An easy to read calculus book

[Weissritter]

O hai again, PF.
So...for the next semester, which starts roughly in January, I'll be taking calculus. However, I will meet again with the toughest teacher in my school. So, it will be harder for me to actually understand calculus.
And so, I send this distress call: I want to start studying a bit already. I am in the search of an easy-to-read book, easy, or low leveled, as you want to call it. Something easy to digest.
So...what book do you recommend to this high school student?

 

[micromass]

I would try something like "A first course in calculus" by Serge Lang. The book doesn't deal with epsilon-delta stuff, which makes it easy. On the other hand, everything else is worked out fairly rigorously.

 

[bcrowell]

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

 

[atyy]

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?

 

[Cod]

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

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

 

[bcrowell]

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

I haven't carefully compared them side by side. The amazon page says that it's a pretty major revision: https://www.amazon.com/dp/0312185480/?tag=pfamazon01-20

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...?

 

[micromass]

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.

 

[Weissritter]

Have no worries, my minions, OP has reappeared for clearing up what I said earlier:
"I don't have the slightest idea about calculus, yet I think I am somewhat smart when it comes to math. My knowledge level, anyway, requires a beginning textbook"
And now, I proceed to ask for forgiveness if you didn't consider yourself my minion...I just wanted to say that.
And yes, beginning textbook.

 

[bcrowell]

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.

 

[micromass]

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.

For example, p.17-18

Let $x$, then, grow a little bit bigger and become $x+dx$; similarly,
will grow a bit bigger and will become $y+dy$. Then, clearly, it will still
be true that the enlarged $y$ will be equal to the square of the enlarged $x$.
Writing this down, we have:
$$y+dy= (x+dx)^2$$
Doing the squaring we get:
$$y+dy=x^2+ 2xdx+ (dx)^2$$:
What does $(dx)^2$ mean? Remember that $dx$ meant a little bit of $x$. Then $(dx)^2$ will mean a little bit of a little bit of $x$; 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.

This is just horrible. They never explain what dx really is. They never explain why dx cannot be dropped while $(dx)^2$ 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 "$(dx)^2$ drops because it is very very small". If I were to read that book, I would have been utterly confused by it all.

 

[Cod]

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 can't see where he asked for a beginning textbook in the original post. He asked for an easy-to-read calculus book originally. Saying Thompson is not a textbook is my personal opinion.

 

[mathwonk]

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.

 

[Weissritter]

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 $(dx)^2$ 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 "$(dx)^2$ 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.

 

[Cod]

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.

You could try The Calculus Lifesaver by Adrian Banner (https://www.amazon.com/dp/0691130884/?tag=pfamazon01-20). I went through it during the semester before I took Calculus I and still use it today if I need a quick reference. The book also does a great job of explaining what can be skipped if you're a beginner. Also, the sections on limits are fantastic.

Oh, and its cheap ($15 usd). Also, you can preview the book on Amazon.

 

[dustbin]

I've seen Courant's calculus text in several other languages, which is available for free on many sites. I do not remember all of the places I've seen translations, as I cannot read in any language other than English.

 

[bcrowell]

This is just horrible. They never explain what dx really is. They never explain why dx cannot be dropped while $(dx)^2$ 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 "$(dx)^2$ drops because it is very very small". If I were to read that book, I would have been utterly confused by it all.

Hee hee...if you'd asked me to give an example of one thing I really liked about this book, it would have been exactly this passage.

For one who wants to see infinitesimals done rigorously, at the freshman calc level, there is this book by Keisler: http://www.math.wisc.edu/~keisler/calc.html But for someone like the OP, I think Thompson is exactly right...for exactly the same reasons that you hate it.