Calculus Made Easy (Free book)
By Murray Bourne, 25 Apr 2009
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:
THOSE BEAUTIFUL METHODS OF RECKONING
WHICH ARE GENERALLY CALLED BY THE
TERRIFYING NAMES OF THE
SILVANUS P. THOMPSON
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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