An easy to read calculus book

Calculus Made Easy by Silvanus Thompson: http://www.gutenberg.org/ebooks/33283

Calculus Made Easy by Silvanus Thompson: http://www.gutenberg.org/ebooks/33283

I love the old version of this book. What are your thoughts about the new edition?

If the OP is not looking for a beginning textbook, then I'll second the recommendation for "Calculus Made Easy".

I'm confused by your statement. The OP specifically stated that s/he was looking for a beginning textbook, and Thompson is a beginning textbook. So...?

I don't think Thompson is rigorous enough as a calculus textbook. It seems very dumbed down and the explanations are inadequate.

Can you give an example of a topic where you think this is a problem? If you refer to the old version on Project Gutenberg, we can all see it.

Let [itex]x[/itex], then, grow a little bit bigger and become [itex]x+dx[/itex]; similarly,
will grow a bit bigger and will become [itex]y+dy[/itex]. Then, clearly, it will still
be true that the enlarged [itex]y[/itex] will be equal to the square of the enlarged [itex]x[/itex].
Writing this down, we have:
[tex]y+dy= (x+dx)^2[/tex]
Doing the squaring we get:
[tex]y+dy=x^2+ 2xdx+ (dx)^2[/tex]:
What does [itex](dx)^2[/itex] mean? Remember that [itex]dx[/itex] meant a little bit of [itex]x[/itex]. Then [itex](dx)^2[/itex] will mean a little bit of a little bit of [itex]x[/itex]; that is, as explained above (p.4), it is a small quantity of the second order of smallness. It may therefore be discarded as quite inconsiderable in comparison with the other terms.

I'm confused by your statement. The OP specifically stated that s/he was looking for a beginning textbook, and Thompson is a beginning textbook. So...?

For example, p.17-18



This is just horrible. They never explain what dx really is. They never explain why dx cannot be dropped while [itex](dx)^2[/itex] can be dropped. It seems more like magic than rigorous math. Maybe somebody in the 17th or 18th century would be ok with this approach, but we can do better now. The purpose of math is to give an explanation and foundation of things, not just to assert that "[itex](dx)^2[/itex] drops because it is very very small". If I were to read that book, I would have been utterly confused by it all.

i hink we should ask the OP whether he has looked at any calculus books and which ones he finds hard. then we can scale back and forth from there. i mean some people like silvanus p thompson and some like spivak.

Yes, yes, all hail the Pikachu.
Now, on a serious note:
I haven't looked at a single book for now. However, what micromass quoted was confusing for me. English isn't my main language, and hard English and hard Math do more than synergize. As another example, I could easily read Halo: Ghosts of Onix, but the complexity of Halo: Glasslands made me not read it.
Another way of express what I wanted to say is: a highly popular book either in easy English or famous enough to be translated to more than English, and designed for beginners, or at least not something ridiculously simplified as my future teacher usually does.

This is just horrible. They never explain what dx really is. They never explain why dx cannot be dropped while [itex](dx)^2[/itex] can be dropped. It seems more like magic than rigorous math. Maybe somebody in the 17th or 18th century would be ok with this approach, but we can do better now. The purpose of math is to give an explanation and foundation of things, not just to assert that "[itex](dx)^2[/itex] drops because it is very very small". If I were to read that book, I would have been utterly confused by it all.