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#1 2012-07-15 17:40:37

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Introduction to Calculus

What do you guys think of this page: Introduction to Calculus


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#2 2012-07-15 19:17:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Introduction to Calculus

Hi MathsIsFun;

Very well done. I always enjoyed the manipulations using Δx instead of the dry differentiation rules. That was for me the reason calculus was fun. I think you have passed that on to anyone reading your page.

Also, I liked the use of Sam and Alex telling a story. But next time do not make them so friendly. Purists ( Galileo society ) are not going to appreciate the equation d = 5t^2.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#3 2012-07-15 19:40:08

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Introduction to Calculus

Hi MathsIsFun,

I like this page a lot.  It's a tough subject to explain simply, but you've managed it.

Two suggestions:

(i)

"BUT", says Alex, "again that is an average speed, since the jump, ... I want to know the speed at exactly 1 second, so I can set up the camera properly."

Would you consider re-wording this to

"BUT", says Alex, "again that is an average speed, since you started the jump, ... I want to know the speed at exactly 1 second, so I can set up the camera properly."

(ii)  For the graph y = x^3 at x = 1.

Could you make one of your brilliant interactive demos to show the graph with a user movable point close to (1,1).  At the side is a table showing the coordinates of the point (eg ( 1.1, 1.331), the differences in x and y, and the gradient of the chord joining them.  The user moves the point closer and can see the values 'home in' on the gradient at the point.

Option to zoom in ?

And you could add a modified version to the Derivatives page.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2012-07-15 19:40:52

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

Thanks bobby!

(Locally high gravity ... yes, that's it.)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2012-07-15 23:01:21

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,130

Re: Introduction to Calculus

Hi MathsIsFun,

The page 'Introduction to Calculus' is well presented. Excellent work!


Character is who you are when no one is looking.

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#6 2012-07-15 23:38:20

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

Thank you, ganesh smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2012-07-18 01:23:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Introduction to Calculus

Hi MIF

It all makes sense now. My physics techer always used the terms when delta t approaches zero, but we never learned limits and derivatives applications.

I also suggest a page on integrals.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2012-07-26 20:07:13

debjit625
Member
Registered: 2012-07-23
Posts: 91

Re: Introduction to Calculus

I am not expert in calculus,I am still learning...but that was basic and as all the lessons at MathIsFun site, its also easy to understand ,and I like it...

Just as anonimnystefy said ,in future it would be good to have a page which have all the links to calculus..like functions,limits,differential calculus,integral calculus,some special trigonometric relations,I know it will take time,so keep it up.

Good Luck


Debjit Roy
___________________________________________________
The essence of mathematics lies in its freedom - Georg Cantor

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#9 2012-07-27 09:56:29

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

Thanks anonimnystefy and debjit625, will try to make more pages as time permits smile


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#10 2012-07-27 10:01:45

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Introduction to Calculus

That's great. Your website is getting better by the moment (who knew it was possible).

Last edited by anonimnystefy (2012-07-27 10:01:58)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2012-07-27 18:49:26

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Introduction to Calculus

hi MathsIsFun,

Did you see post #3  ?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#12 2012-07-27 20:00:09

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

No ... no I didn't ... it seems I was replying to bobby while you were posting!

Thank you for those wonderful suggestions, I will work on them.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#13 2012-07-27 22:06:30

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Introduction to Calculus

I thought that might have happened.

Thanks.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2012-07-27 23:00:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Introduction to Calculus

bobbym wrote:

Hi MathsIsFun;

Very well done. I always enjoyed the manipulations using Δx instead of the dry differentiation rules. That was for me the reason calculus was fun. I think you have passed that on to anyone reading your page.

Also, I liked the use of Sam and Alex telling a story. But next time do not make them so friendly. Purists ( Galileo society ) are not going to appreciate the equation d = 5t^2.

Let's see you differentiate sin^11(x) using the delta x operator. roflol

Last edited by anonimnystefy (2012-07-27 23:01:08)


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#15 2012-08-01 15:34:23

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

I have finally finished a draft of the slope interactive (suggested by Bob).

Here it is: Slope of a Function at a Point

What do you think guys? How about the explanation?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#16 2012-08-01 16:32:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Introduction to Calculus

Hi MathsIsFun;

Can you provide an (x,y) pair for A and B?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#17 2012-08-01 18:34:11

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

Will work on it, good idea.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#18 2012-08-01 19:11:33

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Introduction to Calculus

hi MathsIsfun,

That's brilliant and you have done it so quickly!!  smile

I would like to be able to specify the (x,y) coordinates and 'lock them in' for the duration of the interaction.

eg.  Say I want the gradient at (1,1) on y = x^2. 
Point A becomes (1,1) at all zoom levels, and only B can be varied.

There would then need to be a 'change  point A'  button.

Secondly, could you have a 'display table' option so that the calculations can be seen.  (see picture below)

I've shown a table with 3 lines of calculations but, for the page, I'm thinking a single line that changes as B is moved, would be best.

(and I've used dx only because I cannot make a 'delta' in Excel)

Many thanks,  smile

Bob

View Image: slope1.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#19 2012-08-06 11:33:01

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,552

Re: Introduction to Calculus

New version! Slope of a Function at a Point (use refresh)

Shows coords of points, has a calculation box down below, and allows for setting coords of points using "edit" button.

Waddya think?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#20 2012-08-06 18:50:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,455

Re: Introduction to Calculus

Hi MathsIsFun;

Works for me! When I use the edit button it allows me to enter say (3,6). This is not on y = x^2. Could you make it that you only have enter the x value and the y value is computed automatically.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#21 2012-08-06 19:30:06

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,528

Re: Introduction to Calculus

hi MathsIsFun,

Thanks for doing that.

I agree with bobbym about having the y coords calculated for you.  As the aim of this demo is to show the chord gradient approaching the limit as the points get closer, it should always be points on the curve, so you might as well force that. (If someone just wants to play with gradients of any points you already have a demo for that on the straight line page)

When there are many decimals places, the display gets messy and the slope box isn't large enough to show the final calculation.

For my screen shot I had y = sin(x) and A = (1.570796,1)

(i) Do you really need to put the slope value on the graph when it is shown in the box anyway?

(ii)  Could you make the box larger and maybe have a round off limit so the display is always clear?

Thanks,

Bob

View Image: diff.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#22 2012-08-30 00:19:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Introduction to Calculus

I agree with bobbym and Bob. I also found out that when I put the points together, it says "Points too close".


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#23 2012-10-11 02:44:34

ShivamS
Member
Registered: 2011-02-07
Posts: 3,627

Re: Introduction to Calculus

Brilliant. But frankly, I believe that you should create a counterpart site to MIF. That allows you to create more advanced tutorials on a slightly different site.

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