax \NewEntry Triangle Area A = b H/2 A = ½bc sin(A) where b is the base length and H is the height \NewEntry Sphere A = 4 * pi * r² V = 4/3 * pi * r³ area cut off on sphere by parallel planes h apart = 2 * pi * rh \NewEntry Cone V = pi * r²h/3 A = pi * r * l where l=slant length A=area of curved surface \NewEntry Cylinder A = 2 * pi * r(h+r) V = pi * r²h \NewEntry Series ex ex = 1 + x + x²/2! + ... + x**n/n! \NewEntry Cosine Series cos(x) = 1-x²/2! + x**4/4! - ... (-1)**n x**2n / (2n)! + ... \NewEntry Sine Series sin(x) = x - x³/3! + x**5/5! - ... + (-1)**n x**(2n+1) / (2n+1)! + ... \NewEntry Tangent Series tan(x) = x + x³/3 + 2x**5/15 + 17x**7/315 + ... for x=1 \NewEntry Differential tanh-1(x) d/dx tanh**-1(x) = 1/(1-x²) integral(1/(1-x²) dx) = tanh**-1(x) = ½ln((1+x)/(1-x)), where x²<1 \NewEntry Differential coth-1(x) d/dx coth**-1(x) = 1/(1-x²) integral(1/(x²-1) dx) = -coth**-1(x) = ½ln((x-1)/(x+1)), where x²>1 \NewEntry Rules of Differentiation Product Rule: d/dx (uv) = u dv/dx + v du/dx d/dx (uvw) = uv dw/dx + uw dv/dx + vw du/dx Quotient Rule: d/dx (u/v) = 1/v² (v du/dx - u dv/dx) Chain Rule (function of a function): dy/dt = dy/dx dx/dt (where y is a function of x and x is a function of t) \NewEntry Rules of Integration integral(uv dx) = uw - integral(du/dx w dx), where w = integral(v dx) \NewEntry Trigonometric Rules 1 2sin(A)cos(B) = sin(A-B)+sin(A+B) 2cos(A)cos(B) = cos(A-B)+cos(A+B) 2sin(A)sin(B) = cos(A-B)-cos(A+B) sin(A)+sin(B) = 2sin½(A+B)cos½(A-B) sin(A)-sin(B) = 2cos½(A+B)sin½(A-B) cos(A)+cos(B) = 2cos½(A+B)cos½(A-B) cos(A)-cos(B) = -2sin½(A+B)sin½(A-B) sin(A±B)=sin(A)cos(B)+/-cos(A)sin(B) cos(A±B)=cos(A)cos(B)-/+sin(A)sin(B) tan(A±B)=(tan(A)+/-tan(B))/(1-/+tan(A)tan(B)) sin²(A)+cos²(A) = 1 sec²(A) = tan²(A)+1 \NewEntry Trigonometric Rules 2 In triangle ABC with sides abc and angle ABC (side a is opposite angle A) a/sin(A) = b/sin(B) = c/sin(C) (sine rule) sin(A)=2/bc sqrt(s(s-a)(s-b)(s-c)), where s=(a+b+c)/2 = (2/bc)area a² = b² + c² - 2bc cos(A) (cosine rule) \NewEntry Roots of a Quadratic Equation (-b ± sqrt(b2-4ac))/2a \NewEntry Quadratic Expansion a²-b² = (a+b)(a-b) a³-b³ = (a-b)(a²+ab+b²) \NewEntry Sums sum(r) = ½n(n+1) : r=1..n r² = n(n+1)(2n+1)/6 : r=1..n r³ = ¼n²(n+1)² : r=1..n a**r = (1-a**n)/(1-a) : r=0..n-1 ...where sum(r) is the sum of all terms r - normally represented by a Greek capital sigma. \NewEntry Taylor's expansion f(a+x)=f(a) + xf'(a) + x²/2!f''(a) + x³/3!f'''(a) + ... \NewEntry Binomial (1+x)**n = 1 + nx + n(n-1)x²/2! + n(n-1)(n-2)x³/3! + ... where |x| < 1 \NewEntry Simpson's Rule integral(f(x) dx) ~= h(y0 + 4y1 + y2)/3 where a and b are the limits of the integral h = (b - a)/2 y0 = f(a) y1 = f((a+b)/2) y2 = f(b) \EndFolder \NewEntry Physics \NewFolder \NewEntry Loudness 0 threshold of hearing 10 virtual silence 20 quiet room 30 watch ticking at 1m 40 quiet street 50 quiet conversation 60 quiet motor at 1m 70 loud conversation 80 door slamming 90 busy typing room 100 near loud motor horn 110 pneumatic drill 120 near aero engine 130 threshold of pain \NewEntry Sound velocity Air (0°C) 331.3 m/s Hydrogen (0°C) 1284 m/s Oxygen (0°C) 316 m/s Water (25°C) 1498 m/s \NewEntry Refractive index Air 1.000292 Water 1.333 Glass 1.48-1.61 Diamond 2.417 \NewEntry Temperatures All in °C Absolute zero -273.15 BP Helium -268.93 (4.216°K) FP hydrogen -259.2 (14°K) BP hydrogen -252.8 (20.4°K) FP nitrogen -209.9 (63.3°K) BP nitrogen -195.8 (77.32°K) FP oxygen -218.4 (54.8°K) BP oxygen -182.97 FP mercury -38.87 FP water 0 BP water 100 FP lead 327.3 BP mercury 356.58 BP sulphur 444.6 Dull red heat 500-600 FP aluminium 660.1 FP silver 960.8 FP gold 1063 White heat 1500-1800 \NewEntry Hardness (Moh's scale) 1 Talc 2 rock salt (2.5 finger nail) 3 calcite 4 fluorite 5 apatite 6 felspar (6 penknife) 7 quartz 8 topaz 9 corundum (emery) 10 diamond \NewEntry Newtons Laws 1. An object will remain at rest or in uniform motion in a straight line unless acted on by an external, unbalanced force. 2. The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the applied net force. (ie. F=ma) 3. For every action there is an equal and opposite reaction. \NewEntry Basic Motion Laws u = initial velocity v = final velocity s = distance a = acceleration t = time s = ½(u+v)t v = u+at s = ut+½at² v² = u²+2as \EndFolder