What is Calculus?

Question

I took calculus in college(not sure why) and got an A in both semesters but I never understood what it was good for. I just memorized the equations and plugged them in. What does calculus calculate?

Answer 1

Calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.

Examples of typical differential calculus problems include:

finding the acceleration and velocity of a free-falling body at a particular moment.
finding the optimal number of units a company should produce to maximize its profit.
Examples of integral calculus problems include:

finding areas and volumes
finding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure
finding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.

Answer 2

'Guess that's the sad thing about American Educaton: people going through it without asking why.

Math before calculus dealt with stationary objects or specific point in time. Calculus takes a look at how something changes with time. The time element is what makes calculus special: revolving objects, rate of change at a certain point in time, relationships between different objects as they move in time and space, etc.

To be quite honest, though, unless you plan to practice specific engineering or mathematics, you may never actually use it in your daily life. But, what's important is that it's a good tool to develop your logics and challenge your brain to think in terms of the bigger picture. That's why the colleges require for their degrees because if you can handle calculus, it does give you some minimal assurance that you can think logically and show some sign of intelligence. :)

Answer 3

Calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.
Examples of typical differential calculus problems include:
finding the acceleration and velocity of a free-falling body at a particular moment.
finding the optimal number of units a company should produce to maximize its profit.
Examples of integral calculus problems include:
finding areas and volumes
finding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure
finding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.

Basically it is a marriage of geometry and algebra to find answers to problems with changing rates and defined limits/parameters..
Well done on the A's

Answer 4

I think the most succinct way to describe Calculus ('the' Calculus, as conceived by Leibniz and Newton) is as a collection of techniques used to study curvature. With differentiation, you are able to examine the changes a curve is undergoing at a point or over a set of points. With integration, are are able to examine the area under a set of points on a curve.

What I find interesting about Calculus is that it relies on techniques which harness unbounded (infinite) behaviour. Which is why limits come into play.

Answer 5

Calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behaviour of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.

Examples of typical differential calculus problems include:

finding the acceleration and velocity of a free-falling body at a particular moment.
finding the optimal number of units a company should produce to maximize its profit.
Examples of integral calculus problems include:

finding areas and volumes
finding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure
finding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
Today, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimal solution to a problem that can be given in mathematical form.

Answer 6

Calculus in mainly used to find a the slope along a curved line or an area under a curved line. It is that simple. As far as applications go; a few that come to mind are rates of change in non linear (not constant motion) and heat transfer problems.

Answer 7

It's a set of methods for calculating volumes of difficult shapes, of finding instantaneous rates of change of weird formulas, and a framework for all sorts of optimization problems. If there is a central idea, it is that smooth surfaces and curves can be approximated by tiny flat bits all stitched together. The methods of the calculus do everything by exploiting this basic idea.

Answer 8

The reality is that many physical processes that engineers deal with every day will involve some calculus.

Differential equations are used to model many situations in physics and engineering.

The reality is that while you do not need to know calculus to drive a car; it is essential to a person building one.

There are too many applications to discuss. But lets face it. You got an A in two intro calculus courses. YOU DO NOT KNOW 'CALCULUS'.

Answer 9

Don't worry, there are many with Phds in mathematics who still don't really know what it is. Forget about all the responses you received - most are incomplete or incorrect.

Calculus is about finding the limit of infinite average sums. Both the integral and derivative can be expressed in terms of an infinite average sum. Since both are expressable in terms of an infinite average sum, it follows they are related. In one aspect, they are reverse processes of each other. This is the least important. The most important aspect is calculating instantaneous rates of change.

Answer 10

There are two kinds:

1) differential calculus which deals with rates of change.

2) integral calculus which studies the accumulation of quantities.

Both are very handy in the physics of everything from air travel to air-conditioning.