The Differential and  Integral Calculus

Basic Calculus is not hard. It helps to have graph paper and draw the curves. It comes natural to remember the pictures. If you have an electronic oscilloscope you are way ahead. It draws curves for you. Can you plot a graph? Try y = 3,  Try y = x2, These are important graphs

Now consider limits. Graph   y = 2/x.  Look at the point x = 1. from either side as x gets closer to 1, y gets closer to 2. Then the limit as x approaches 1 is 2.

Consider the slope of y = 3x. At x = 1, y = 3. At x = 2, y = 6. I  claim that the slope is the change in y divided by the change in x. that comes to (6-3)/(2-1) = 3.

I also am too lazy to keep writing "the change in x" or y or whatever it is, so I say delta x or delta y, and there is even a symbol for "delta."  It looks like a triangle D and sometimes like d.
So then Dy / Dx =3.

Try this for y= x2 and see what kind of trouble you get into. The "slope" depends on where you pick the two x values. It even depends on how far apart they are.

Now consider what happens as Dx gets smaller and smaller. The results you get converge on a unique number. This number is the "true slope" and it depends on the point x.

The function of x which is made from these numbers is called the DERIVATIVE and it is denoted by dy/dx. of y'. dy/dx is the limit as Dx goes to 0 of Dy / Dx.

Derivatives are not so strange as you may think. If x is the location of a car and t is time then
dx/dt is the speed and the derivative of the speed denoted d2x/dt2 is the acceleration.

The derivative exists for most functions and is formally expressed as the limit as Dx goes to zero of
 Dy / Dx. The derivative is also a function of x..

Now consider the opposite of the derivative. The integral is sometimes called the antiderivitive. If you integrate a function and then differentiate that you get the original function back. If you plot the graph of a function, the integral is sometimes called the area under the curve. This works so long as you bound the area with the x axis and consider area when the function is negative to be negative area.

The symbol for the integral isand it is used in the context f(x) dx. This is the indefinite integral because the limits for the integration are not specified. If they are specified you have the definite integral which is defined as, where G is some function which when differentiated gives f(x).
There are a number of excellent calculus web sites:
 Read this   from a university
 or this   From overseas