Differ. Calculus Explanation

[GutZ]

I am no genius, but I am sure Calculus shouldn't be so difficult for me to understand. I am having an awful time trying to grasp the main purpose for it. Through that I can figure it out myself....so I was hoping one of you people could take the time to explain it to me in plain basic english on how it works.

 

I believe that everything should be able to be explained simply. I think my brain work on some sort of deductive method of seeing the whole picture, or tries to anyway, and then gets confused not know the basics and can't see the basics.

 

SO.

 

What I gather is that your trying to find the instanteous rate of change between "Something" as it reaches 0, or the limit of 0. Why Zero? whats the significance? and Instanteous? How? Why is that relevant?

 

I didn't want to make a new thread about it...but I might need to ask more questions as someone explains.

 

I also would like to thank all those who help so I can get over this barrier. I enjoy science, but without the mathematical knowledge its hard to get past the basics. Not that I will ever get past them, hell I am still figuring out SP/GR and QM and Ferimons, and....Gluons, and warped space time ( Still having a hard time visualizing it but I am getting there. )

 

For a mere Metal Casting tech I bet I am treading in increasingly deeper waters without the knowledge of how to swim, but i'll see how far I can get.

 

p.s.

 

Sorry for the long read, I am sure most of it is pointless but yeah.

[Yggdrasil]

Basically, taking a derivative allows you to find the slope of a line tangent to a curve at a specific point. This is important because many slopes have important physical meanings (e.g. in a distance v. time graph, the slopes represent velocities).

[Dave]

Look up the couple of calculus lessons that I've posted in this forum. I've tried to explain the concept of a limit there, and how it all ties together with the derivative.

[RyanJ]

Look up the couple of calculus lessons that I've posted in this forum. I've tried to explain the concept of a limit there, and how it all ties together with the derivative.

 

Too add to that Wikibooks has a good book too start from. Its not finished yet but the section you need is finished: here.

 

Also, check out the useful links thread. It has some good links you may find useful.

 

Oh and here are the links for Dave's tutorials:

 

• Calculus I: Lesson 1 - A background to differentation
  
• Calculus I - Lesson 2: A continuation from first principles
  
• Calculus I - Lesson 3: Properties of the derivative
  

 

Cheers,

 

Ryan Jones

[Dave]

Specifically, the first and second tutorials will be most useful.

[matt grime]

You get in a car and it accelerates away. What was your velocity at any given time? How could you work it out?

 

Well, you could average the distance travelled over the time taken, but that would only be a rough estimate of your speed at any given instant, the so-called instantaneous thing you're thinking about. So, to get a better idea of your speed at some given time you could measure the distance travelled in a small time period about that instant dividing by the length of the time period. The key idea is that as we let that time period get smaller and smaller, the better and better that estimate will be of the actual velocity you were travelling at that instant.

 

In less physical terms, suppose you want to estimate the tangent slope to a curve, then you should try to draw a little chord on the graph to estimate it, the smaller the chord the better the approximation.

 

The limits as these little time periods tend to zero, or little chord lengths tend to zero, is the instanteous 'rate of change'. In the first case it is distance over time, ie velocity (ok, displacement), the second it is just the abstract y with respect to x.

[GutZ]

 

I am a happy man, thank you.

 

I'll have to read it all over but what I am getting is that:

 

Your measuring a curve (essentially?). I guess you can average it out but that makes it less accurate in a sense (Kind of like taking a bunch of rounded numbers and adding them up...well not exactly but you know...). With Calculus you can take any given section or point (instanteous?) and find out the rate of change to a more accurate/percise calculation?

 

You know I've take a course with Calculus in college and some how pasted it. I must of done REALLY well on the 2/3 rd's of the semesters material. Eeek.

[matt grime]

Why do so many people attempt to make inaccurate and unhelpful 'kind of like...' statements? It is what it is, nothing to do with rounding up or anything.

 

"With Calculus you can take any given section or point (instanteous?) and find out the rate of change to a more accurate/percise calculation?" doesn't make sense as a sentence.

[GutZ]

Well it was more of an example...nothing to do with Calculus.

 

Like what you said:

 

Non - Calculus Method

"you could average the distance travelled" vs "over the time taken"

1)^ Simplification

 

General Mathematics

"Rounding numbers"

2)^Simplification

 

 

1 and 2 are common.

 

I don't think it's an attempt either, it's much easier to explain it properly.

 

But thanks for the deep analysis! I will try and construct my sentences in a more formal matter, using more precise/perfected ideas.

[matt grime]

The important part of language and communication is that you manage to express to someone else what it is that you wish to express. I have no idea from what you asked what is that you wish to know, or communicate.

[GutZ]

Yeah well I get lazy from time to time, and incoherent messages happen. My apologizes, but really the analysis wasn't really needed. I guess though if that's what you do primarily for long periods of time (i.e. Scienists), you do it subconsciously.

 

Anyways I got it now. So I will work on it again with my old math book that has been collecting dust.

 

So I believe this thread can be closed or whatever you guys do with threads that are pointless to keep open. Been to many forums, so Im assuming thats what most do, so don't kill me if I am wrong.

 

[Dave]

Don't worry, they just become inactive over time

[matt grime]

Yeah well I get lazy from time to time, and incoherent messages happen. My apologizes, but really the analysis wasn't really needed. I guess though if that's what you do primarily for long periods of time (i.e. Scienists), you do it subconsciously

 

I just didn't wish you to think I was being crabby and rude; replies often appear that way because you write what you'd say in person, and the intent is less clear.