Best Calculus Textbooks: Thomas/Finney 9th Edition

[VertexOperator]

Hi,
What is the best calculus textbook?
I borrowed Thomas/Finney 9th Edition from the library the other day and I like it a lot but I don't know if it is the best textbook out there.
The good thing about Thomas/Finney Calculus is that is covers a lot of topics ranging from conic sections to real analysis.

 

[micromass]

It depends on what you're looking for in a calculus textbook.

In my opinion, Spivak is the absolute best calculus textbook out there. But of course, the book is fairly rigorous and proofy. It is hardly a book that one should use for a first encounter to calculus.

 

[VertexOperator]

It depends on what you're looking for in a calculus textbook.

In my opinion, Spivak is the absolute best calculus textbook out there. But of course, the book is fairly rigorous and proofy. It is hardly a book that one should use for a first encounter to calculus.

I have learned most of calculus (it is a huge part of the school curriculum) so I will have a look at Spivak, I might like it more than Finney.
Why is real analysis a topic that is partially covered in most calculus textbooks? Why isn't there a separate book dedicated for analysis? Or is analysis a part of calculus?

 

[micromass]

I have learned most of calculus (it is a huge part of the school curriculum) so I will have a look at Spivak, I might like it more than Finney.
Why is real analysis a topic that is partially covered in most calculus textbooks? Why isn't there a separate book dedicated for analysis? Or is analysis a part of calculus?

There absolutely are textbooks dedicated to analysis. Calculus is actually a subset if mathematical analysis. One could say that calculus is analysis but without proofs.

To be able to start learning analysis, you need to have a good grasp on both calculus and proofs. The first thing you'll do in analysis will be to rigorously define and work out the calculus concepts. For example, you will rigorously define continuity and limits using $\varepsilon-\delta$ definitions and you will prove all the limit, derivative and integral identities you encountered in calculus.
After that, analysis deals with topics which are not covered in calculus anymore. For example, Fourier series, functional analysis, complex analysis, etc.

If you want separate books dedicated to analysis, then I would suggest
- Knapp: "Basic real analysis"
- Carothers: "Real analysis"
- Bridges: "Foundations of Real and Abstract Analysis"
- Berberian: "A First Course in Real Analysis"
- Apostol: "Mathemathical Analysis"
- Lang: "Undergraduate Analysis"
- Abbott: "Understanding Analysis"

Some of these books are more advanced than others. Finally there is of course also Baby Rudin, but I don't like it very much...

 

[VertexOperator]

There absolutely are textbooks dedicated to analysis. Calculus is actually a subset if mathematical analysis. One could say that calculus is analysis but without proofs.

To be able to start learning analysis, you need to have a good grasp on both calculus and proofs. The first thing you'll do in analysis will be to rigorously define and work out the calculus concepts. For example, you will rigorously define continuity and limits using $\varepsilon-\delta$ definitions and you will prove all the limit, derivative and integral identities you encountered in calculus.
After that, analysis deals with topics which are not covered in calculus anymore. For example, Fourier series, functional analysis, complex analysis, etc.

If you want separate books dedicated to analysis, then I would suggest
- Knapp: "Basic real analysis"
- Carothers: "Real analysis"
- Bridges: "Foundations of Real and Abstract Analysis"
- Berberian: "A First Course in Real Analysis"
- Apostol: "Mathemathical Analysis"
- Lang: "Undergraduate Analysis"
- Abbott: "Understanding Analysis"

Some of these books are more advanced than others. Finally there is of course also Baby Rudin, but I don't like it very much...

Thank you for the suggestions. I will try to find PDF's of these books online to see which one I like the most.
At the moment I can't really prove series questions unless I am given steps which lead to the answer (or by induction). Should improve with practice :)

 

[autodidude]

I personally prefer Stewart's text (no need for the newest edition) to Thomas and Finney's, but that's just me. I think Stewart is a tad more rigorous - there are some things in T&F that are just given and not proven or explained. But in the end, no matter what book you're learning from, you'll get the most benefit if you don't shy away from the harder questions :p

 

[VertexOperator]

I personally prefer Stewart's text (no need for the newest edition) to Thomas and Finney's, but that's just me. I think Stewart is a tad more rigorous - there are some things in T&F that are just given and not proven or explained. But in the end, no matter what book you're learning from, you'll get the most benefit if you don't shy away from the harder questions :p

I have all the calculus textbooks as PDF's but I prefer actual books, which is why I like Finney's haha.

 

[autodidude]

I have all the calculus textbooks as PDF's but I prefer actual books, which is why I like Finney's haha.

Oh, I see. Yeah, I prefer hard copies too. My old library had a bunch of different 'standard' calculus books (plus I bought a couple of cheap, used ones) so I've looked at all of them and decided I like Stewart's the best out of all of them.

 

[VertexOperator]

Oh, I see. Yeah, I prefer hard copies too. My old library had a bunch of different 'standard' calculus books (plus I bought a couple of cheap, used ones) so I've looked at all of them and decided I like Stewart's the best out of all of them.

I will try and find a cheap Stewart hard copy, or hopefully find it at the library.

 

[micromass]

In my opinion, Stewart is a truly horrible book. It shouldn't even be called a math book. The calculus books by Spivak, Apostol, Lang or Kleppner are vastly superior.

 

[VertexOperator]

In my opinion, Stewart is a truly horrible book. It shouldn't even be called a math book. The calculus books by Spivak, Apostol, Lang or Kleppner are vastly superior.

I was just looking through the Spivak PDF and I like it a lot. Not as pretty as the others but I like the structure. Explanation of the concept followed by about 30 questions per chapter. Wish I can find solutions.

 

[dustbin]

There are solutions on scribd.