I think this is not specific enough to answer.Originally Posted by mHadad
Is this a question about target azimuth, elevation, range, Doppler for
a radar like system?
i wanted to know is the following steps are what i should do to derive a function for a real world incident (to be more specific Digital Signals and moving objects):
1-i should know all the independant variable that may affect my dependant variable that i want to know about.
2-study the relation between each independant variable and the dependant variable from the point of view for it's(the independant variable like time for example) sign (can't be negative) .
don't know what's next to derive a function to describe it's behavior.and when should i use a cos,tan ,cot in a function (for example u raise a term by 2 then take the square root of it to make sure it is not negative or gets the absolute value for this term).
sorry guys my q might seem silly but i'm not native english so i'm not quite familiar with english terms for mathmatics like real number ,rational ,irrational ,imaginary numbers ..etc
thanks again and sorry for the long post
well i can not be more specific as i'm not having a specific problem yet.well i think that i must be more specific regarding my problem as i don't think that the answear will be from one part of mathmatics but i'm sure that it will be mostly a calculus answear.thanks captain jack.
captain are rational numbers any number that is represented by a two number division which means a decimal number (or as we say it in programming a float) and irrational numbers are the opposite which are integers?
how can a number that is raised by the power of 2 be negative ,i mean how can i^2 = -1 (can u show me a real world example where i^2 = - 1 so i can understand it more)?
thanks again captain jack
Loosely speaking a rational number is a number that can be expressed as theOriginally Posted by mHadad
ratio of two integers.
Again loosely speaking decimal numbers with no restriction on the length of the
decimal are what we call real numbers.
Floats are meant to be a computer representation of numbers. But the
restrictions of computer hardware result in them in fact being a subset
of the rationals, also floating arithmetic is not the same as normal arithmetic,
see What Every Computer Scientist Should Know about Floating Point Arithmetic.
We introduce an ideal element i into the number system so that i^2=-1,Originally Posted by mHadad
then develop the idea from there.
I can no more point to a complex or imaginary number than I can point
to the integer 7. These are mathematical constructs and are judged by
their usefullness (and/or interest) within mathematics and/or its
Complex numbers were originally introduced because they were usefully
when finding the real roots of cubics, and today they are used
in vast tracts of mathematics. They are also interesting in their own right
and further development of the ideas have been fruitfully in all sorts of ways.
In real life a spend a lot of my time working with signal processing
algorithms, and these would be considerably more difficult to handle
without the use of the complex representation of signals.
Name a real world problem that uses -5? Same idea -5 does not really exists in "the real world". But you still use it. There are several examples in electricity where this number is used. Another excellent place is in calculus. Sometimes it is easier to do calculus using this number to simplify your work.Originally Posted by mHadad
If you are curious there is a further extension to the number "i". Called j and k. The system they compose are called the "quaternions". They are even stranger in the sense that . But these too also have real world applications.
well as i know about Digital Signal Processing as i'm yet a begginer in that science that i have seen a usage for complex numbers where they call it ,the imaginary part.i think it was used in convolution.but what i meant by a real world example is that u raise a unit of time by the power of 2 then take the square root of it so it can not be negative or you subtract one point from another in a coordinate plane then raise the result by 2 then take the square root of it to get the absolute value ,like in the distance formula:
d(a,b) = sqrt. ( ( x2 - x1 ) ^ 2 + ( y2 - y1 ) ^ 2 )
but i can not say that i can understand a real world incident by i^2 = -1 ,unless it means something like the following : imagine a rubber band that is held between the two fingers for example.if i apply a pressure againset it ,as i'm increasing my pressure it's resistance(the rubber band) will decrease (to a certain point ,which is denoted by the negative number for example).mmm that what came into my mind while typing ,don't know if it holds true or not because what if i increase the pressure againset this rubber band then what is the power of i and does it have to continue to be negative?
correct me if i'm wrong.
I can't speak to your example, but energy loss due to resistive forces like friction can often be modelled using "i." A common example of this is in optics where the index of refraction takes a real and complex part, the complex part indicating the amount of loss of intensity of the light as it passes through the material.Originally Posted by mHadad