Contents


Contents


1. Reformatted for gjots from engmath.s5 from http://3lib.ukonline.co.uk/pocketinfo/index.html


by

Bob Hepple, bhepple @freeshell.org, Nov 2002

Contents


2.



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

Contents


3. astro


Contents


3.1 Earth


Polar radius 		6356.8km
Equatorial radius 	6378.2km
Mean radius	 	6371km
Surface area	 	5.101*10**14 m
Volume 			1.083*10**21 m
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

Contents


3.2 Moon


radius				1738km
Surface area		3.796*10**m
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
					 degree approx

Contents


3.3 Sun


Radius				6.960*10**8 m
Surface area		6.087*10**m
Mass				1.99*10**30 kg

Contents


3.4 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

Contents


3.5 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

Contents


4. General


Contents


4.1 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
	micro	10**-6
n	nano	10**-9
p	pico	10**-12

Contents


5. Maths


Contents


5.1 Circle Equation


x+y=a
A = pi*r = (pi/4)D

Contents


5.2 Ellipse Equation


x/a + y/b = 1
A =  pi*r1*r2 =  pi*D1*D2 / 4

Contents


5.3 Hyperbola Equation


x/a - y/b = 1

Contents


5.4 Parabola Equation


y = ax

Contents


5.5 Triangle Area


A = b H/2
A = bc sin(A)
 
where b is the base length and H is the height

Contents


5.6 Sphere


A = 4 * pi * r
V = 4/3 * pi * r
area cut off on sphere by parallel planes h apart = 2 * pi * rh

Contents


5.7 Cone


V = pi * rh/3
A = pi * r * l 

where l=slant length A=area of curved surface

Contents


5.8 Cylinder


A = 2 * pi * r(h+r)
V = pi * rh

Contents


5.9 Series ex


ex = 1 + x + x/2! + ... + x**n/n!

Contents


5.10 Cosine Series


cos(x) = 1-x/2! + x**4/4! - ... (-1)**n x**2n / (2n)! + ...

Contents


5.11 Sine Series


sin(x) = x - x/3! + x**5/5! - ... + (-1)**n x**(2n+1) / (2n+1)! + ...

Contents


5.12 Tangent Series


tan(x) = x + x/3 + 2x**5/15 + 17x**7/315 + ...
 
for x<pi/2

Contents


5.13 Logs


ln(1+x) = x - x/2 + x/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

Contents


5.14 Differential/Integral xn


d/dx x**n = n x**n-1

integral(x**n dx) = x**n+1 / (n+1)

Contents


5.15 Differential ln(x)/Integral 1/x


d/dx ln(x) = 1/x
 
integral(1/x dx) = ln(x)

Contents


5.16 Differential/Integral eax


d/dx e**ax = a e**ax
 
 integral(eax dx) = (e**x)/a

Contents


5.17 Differential/Integral ax


d/dx a**x = a**x ln(a)
 
integral(a**x dx) = a**x / ln(a)

Contents


5.18 Differential/Integral xx


d/dx x**x = x**x (1+ln(x))
 
 integral(ln(x) dx) = x(ln(x)-1)

Contents


5.19 Differential sin(x)


d/dx sin(x) = cos(x)
 
integral(cos(x) dx) = sin(x)

Contents


5.20 Differential cos(x)


d/dx cos(x) = -sin(x)
 
integral(sin(x) dx) = -cos(x)

Contents


5.21 Differential tan(x)


d/dx tan(x) = sec(x)
 
integral(sec(x) dx) = tan(x)

Contents


5.22 Differential cot(x)


d/dx cot(x) = -cosec(x)
 
integral(cosec(x) dx) = -cot(x)

Contents


5.23 Differential sin-1(x)


d/dx sin-1(x) = 1/(1-x)
 
integral(1/sqrt(1-x) dx) = sin**-1(x), |x| < 1

Contents


5.24 Differential tan-1(x)


d/dx tan**-1(x) = 1/(1+x)
 
integral(1/(1+x) dx) = tan**-1(x)

Contents


5.25 Differential cosh(x)


d/dx cosh(x) = sinh(x)
 
integral(sinh(x) dx) = cosh(x)

Contents


5.26 Differential sinh(x)


d/dx sinh(x) = cosh(x)
 
integral(cosh(x) dx) = sinh(x)

Contents


5.27 Differential tanh(x)


d/dx tanh(x) = sech2(x)
 
integral(sech(x) dx) = tanh(x)

Contents


5.28 Differential coth(x)


d/dx coth(x) = -cosech2(x)
 
integral(cosech(x) dx) = -coth(x)

Contents


5.29 Differential sinh-1(x)


d/dx sinh-1(x) = 1/sqrt(1+x)
 
integral(1/sqrt(1+x) dx) = sinh**-1(x)

= ln(x + sqrt(x+1))

Contents


5.30 Differential cosh-1(x)


d/dx cosh**-1(x) = 1/sqrt(x-1)
 
integral(1/sqrt(x-1) dx) = cosh**-1(x)

= ln(x + sqrt(x-1)), where x>=1

Contents


5.31 Differential tanh-1(x)


d/dx tanh**-1(x) = 1/(1-x)
 
integral(1/(1-x) dx) = tanh**-1(x)

= ln((1+x)/(1-x)), where x<1

Contents


5.32 Differential coth-1(x)


d/dx coth**-1(x) = 1/(1-x)
 
integral(1/(x-1) dx) = -coth**-1(x)

= ln((x-1)/(x+1)), where x>1

Contents


5.33 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/v (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)

Contents


5.34 Rules of Integration


integral(uv dx) = uw - integral(du/dx w dx), 

where w = integral(v dx)

Contents


5.35 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) = 2sin(A+B)cos(A-B)
sin(A)-sin(B) = 2cos(A+B)sin(A-B)
cos(A)+cos(B) = 2cos(A+B)cos(A-B)
cos(A)-cos(B) = -2sin(A+B)sin(A-B)

sin(AB)=sin(A)cos(B)+/-cos(A)sin(B)
cos(AB)=cos(A)cos(B)-/+sin(A)sin(B)
tan(AB)=(tan(A)+/-tan(B))/(1-/+tan(A)tan(B))

sin(A)+cos(A) = 1
sec(A) = tan(A)+1

Contents


5.36 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

a = b + c - 2bc cos(A) (cosine rule)

Contents


5.37 Roots of a Quadratic Equation


(-b  sqrt(b2-4ac))/2a

Contents


5.38 Quadratic Expansion


a-b = (a+b)(a-b)

a-b = (a-b)(a+ab+b)

Contents


5.39 Sums


sum(r) = n(n+1) : r=1..n
r = n(n+1)(2n+1)/6 : r=1..n
r = n(n+1) : 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.

Contents


5.40 Taylor's expansion


f(a+x)=f(a) + xf'(a) + x/2!f''(a) + x/3!f'''(a) + ...

Contents


5.41 Binomial


(1+x)**n = 1 + nx + n(n-1)x/2! + n(n-1)(n-2)x/3! + ...

where |x| < 1

Contents


5.42 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)

Contents


6. Physics


Contents


6.1 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

Contents


6.2 Sound velocity


Air (0C)	331.3 m/s
Hydrogen (0C)	1284 m/s
Oxygen (0C)	316 m/s
Water (25C)	1498 m/s

Contents


6.3 Refractive index


Air 1.000292
Water 1.333
Glass 1.48-1.61
Diamond 2.417

Contents


6.4 Temperatures


All in  C
Absolute zero 	-273.15
BP Helium 	-268.93 (4.216K)
FP hydrogen 	-259.2 (14K)
BP hydrogen 	-252.8 (20.4K)
FP nitrogen 	-209.9 (63.3K)
BP nitrogen 	-195.8 (77.32K)
FP oxygen 	-218.4 (54.8K)
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

Contents


6.5 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

Contents


6.6 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.

Contents


6.7 Basic Motion Laws


u = initial velocity
v = final velocity
s = distance
a = acceleration
t = time

s = (u+v)t
v = u+at
s = ut+at
v = u+2as