Could someone please give me a condensed explanation of Calculus?

Question

I have never studied this at all and would like to find out something about what to expect when I take a calculus course. Someone said it 'takes time out of the equation...'. What were they talking about?

Wow, these answers are great! Thanks to everyone! (Even those who consider it torture, I may find myself in a 'similar situation' someday)

Answer 1

Probably nothing sensible; it does nothing of the sort.

Calculus is primarily a tool for studying rates of change - not necessarily time-based; the rate at which one thing changes as something else changes.

To start with, you'll only be looking at functions of a single variable, and finding how quickly the function is changing at any particular point. This process is called differentiation. You can use this to find where a function is increasing or decreasing, where it has maximum or minimum values, and so on. For instance, if you are given a function describing an object's position, you can differentiate it to get its velocity and acceleration. More advanced topics allow you to find rates of change without an explicit function representation (related rates, implicit differentitation).

There is also the reverse process, called integration. In this case we are (broadly speaking) given the rate of change and have to reconstruct the original function. This can be used to find out useful things like the area under a relatively general curve between two points, whereas previously the only area formulae you've known are for regular shapes like rectangles, triangles and circles. More advanced topics allow you to calculate volumes of rotation solids with given cross-sections.

There are a whole bunch of advanced (college-level) topics in calculus, such as generalisation to multi-dimensional space, or to abstract spaces. But I don't want to scare you off just yet!

Answer 2

Calculus the condensed non mathematical (as much as possible) version....

Basically Calculus is concerned with a few things in the graphing of functions. I'll assume you know what a graph of a general function looks like.
Lets say we have some function.. we can take the Sin wave function just because I think it is familiar.
Now as you look at this graph there are some questions we can ask about it.
question 1. What is the slope of this function at any given point?
Question 2. What is the area underneath this graph between the x axis and the function from one point to another.

those are the 2 most important parts of calculus... those 2 questions. the answer to the first question is by finding the derivitive of the function the answer to the 2nd question concerns integration.

The first year of calculus deals with finding derivitives (a formula to find the slope of the tangent line to a point anywhere on the function). There are many techniques to do this depending on what type of function you are doing. The whole year you learn methods to find derivitives ... you also spend some time on limits and some types of harmonic functions..
The 2nd year you do the same exact thing with integration. You learn all the techniques to integrate functions. You will do some application and some power series along with that, and some summations. If you go on to some more advanced calculus you will learn about calculus in 3 dimensions (which I must say is rather easy once you have mastered the 2 dimensional form>)

Answer 3

Well, this is a big question, and I will try to keep it condensed.

There are two types of calculus, differential and integral.

Differential calculus deals with rates of change. So problems dealing with anything that changes would be a good place to use differential calculus.

Integral calculus is like summing things up, and it is used, for example, to find the area under a curve.

Calculus is fundamental to studying more advanced math, as well as any of the sciences, engineering, or economics.

Answer 4

In high school algebra, you are dealing with variables that represent simple quantities. In first semester calculus you are dealing with varialbes that represent rates of change. In second semester calculus you are dealing with variables that represent cumulative values or areas under curves.
Contrary to what your first answerer said, calculus has made possible the entire development of science and technology within the past half millenia. It makes posslbe the technology and scientific understanding that distinguishes us from our ancestors of 500 or more years ago, or from our distant cousins who live in isolated pockets of the world where people still live as they lived hundreds or thousands of years ago.
If you think calculus is useless, imagine roughing it in a remote rural area of a third world country, where people live without any sort of modern technology, where you may never even see a bicycle or a cigarette lighter or any sort of electric device. That's how we all lived, before calculus was invented.
For more information, put introduction to calculus in your search window. You'll turn up quite a few links, some more suited to the newcomer than others. Here's one of the better ones...
http://www.saltspring.com/brochmann/math/calculus/calculus.htm

Answer 5

It is essentially based around the idea of the limit, which is a concept which deals with the idea that something can infinitely approach something else, but never reach it. It is obviously way more complicated than that but it's a really interesting subject and it has a wide array of applications such as astronomy and physics. I actually really liked taking it although it was hard work. Here are a few introductory websits that can give you a good idea of what its all about.
http://www.math.vanderbilt.edu/~schectex/courses/whystudy.html
http://www-math.mit.edu/~djk/calculus_beginners/chapter01/contents.html
http://www.arachnoid.com/calculus/index.html
http://en.wikibooks.org/wiki/Calculus/Introduction

Answer 6

Calculus was developed by Sir Isaac Newton to explain his laws of physics. It's basic function is to calculate the exact slope of a line and also the area under it. That helps to calculate trajectories and such. It's useful for science and engineering.

My brother said it is also useful for making someone bleed out their eyeballs. :)

Answer 7

calculus essentially allows you to find areas of regions (integrals), and slopes of lines (derivitives). Overall possibly the most powerful tool ever created, and can be used for innumerable applications, from physics to accounting to efficiency calculations to pretty much anything, given the correct knowledge.

in a basic college level course (calc 1&2 if your school splits it into 2 semesters, 1,2, and multivariable if they split it into 3), you will prob learn to differentiate and integrate bunches of kinds of functions, how to use it for efficiency purposes (legrange multipliers and extrema), how to find areas and volumes under surfaces and lines, find some physics applications, and tons of other stuff.

Answer 8

The spinoff is cos(t) * e^(sin t). i'm fascinated in potential of the unique function x(t) = e^(sin t). The sin(t) area is doing its elementary sine wave component. At t=0 it rather is 0, so x(0) = e^0 = a million. this is in the middle of a wave. on the top of a wave you have gotten sin(t) = a million, which will make x(t) = e^a million = e = 2.7. on the backside of a wave you have sin(t) = -a million, which might make x(t) = e^-a million = a million/e = 0.4. So while sin(t) is going from -a million as much as a million and then go into opposite, x(t) is going from 0.4 as much as two.7 and then go into reverse. this might could desire to help you paintings out the dilemma. once you're attempting to make certain the sign of the by potential of-product, bear in ideas that e^(something) is continuously confident.

Answer 9

Really quick:
Calculus helps you calculate the exact slope of a curved line, which in tern helps you calculate an area more exactly... does that help?

Answer 10

It's a torture mechanism for college students involving useless equations and imaginary numbers.
Seriously.
It is math for the sake of math, with very few real applications other than as a base for more pointless math.
It does, however, help determine curvature and my undergrad advisor thought it was beautiful, to quote.