Calculus made easy на русском

Calculus Made Easy

by
Silvanus P. Thompson

What one fool can do, another can.

(Ancient Simian Proverb.)

Table of Contents

About this book

Calculus Made Easy is a book on calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject.

I read «Calculus Made Easy» by Silvanus P. Thompson and it’s still to this day my inspiration for explaining complex technical topics to lay people. It’s a fantastic book, and even if you know math you must read it if you want to understand how to teach complexity to others. (source)

Thompson creates a warm, inviting environment where students will learn and grasp the true essence of calculus without any added fluff or overt technicality. (source)

Most college calculus texts weigh a ton; this one does not — it just gets to the point. This is how I learned calculus: my uncle gave me a copy. (source)

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What next?

About this edition & thanks

Thanks to Paula Appling, Don Bindner, Chris Curnow, Andrew D. Hwang and Project Gutenberg Online Distributed Proofreading Team for preparing the original PDF.

The theme is borrowed from Dive Into HTML5 by Mark Pilgrim released under the CC-BY-3.0 license.

Sums, Differences, Products and Quotients

The answer to this question is quite simple: just differentiate them, one after the other, thus: \[ \dfrac = 2x + 4ax^3. (Ans.) \]

If you have any doubt whether this is right, try a more general case, working it by first principles. And this is the way.

And we shall have:

This justifies the procedure. You differentiate each function separately and add the results. So if now we take the example of the preceding paragraph, and put in the values of the two functions, we shall have, using the notation shown (chapter III), \begin <2>\frac & = \frac &&+ \frac \\ & = 2x &&+ 4ax^3, \end exactly as before.

But when we come to do with Products, the thing is not quite so simple.

Now there are two ways in which we may go to work.

First way. Do the multiplying first, and, having worked it out, then differentiate.

Now differentiate, and we get: \[ \dfrac = 6ax^5 + 4acx^3 + 2bx. \]

Now, having found this rule, apply it to the concrete example which was considered above.

We want to differentiate the product \[ (x^2 + c) × (ax^4 + b). \]

Then, by the general rule just established, we may write: \begin <2>\dfrac &= (x^2 + c)\, \frac &&+ (ax^4 + b)\, \frac \\ &= (x^2 + c)\, 4ax^3 &&+ (ax^4 + b)\, 2x \\ &= 4ax^5 + 4acx^3 &&+ 2ax^5 + 2bx, \\ \dfrac &= 6ax^5 + 4acx^3 &&+ 2bx, \end exactly as before.

Lastly, we have to differentiate quotients.

As both these remainders are small quantities of the second order, they may be neglected, and the division may stop here, since any further remainders would be of still smaller magnitudes.

This gives us our instructions as to how to differentiate a quotient of two functions. Multiply the divisor function by the differential coefficient of the dividend function; then multiply the dividend function by the differential coefficient of the divisor function; and subtract. Lastly divide by the square of the divisor function.

The working out of quotients is often tedious, but there is nothing difficult about it.

Some further examples fully worked out are given hereafter.

A direct way of doing this will be explained later (see here); but we can nevertheless manage it now without any difficulty.

Same remarks as for preceding example.

This, again, could be obtained more simply by multiplying the two factors first, and differentiating afterwards. This is not, however, always possible; see, for instance, here, example 8, in which the rule for differentiating a product must be used.

Exercises III

Find the differential coefficients of

Find an expression giving the variation of the current corresponding to a variation of temperature.

Find the rate of variation of the resistance with regard to temperature as given by each of these formulae.

Find an expression for the variation of the electromotive-force (a) with regard to the length of the arc; (b) with regard to the strength of the current.

Answers

Calculus Made Easy

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Calculus Made Easy

LibriVox recording of Calculus Made Easy by Silvanus P. Thompson.
Read in English by LibriVox volunteers.

Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus is is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject. (from Wikipedia)

Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the textbooks of advanced mathematics—and they are mostly clever fools—seldom take the trouble to show you how easy the easy calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can. (from the Prologue)

For further information, including links to online text, reader information, RSS feeds, CD cover or other formats (if available), please go to the LibriVox catalog page for this recording.

Calculus Made Easy (Free book)

OK, it looks old and dusty, but Calculus Made Easy [PDF] is an excellent book and I strongly recommend it to those of you who are struggling with calculus concepts. It’s also great for teachers, to give you ideas on how to explain calculus so it doesn’t confuse the hell out of everyone. He quite rightly points out that many math text book writers are more interested in impressing the reader with sophisticated calculus techniques than explaining the basic concepts.

One of the early pages has:

In other words, this was one of the first ever «Calculus for Dummies» books. Thompson puts great effort into explaining what is going on, rather than jumping straight into the calculations. He humbly calls himself a «fool», but doesn’t treat the reader as one.

He quotes from an «ancient Simian proverb»:

«What one fool can do another can.»

To give you an idea of how the book is written, in Chapter 1, «To Deliver You From the Preliminary Terrors», we read:

∫ which is merely a long S, and may be called (if you like) «the sum of.» Thus ∫dx means the sum of all the little bits of x; or ∫dt means the sum of all the little bits of t. Ordinary mathematicians call this symbol «the integral of».

Now any fool can see that if x is considered as made up of a lot of little bits, each of which is called dx, if you add them all up together you get the sum of all the dx‘s, (which is the same thing as the whole of x). The word «integral» simply means «the whole».

The book is now copyright free. Grab the PDF: Calculus Made Easy.

[Thanks to Denise at LetsPlayMath for the link.]

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44 Comments on “Calculus Made Easy (Free book)”

thanks so much for sharing this excellent book!

best regards,
an old fool

You’re welcome Solarhene. I’m glad that you find it useful.

i believe it can work and it will work

I’m so interested in re-learning calculus that I watched many different video tutorials, but I found this book summarizing Integral Calculus in its first 2 pages!

Thank you so much!

Thanks so much for posting this. I’m so glad I clicked on your link while viewing my friend Dana’s blog. My 9 year old read it and was very excited that it made so much sense. He’s currently taking Physics and some of the math problems were made to be so confusing so this will help him so much.

Good DAY SIR,i want to know how i can get this text book,calculus made easy.i am mailing from Lagos Nigeria.thank u sir.

This is an e-book in PDF form (not a physical book). The link is in the article above, in the first line.

You could print it out from the PDF if you would rather hard copy.

Its a brilliant book. Thanks for sharing the book

Thanks for sharing this book! It will be a great tool for my independent study students!

Thanks for great job well done. Do the same with other topics such as trigonometry and complex numbers

the way you have started culculus is very interesting but how could one get the whole PDF paper?

Hi Judith. The link to the PDF is in the article above! Do you mean that you want a hard copy? You would need to print it yourself.

if every mathematics topic could be introduced the way this has, then i sure no one will think of maths as the hardest of courses.

make me realize the math is easy

one of the greatest books.. many thanks for sharing with us

You’re welcome, Rod. Glad you found it useful.

@Fatemeh: I’ll look for such materials and post it if I find any good ones.

thanks! and great work which nobody cannot be appreciated for your effort for sharing such good book.

It can be downloaded at
http://www.gutenberg.org/ebooks/33283
which is typed in LaTeX and the file size is reduced tenfold.

@Dalcde: Thanks for the tip!

Hi :
Thanks for the pdf on Calculus Made Easy.
I have always been curious and terrified at the same time of calculus.

Chapter One says it all. Getting past the fancy notation, helps a huge amount.

Kind Regards Ian Thomson

Hi! Ian,My name is percy and I teach Maths in grade 12. Please foreward me the calculus doc as I also struggle on calculus section.

@Percival: The link to the PDF is at the top (and again at the bottom) of the article.

Dear Murray
I am surprised and delighted to see my old Dear Friend Sylvanus P. Thompson here. As a very discouraged high school dropout I found an original hardback version at the rubbish tip site where I used to spend my spare time. I picked it up and the proverb just grabbed me. I read the book it and loved it. I went back to school and excelled at the age of 25. Now after 40 years in senior positions in Telecommunications in Australia my copy is very much treasured and repaired and again being used as I transition into becoming a teacher myself! The bit that initially grabbed me was «What one fool can do another can» I ask that you put that wonderful saying up on this site. It was so powerfuly encouraging it got me off the bad path I was on and led to a wonderful career and a wonderful wife and family. Imagine, it hardly seems possible that an ancient seven word proverb, repeated in one book by a man long dead could do so much good.
I love this guy and would have loved to have met him.

Kind Regards
Joe Kenyon

Thanks for your inspiring story, Joe!

I have included the quote in the article.

Hi,
I have been searching such work for past couple of months and at last I got here in the form of «Calculus Made Easy» May GOD Bless all who have made such efforts in preparing such an excellent book.

Sachin Sharma
India

Thanks for posting this. and for free! While I struggled with math from grade school to grad school, I’m now a bit of a math junkie and books with subjects like this really pique my interest. I wish I could get my hands on an actual copy of that book for myself.

One question comes to mind, though. I noticed there are two different dates in the front of the book that confuse me (I’m a sucker for old books). There is a date of 1914 in the preface and another of 1943 by itself on another page. Do you know which date was the actual date of publication? There isn’t an actual copyright year specified and as I read through the text, the absence of that date combined with the style and choice of words lead me to believe this was a work from the early 20th century. I rely on a barely mediocre literary acumen to make that assessment, so take it with an enormous grain of salt.

Thanks and best wishes!

@drcobol2000 The publication date would be 1914, as that’s when he wrote the Preface to this second edition. So your «early 20th century» language observation is right on the button.

I don’t believe the «6-14-43» on the separate page is a date, since in the US, the date order is normally day then month. I suspect it’s there to trigger thought.

Thanks you so much sir for this ebook 🙂

I am an engineering student, and i am struggling with calculus.

This book helped me a lot even though this book is quite old.

Thank you really really much sir. You help me a lot.

thank u so much its very helpful

hi Murry, thanks for sharing the brilliant book,hope you have a lovley day!

Glad you found it useful, Rahillah.

I’m not sure if it’ll work but I’ll give it a try. I’ll write back at the end of the semester to let you know how it worked for me.

Extremely thankful for uploading this book. My father left this book when he expired and I learnt calculus from this book. But I donated this book to some and later when my son started studying calculus I remembered this book and started searching. Once again thanks

@gururaj: You are welcome!

Calculus made easy is the simplest book to understand in self studies.

Calculus Made Easy 4+

D.P STACE & G.J STACE & S.A WILLIAMS

Розроблено для iPhone

Знімки екрана iPhone

Calculus made Easy is an app for students wanting to master Calculus the easy way. Using the knowledge of a teacher who has taught for over 38 years with a Pure and Applied Mathematics Degree, you will find learning calculus a breeze.

Calculus made Easy has tutored lessons which shows step by step worked examples. Calculus Made Easy is designed to help you understand Calculus, having your own Maths Tutor when and where you need it.

This app covers the following topics:
* Definition of Function
* First Principles for Differentiation
* The Gradient of a Tangent
* Rules for Differentiation
* Function of a function rule
* Product Rule
* Quotient Rule
* The derivatives of the function of Trigonometry.

“iTeachers” aim to provide easy to understand lessons using new age
technology, taught the old fashioned way.

With our International content, easy to understand, fast-paced lessons. You will soon be top of the class.

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