Contents
by
Bob Hepple, bhepple @freeshell.org, Nov 2002
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
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
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
Radius 6.960*10**8 m
Surface area 6.087*10**m²
Mass 1.99*10**30 kg
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
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
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
x²+y²=a²
A = pi*r² = (pi/4)D²
x²/a² + y²/b² = 1
A = pi*r1*r2 = pi*D1*D2 / 4
x²/a² - y²/b² = 1
y² = ax
A = b H/2
A = ½bc sin(A)
where b is the base length and H is the height
A = 4 * pi * r²
V = 4/3 * pi * r³
area cut off on sphere by parallel planes h apart = 2 * pi * rh
V = pi * r²h/3
A = pi * r * l
where l=slant length A=area of curved surface
A = 2 * pi * r(h+r)
V = pi * r²h
ex = 1 + x + x²/2! + ... + x**n/n!
cos(x) = 1-x²/2! + x**4/4! - ... (-1)**n x**2n / (2n)! + ...
sin(x) = x - x³/3! + x**5/5! - ... + (-1)**n x**(2n+1) / (2n+1)! + ...
tan(x) = x + x³/3 + 2x**5/15 + 17x**7/315 + ...
for x<pi/2
ln(1+x) = x - x²/2 + x³/3 - ... + (-1)**n x**(n+1) / (n+1)
for -1 < x <= 1
log-a(x) = y iff x=a**y
log-q(p)p = log-q(r) * log-r(p)
where log-q(x) is the log to base q of x
d/dx x**n = n x**n-1
integral(x**n dx) = x**n+1 / (n+1)
d/dx ln(x) = 1/x
integral(1/x dx) = ln(x)
d/dx e**ax = a e**ax
integral(eax dx) = (e**x)/a
d/dx a**x = a**x ln(a)
integral(a**x dx) = a**x / ln(a)
d/dx x**x = x**x (1+ln(x))
integral(ln(x) dx) = x(ln(x)-1)
d/dx sin(x) = cos(x)
integral(cos(x) dx) = sin(x)
d/dx cos(x) = -sin(x)
integral(sin(x) dx) = -cos(x)
d/dx tan(x) = sec²(x)
integral(sec²(x) dx) = tan(x)
d/dx cot(x) = -cosec²(x)
integral(cosec²(x) dx) = -cot(x)
d/dx sin-1(x) = 1/(1-x²)
integral(1/sqrt(1-x²) dx) = sin**-1(x), |x| < 1
d/dx tan**-1(x) = 1/(1+x²)
integral(1/(1+x²) dx) = tan**-1(x)
d/dx cosh(x) = sinh(x)
integral(sinh(x) dx) = cosh(x)
d/dx sinh(x) = cosh(x)
integral(cosh(x) dx) = sinh(x)
d/dx tanh(x) = sech2(x)
integral(sech²(x) dx) = tanh(x)
d/dx coth(x) = -cosech2(x)
integral(cosech²(x) dx) = -coth(x)
d/dx sinh-1(x) = 1/sqrt(1+x²)
integral(1/sqrt(1+x²) dx) = sinh**-1(x)
= ln(x + sqrt(x²+1))
d/dx cosh**-1(x) = 1/sqrt(x²-1)
integral(1/sqrt(x²-1) dx) = cosh**-1(x)
= ln(x + sqrt(x²-1)), where x>=1
d/dx tanh**-1(x) = 1/(1-x²)
integral(1/(1-x²) dx) = tanh**-1(x)
= ½ln((1+x)/(1-x)), where x²<1
d/dx coth**-1(x) = 1/(1-x²)
integral(1/(x²-1) dx) = -coth**-1(x)
= ½ln((x-1)/(x+1)), where x²>1
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)
integral(uv dx) = uw - integral(du/dx w dx),
where w = integral(v dx)
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
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)
(-b ± sqrt(b2-4ac))/2a
a²-b² = (a+b)(a-b)
a³-b³ = (a-b)(a²+ab+b²)
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.
f(a+x)=f(a) + xf'(a) + x²/2!f''(a) + x³/3!f'''(a) + ...
(1+x)**n = 1 + nx + n(n-1)x²/2! + n(n-1)(n-2)x³/3! + ...
where |x| < 1
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)
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
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
Air 1.000292
Water 1.333
Glass 1.48-1.61
Diamond 2.417
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
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
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.
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