mathematical principles Flashcards
Draw graph for y=x
Y=x - straight line from corner at 45degrees
Draw graph for y=ax+b
This line should cross y axis at a value of b, because when x is 0, y must be 0+b.
Slope =a, when y=2x slope will twice as steep as when y=1x
draw the graph for y=k/x
Hyperbolic relationships= any inverse relationship.
commonest value for k in anaesthetics is 1, which gives rise to a curve known as rectangular hyperbola, where the line never crosses the x or y axis (asymptotic to them)
e.g boyles law (volume=1/pressure)
define asymptote (graphically)
a curve that continually approaches a given line but does not meet it at any distance
Draw the graph y=kx^2
=parabolic relationships. These curves describe the relationship of y=x^2 and so there can be no negative value for y.
the value for k alters the slope of the curve in the same way that a does in the equation y=ax +b. The curve crosses the y a 0 unless written y=kx^2 +b in which case the whole curve is shifted upwards and crosses at the value of b
What is Euler’s number
2.71828
the base of natural logarithms
represented by ‘e’
What is an exponential process
A condition where the rate of change is proportional to the value of the variable at that time
y=e^x (the x variable becomes the exponent of the equation)
what are logarithms
the power(x) to which a base must be raised in order to produce the number given for the equation. Log10 (100). for 10^2=100, therefore the answer is x=2
rules of logs
1. multiplication
2 division
3. reciprocal
4. Power
5. log of it’s own base
6. log of 1
- log(xy)= log(x) + log(y) -> multiplication becomes addition
- division becomes subtraction
- reciprocal becomes negative
log (1/x)= -log (x) - Power becomes multiplication
log x^n =n.log(x) - Any log of its own base is 1
- log of 1 is zero, because n^0 always equals 1
log10^1 =0, and In(1)= 0
Is reynolds a dimensionless number?
Reynolds number is a dimentionless number
