Choice between 3 Calculus textbooks -

[christian0710]

I've taken a Calculus course with Steward Calclulus, and to be honest I didn't really like that book, so I'm looking for a new book to have in case I'll need to review some differentiation or integration during my science studies.

I've seen many mathematicians speak about Michael spivak, however my goal is not to become good at mathematical proofs, just to understand how to calculate and interprete derivatives, log functions, integrals etc (often used in biological science and chemistry), just with better and quicker explanations than Steward's book - not towordy and not heavy on proofs.

So far I've come down to the choice between
1) Calculus and Analytic Geometry by George B Thomas and Ross Finney
2) Calculus With Analytic Geometry, Seventh Edition by Ron Larson
3) Calculus With Analytic Geometry by George Simmons

Can anyone recommend one of them for my purpose?

 

[jedishrfu]

Looks like 1 and 3 are the same.

Did you mean same title different editions or same title different authors or some other combination?

 

[christian0710]

Looks like 1 and 3 are the same.

Did you mean same title different editions or same title different authors or some other combination?

Oops you are right, Thank you for spotting that! It's corrected now :)

 

[micromass]

I've taken a Calculus course with Steward Calclulus, and to be honest I didn't really like that book

Why didn't you like the book? This may help us to see what it is you want.

 

[Radarithm]

I recommend A first course in calculus, by Serge Lang:
https://www.amazon.com/dp/0387962018/?tag=pfamazon01-20

Very good book in my opinion; then again, it depends on your tastes.

 

[micromass]

I recommend A first course in calculus, by Serge Lang:
https://www.amazon.com/dp/0387962018/?tag=pfamazon01-20

Very good book in my opinion; then again, it depends on your tastes.

People who know my posts won't be surprised to see me second this book. It's not as theoretical as Spivak, but it does very nicely explain why things are true instead of just letting you memorize the formulas.

One of the major complaints about Lang's book is that it doesn't have enough exercises. Personally, I think there are enough exercises in this book. But if necessary, you can always find tons of calculus exercises online.

 

[Radarithm]

it does very nicely explain why things are true instead of just letting you memorize the formulas.

I vouch; it goes very in depth and although I did get lost at times, it's definitely worth expending some extra brainpower. If you're not into pure math then you can skim through them.

 

[micromass]

I vouch; it goes very in depth and although I did get lost at times, it's definitely worth expending some extra brainpower.

It's certainly no bedtime reading!

 

[christian0710]

Why didn't you like the book? This may help us to see what it is you want.

Great recommendation! That looks like a good book. What specifically do you like about it? . A first course in calculus, by Serge Lang


With respect to Stwardt – what I don’t like: Good point :)

4 Things I did not like about this book compared to the Danish math books I red when studying precalculus. .
1) I Found that there is too much text on some of the pages, missing structure (they seem a bit messy sometimes) and some of the explanations were not as clear and concise as they could be – quite vague and sometimes leaving me wondering what the conclusion is – unfortunately I’d have to read the book again to find specific examples.
2) In many of the calculations he did not say what he was doing explicitly such as “now we can apply the chain rule” or “Now we apply X rule in because we are in Y situation”.
3) The part about integration is too long for review – too many figures (even though I generally love figures) and explanations , while some of the examples were to short – not enough examples especially
4) I know it's a bit anal, but I'd like to have a book half the size, or then perhaps in 2 volumes.

So what is it I’m looking for?
Something shorter and more concise/to the point. Such as:
1) This is differentiation, when you integrate a function you find the tangent to a function which shows you the rate of change of that graph at that spot – here is an example explaining what was just written.
2) Here is a list of the rules with respect to differentiation which we will explore, with some visual figures to it and a short explanation to each figure.
3) Here are a TON of examples for each rule, going through each example without skipping large chunks mathematical rules (Not just applying the chain rule without stating that he is doing it), and doing a good job at distinguishing.
4) Here are some real world situations showing how it’s used, and how to interprete the result we get.
5) Done!

Does it make a bit sence?

 

[verty]

So what is it I’m looking for?
Something shorter and more concise/to the point. Such as:
1) This is differentiation, when you integrate a function you find the tangent to a function which shows you the rate of change of that graph at that spot – here is an example explaining what was just written.
2) Here is a list of the rules with respect to differentiation which we will explore, with some visual figures to it and a short explanation to each figure.
3) Here are a TON of examples for each rule, going through each example without skipping large chunks mathematical rules (Not just applying the chain rule without stating that he is doing it), and doing a good job at distinguishing.
4) Here are some real world situations showing how it’s used, and how to interprete the result we get.
5) Done!

Does it make a bit sence?

So pictures, examples, good coverage of techniques and some real world applications. These don't sound like qualities a calculus book would have but this is a possibility:

https://www.amazon.com/dp/0486404536/?tag=pfamazon01-20

But I think a better idea is to catch up on your math first like you mentioned in the other thread because there won't always be a perfect book, so I think it's better to get back to standard. So if you want to get a book now, I will choose Thomas because it has layout that is very standard and it will have many exercises to cover all the aspects of what is being taught. However if you do get Lang's Basic Mathematics (in the other thread), it may turn out that you like that style of learning.

 

[coffeejunky]

I've been using Ron Larson's 10th edition Calculus textbook, which came out last year. I can't stress how much I liked the book, but here are a few reasons why:

1. The textbook is very easy to read, even if you need "all steps" written down.
2. The 10th edition (not single or multivariable, just Calculus) also covers some differential equations. I'm not sure if all of them do or other textbooks do.
3. There are many examples of what you learn in the beginning of a chapter applied to a real world problem from the natural, physical or social sciences. These examples are not easy and certainly require some thinking, but the book also includes Fourier Series, Laplace Transforms (a few questions) which are interesting as well.
4. Chapter 7 covers "Work" and gives a very brief introduction you might encounter in a physics course, such as Hooke's Law, the spring problem, etc.
5. There is something for every learner, in my opinion. If you learn analytically, you'll be given enough challenging problems. If you learn geometrically, you're in good shape: Applications of integrations will be something you'll never forget. If you learn with applied examples, as mentioned, you'll be happy with this book.

I also own Kline's book, although I never referred as much to it as a supplemental reader. Ron Larson explains it well enough for me, but the price of Kline's book definitely tops every book out there. I would love to see Kline's book as a hardcover on better quality paper with more graphics, but of course that's not what you pay for.

 

[verty]

Isn't Larson one of those money-mill books with a new edition every 3 or 4 years, with a lot of stuff on the CD to get you to buy the new edition, with reviews on review sites that one can hardly trust and including topics that you shouldn't learn yet like Laplace transforms to make the book look more complete?

I mean look at https://www.amazon.com/dp/0618141804/?tag=pfamazon01-20. You've got one guy, not using his own name, who gives it 5 stars and calls it "the best all purpose high school and undergraduate book of it's kind", are you telling me he's surveyed all the calculus books? But he only mentions Stewart in the review.

Then you've got another one saying "The Thomas text's examples were extremely difficult and unrelated/inconsistent with the exercises. I'd say that this book (Larson) made calculus less scary and much more manageable." It just doesn't ring true.

Have you heard of the phrase "fruit of the poisonous tree"? It's the idea that even if something is suspect, it just might work out so it may be worth trying. But the point is: there are alternatives from trees that aren't poisonous.

 

[Radarithm]

If you're looking for a book that simply gives you the steps then Lang's book might not be for you, and I'll second Kline. If you want to know WHY certain things are the way they are then go for it. Personally I've preferred Lang over Kline.

 

[christian0710]

If you're looking for a book that simply gives you the steps then Lang's book might not be for you, and I'll second Kline. If you want to know WHY certain things are the way they are then go for it. Personally I've preferred Lang over Kline.

I do want to understand Visually what i’m doing, and be able to interprete the results – what they mean - not in a mathematical abstract way for mathematicians but if i were to interprete scientific data and solve for different variables it's nice to know that the derivative is the rate of change of the function at that point. Also I want to be able to se why it works mathematically from the figures/pictures, In a more short and concise form, basically – I just need a concise but understandable book with explanations if I need to Use fx logrythmic functions, or integrals in some chemistry experiment and forgot how it works.

 

[Radarithm]

I'd recommend picking up Kline then

 

[micromass]

I'd recommend picking up Kline then

Agreed. It seems Kline is exactly what you want.

 

[coffeejunky]

Isn't Larson one of those money-mill books with a new edition every 3 or 4 years, with a lot of stuff on the CD to get you to buy the new edition, with reviews on review sites that one can hardly trust and including topics that you shouldn't learn yet like Laplace transforms to make the book look more complete?

The examples with Laplace transforms or Fourier Series all include something students should have done in the previous exercises. If you mean whether these problems should introduce them to a new topic, then I agree that this is a horrible way to do so. But it certainly gives you some kind of idea of what's out there. It didn't occur to me to think in a way as if the problems were just thrown in there to make it seem more complete, but I guess that's just my opinion.

His company, Larson Texts, Inc. certainly publishes a new edition every 3 or so years that are identical to the previous editions regarding the book itself. An instructor told me the only difference he could spot was the arrangement of the problems. Other than that, the cover itself always has a new picture of these weird 3D shapes and a new color.

I'm probably going to look at a few suggestions in this topic, since Larson seems like a bad choice now. :tongue:

 

[micromass]

His company, Larson Texts, Inc. certainly publishes a new edition every 3 or so years that are identical to the previous editions regarding the book itself. An instructor told me the only difference he could spot was the arrangement of the problems.

Right. College professors assign problem sets to their students like "solve problems 10, 11, 12 in Larson". So the students are forced to buy a 200$ textbook in order to follow in the class. They can't just buy an older edition (which is the same thing) because the problems will be ordered differently.

The books are ridiculously overpriced and are taking advantage of an already financially struggling group of people (students). I will never recommend books like Larson or Stewart to people for this reason. It disgusts me. The texts aren't even that good.

 

[verty]

The examples with Laplace transforms or Fourier Series all include something students should have done in the previous exercises. If you mean whether these problems should introduce them to a new topic, then I agree that this is a horrible way to do so. But it certainly gives you some kind of idea of what's out there. It didn't occur to me to think in a way as if the problems were just thrown in there to make it seem more complete, but I guess that's just my opinion.

I'm probably going to look at a few suggestions in this topic, since Larson seems like a bad choice now. :tongue:

I think Laplace transforms, usually being taught in the second half of dedicated ODE classes, are too difficult to be a calculus book, that's a bit too dictionary like.

Larson, with so many editions, probably has decent content because they've had many revisions to look at other books and have whatever they have, so I'm not too surprised that you liked it. I just hate the whole content on the CD, pay to access the website business, I mean they are charging $220 for it so they can afford to print a large book with everything in the book. Most people who study are going to buy new books for their course anyway so why shouldn't they be able to buy used books to learn beforehand or as a secondary book for their studies? So I'm not against the content, I'm against the principle and the publisher.

It's just one of those things I guess.

 

[christian0710]

Perfect! I just bough Calculus: An Intuitive and Physical Approach! I was really thinking about getting Calculus and Analytic Geometry by George B Thomas and Ross Finney due to the nice layout and visuals - tough decision', but i went with klines and I can't wait to look through it.

Thank you so mcuh guys - I really appreciate your help :)