1.2 what is calculus and why do we study it

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1.2 What Is Calculus and Wh do we Stud it?

C . I ,

.

I have been around for a while, and know how things change, more or less. What can calculus add to that?

I . A . F

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So what does calculus add for me?

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To what end?

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A. A

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Are you trying to claim that I will know enough about calculus to model systems and deduce enough to

control them?

I I . N ,

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OK, but how does calculus models change? What is calculus lik e?

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And what good is that?

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And so?

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So what does one study in learning about calculus?


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T .

T function. A

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I will get bogged down if I read about such stuff. Must I?

I , I , , , . H ,

. (T I .)

And what comes after numbers and functions?

A :

1. H ( "") . (T

"differentiation".)

2. H .

3. H . (T "integration".)

4. S .

5. H ,

.

T . T

, "" .

So where does this empower me to do what?

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. M

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. T " "

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So wh this nonsense about empowerment?

T . I ,


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b a ea i .

And how will it try to perform this wonder?

Tadiia cac ce ehaie agebaic ehd f efig diffeeiaig ad iegaig. We i

decibe ch ehd, b a h h ca ef diffeeiai ad iegai (ad a i f

dia diffeeia eai) a ce eadhee ih a eabe a f eff. We i a

ae hich d he ae aaica ih ee e eff. Wih hee ae, a eadhee, ca a he

f cac ih geae eae ad feibii ha ha bee ibe befe. (Thee ae e adaced ga

ha ae fe aaiabe, ch a MAPLE ad Maheaica, hich a d ch e ih iia eae.) Wihhe ca dedce he ceece f de f ai id i a ide aie f ce.

A, e i ch geae ehai deig e. Wih idea deig ad ehd f ig he

diffeeia eai he ead , ca achiee he eee e hae caied.

And I will be able to use this to some worthwhile end?

Oa, bab . B igh. Ad a igh be ed ea e ab he e a

d ab aheaic, ie chace d . A igh be abe dead he babe

ceece f de a ie bee ha d .

Well, what is in the introductory chapter on numbers?

We a ih he aa be (1,2,3,...,) ad e h he eai f baci, diii ad aig he

ae ead eedig be e icde egaie be, faci (caed aia be)

ad ce be. We a decibe decia eai ad eaie he i f cabii.

And in the chapter about functions?

We a ih a abac defiii f a fci (a a e f age-ae ai) ad he decibe he adad

fci. Thee ae he baied b aig ih he idei fci (ae=age) ad he eeia

fci, ad ig ai eai he.

Operations, what operations?

Thee ae addii, baci, iicai, diii, bii ad iei.

But what is the exponential function, and what are substitution and inversion?

Hee ae e eece ae: if a e ead he chae!

The eeia fci i ei defied ig cac: i i he fci ha i i deiaie, defied

hae he ae 1 a age 0. I , hee, be ehig hae ee befe. Ad i bea a

ce eai he ie fci f ige.

Sbii f e fci f i ahe g dce a e fci, he fci defied hae, a age , he

ae f f a a age hich i he ae f g a age . Thi i ie ha i d.

A iee f a fci i a fci baied b ichig i ae ih i age. F eae he ae

fci, a ie a 2ha he ae fci a a iee.

And ?

I he ia d f Fahe Wiia hi ehe, a eed b Lei Ca, h a a aheaicia:

I hae aeed hee ei ad ha i egh,


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Said the sage, dont give yourself airs.

Do you think I can listen all day to such stuff?

Be off or Ill kick you downstairs!

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