okay here i go trying to reacall a 3 yer old add math lecture.
e or the exponention function is just a contant, the constant equal to ~ 2.718, the function is defined as...
now speaking as an analogue, e^x has the same properties as 2^x, the graph looks the same if you adjust the scale. the only thing sepcial abt this function is that its dervitive is its self, so basically on a graph of e^x, the gradient at any point x can be found by simple putting the value of x in the original function.....
cont.....
---------- Post added at 09:12 PM ---------- Previous post was at 09:04 PM ----------
now coming to log, log is basically used to approximate powers and verry large, or very small numbers.
basically if y=2^x, x=log with base 2 and the other thing Y.
the log in your scientific calculators is log to base 10,
now note if 10=10^x, x would be 1 ryt.
so when log 10 (base is 10 in this context) the answer would be one.
similarly 100=10^x, would give x=2
and log 100 would give 2
now 10 is a constant, so is e, so some nutcase decided it would be fun to tourture innocent souls by combining one semi confusing thing with another semi confusing thing to make something.
moving on....
so the crackpot made an expression og log with base e, its know as natural logarithm or ln
using the examples above we now that ln e would simple be 1
and hence ln e^x would simply be x,
and e^ln x, is also x yea its a really twisted function.
we use ln and e for various reasons, at add maths level we used e to cancel out ln, and ln to cancel out e, which is really a Abuses will lead to ban cause they made the functions up in the first place.
---------- Post added at 09:14 PM ---------- Previous post was at 09:12 PM ----------
a linear function is one when plotted on an x/y plane (graph) would give a straight line, i.e y=2x, y=2x+ any constant(e maybe)
non liner is any function which is NOT linear, rocket science aint it
---------- Post added at 09:15 PM ---------- Previous post was at 09:14 PM ----------
homogenity...
im going to over simplify it .
in an equation where x^2 +y^2 =xy
this equation would be homogenous because the the units would add up, basically suppose x and y have any unit say cm (centimeter) or a(any unit
)
it would be homogenous because the units would become a^2 + a^2 =a^2
all the equations in physics etc are homogenous, eg
e=mc^2
m=Kg
c=speed of light=m/s^2
so energy is Kg.m^2/c^4
now using the formulae of potential energy, e=mgh, e would again add up with the same units.
homogenity of equations is pretty simple till is come into the context of homogenous differential equations, and finding out weather a differential equation is homogenous or not...that gets a bit more complex and i cant really explain over a forum.
oh boy differentiation and integration...
cont...