calculus help?

Question

i am a high school student, top of my class in maths...atm we are doing trig and so on but i would be interested in learning the methods for or how to do calculus...e.g what notation do i need to learn...any helpful sites or just anything to help advice...theorems would be appreciated

Answer 1

Calculus is in two parts 'DIFFERENTIATION' and 'INTEGRATION'.

Differentiation converts equations to find the 'slope'/gradient at a given point.
Its notations is y = x^n
dy/dx = nx^(n-1)
NB the easiest way to note what is going on is to remember the index number 'n' becomes the coefficient of the equation and the index number is reduced by one .
In double differentiation
dy^2/d^2x = (n-1)nx^(n-2)
This calculates the 'points of inflection' of a curve - the point were a steepening/shallowing curve becomes shallower/steeper.
Integration converts equations to find the area under a curve between two given points.
It 's notation is the elongated 'S' with numbers top and bottom to indicate the limits of calculation.
It is the inverse function of differentiation.

y = x^n
'S' = [x^(n+1)] / n+1

Here NB the index number 'n' has 'one' added to become (n+1) and this value (n+1) becomes a denominator to the whole equation.

Integration is very good at calculating volumes of large asymmetrical shapes, such ships' hulls.