Calculus Calculus Made Easy by Silvanus P. Thompson

[bcrowell]

• Author: Silvanus P. Thompson
• Title: Calculus Made Easy
• Amazon Link: https://www.amazon.com/dp/0312185480/?tag=pfamazon01-20
• Download Link: http://www.gutenberg.org/ebooks/33283
• Prerequisities:

Table of Contents:

[LIST]
[*] Prologue
[*] To deliver you from the Preliminary Terrors
[*] On Different Degrees of Smallness
[*] On Relative Growings
[*] Simplest Cases
[*] Next Stage. What to do with Constants
[*] Sums, Differences, Products and Quotients
[*] Successive Differentiation
[*] When Time Varies
[*] Introducing a Useful Dodge
[*] Geometrical Meaning of Differentiation
[*] Maxima and Minima
[*] Curvature of Curves
[*] Other Useful Dodges 
[*] On true Compound Interest and the Law of Organic Growth
[*] How to deal with Sines and Cosines
[*] Partial Differentiation
[*] Integration
[*] Integrating as the Reverse of Differentiating
[*] On Finding Areas by Integrating
[*] Dodges, Pitfalls, and Triumphs
[*] Finding some Solutions
[*]Table of Standard Forms
[*] Answers to Exercises
[/LIST]

 

[bcrowell]

This is a wonderful, friendly, brief introduction to calculus, from 1910. Many 20th-century scientists and mathematicians learned calculus from it. The Project Gutenberg version has been converted into LaTeX. The version currently in print has been revised by Martin Gardner.

 

[MarneMath]

I enjoyed reading this book back in high school. Although, if I do recall it's a bit dated in termology, but it's a short read, and by the end of the book you come out with a fairly good grasp on basic calculus. Enough to give you the courage to learn more.

 

[atyy]

I read the original version. It's very short and accessible.

 

[mathwonk]

i never learned anything from this book but i loved its tone and humor. I have looked again more closely at it recently and still love the style of it but have noticed serious shortcomings related to actually learning calculus from it. Namely he does not explain why the rules he gives should be believed, and many statements are technically false. Thus one who seeks to understand what he reads will be left wanting here.

 

[jimmyly]

I'm reading this right now along side Quick Calculus, Stewart's, and MIT OCW and I am finding it pretty helpful and gives a different perspective than the other book. Great book

 

[davidmoore63@y]

First calculus book I ever read (back in the 1970s), and the best introduction I have ever seen.

 

[davidmoore63@y]

In fact I would expand on my previous post. When I started this book, aged 14 in 1977, I knew no calculus. I read it non stop for about a week, and completed all the exercises, by which time I was very comfortable with single variable calculus. What I particularly remember is how the book opened my eyes to great new things, without seeming to involve much effort. Very natural. My 1977 copy is on the top shelf of my bookcase, waiting for my kids to be old enough to read it...

 

[Tachyon_Jay]

It's what I read when I couldn't understand much from the advanced books. It's really helpful and encouraging.. this book. A must read if you are just starting Calculus.

 

[Imager]

For me calculus was 30 years ago, this sounds like a good refresher.

I order using the link provided, so hopefully Physics Forums get a credit from Amazon!

 

[PhysicsLad]

Very nice book but it assumes you know the binomial expansion for positive and negative exponents. Make sure you review those first.

 

[o49183]

, and many statements are technically false.

Can you elaborate on this? How bad is it?

I have a copy of the updated 1998 edition that I'm intending to go through in order to get a decent conceptual overview of calculus, before learning it properly from Spivak a few months later.

Are there any specific false statements that I should be aware of while reading it, or are they all trivial, considering that I will do Spivak later?

 

[mathwonk]

I don't remember what statements I was talking about, but I am guessing it won't matter to you as a learner. I.e. we learn gradually by degrees, and very likely the false statements will not be visible to a first time learner. So if you read it and learn what you can and then progress to another more precise book, not even necessarily as precise as Spivak, the errors will just become more clear and fall away and you will fill in the more correct versions with no problem. So don't worry about it. Just try to ask yourself why each statement is true, and put an asterisk by anything not completely proved, if you like.

OK here's one: on page 9, line -6 he says that when x changes to x+dx, then y changes to y-dy, because y decreases. This is wrong. y always changes to y+dy, but sometimes dy is negative.

 

[o49183]

Thank you.

 

[WWGD]

i never learned anything from this book but i loved its tone and humor. I have looked again more closely at it recently and still love the style of it but have noticed serious shortcomings related to actually learning calculus from it. Namely he does not explain why the rules he gives should be believed, and many statements are technically false. Thus one who seeks to understand what he reads will be left wanting here.

I agree; if one is willing to put rigor aside temporarily and fill it in later, this book works well. And there is nothing wrong with following a mixed bottom-up and/or top-down approach.

 

[jerromyjon]

Just started reading the download and page 5...
"then 1/ 1,000,000 of 1/ 1,000,000 , that is 1/ 1,000,000,000,000 (or one billionth)"
That's 1 trillionth, right? Not that it discourages me from continuing, I like spotting errors!

 

[mathwonk]

well that is not one of the errors, but rather a change over time in the meaning of the word "billion" in England.

\https://en.wikipedia.org/wiki/1,000,000,000

 

[WWGD]

Pretentious B.S reply: Shouldn't it be Calculus made _hard_? It is already easy...:) . My prof used to say this, jokingly, of course.