can any one explain me some basics of calculus?

Question

i am a dull child

Answer 1

Calculus is a mathematical method that finds the rate something changes in relationship to something else.
This was originally developed because newton had to prove gravity accelerated falling bodes. Acceleration is the rate velocity changes in relation to time. Velocity is the measurement distance changes in relationship to time.

Answer 2

A fundamental understanding of Calculus is extremely simple. It's the mechanics of doing it that get difficult at times. It is best to first have a qualitative understanding of what is going on before getting into all the details.

There are two branches Differential and Integral.

For Differential Calculus:

Geometrical Understanding:
1. Draw on a graph a curve like a parabola just with a sweep of your pencil without any calculation.
2. Draw point A on the curve. Then draw a line tangent to the curve at that point.
3. Draw point B on the curve just a little past Point A.
4. Draw a line through Point A and Point B. This is called a secant line because it cuts the graph at two points. The segment between the points is called a "chord".
5. In your mind think about what would happen if you began drawing point B closer and closer to point A. Would not the secant line start to become the tangent line?

Algebra Understanding:

The idea is "instantaneous rate of change" That is if you look at the change in y over the change in x which is the slope of the tangent line and begin to look at smaller and smaller intervals until
the change in x becomes very small. How small? Well, it's called a limit or when x tends to zero, the value of change in y/change in x becomes constant value at a point.


Integral Calculus is the opposite of Differential calculus and is about finding a sum of infinitely many infinitely small quantities.
Geometrically this is finding the area of a curve under a graph.

I would suggest just looking up "Calculus" in an old fashioned Encyclopedia. You will get the basic ideas without having to sift so much other stuff out. Once you understand fundamentally what is going on then move on to the mechanics of it. Also I did not write much about limits. Understand intuitively what they are before looking at the mathematical definition which could be very confusing to someone just starting out.

Answer 3

Im not gunna sit here and give you a 3 page essay, so here it is briefly. Calculus is the study of limits, which are the slope of the tangent line to a curve at specific point. From this you can go back and forth between the slope and the curve using different techniques

Answer 4

Before we study calculus, we look at constant rates of change, by determning average rate of change. WIth calculus, we can investigate variable rates of change, by looking at "instantaneous" rates of change. The key idea to accomplish this is the concept of limit.

Answer 5

It's best underpinned by working through the concept of limit
such that the concept of limit works for you. It needs paper, pen and enthusiasm to work well.

Answer 6

I will give one example ,and This is my idea of calculas.
When velocity is changing with time we take vti.( velocity time integral) to find distance travelled in time\ average velocity