Finding the Right Calculus Book for Self-Study

[ronaldor9]

I'm looking for an introductory calculus book. I am thinking about purchasing serge Lang's: A First course in Calculus.
Would this be a good self study book? Or would you suggest others. I am looking for a book with a good balance between proofs and examples. I want the exercises though to concentrate on applied math, so no proving in the exercises.

BTW. I looked through the table of context of serge's book and I could not find anything about Newton's method or le hopital rules, indeterminate forms etc. ( I don't know what they are but i just noticed that other textbooks seemed to contain these concepts) this brings questions about the comprehensiveness of the text.

Thus, which would you recommend:

A First course in Calculus Serge Lang
Calculus: A New Horizon by Howard Anton
Calculus and Analytic Geometry by George B. Thomas, Ross L. Finney

thanks

 

[ronaldor9]

Would anyone please be so kind as to guide me as to what text is recommended( I would like to order as soon as possible)?
I would not mind purchasing two books as long as they would complement each other well ( such as explaining hopital rule or Newtons rule etc. where Lang book wouldn't have such info)

 

[slider142]

What is your background? If you have some experience in high school calculus and vector algebra/linear algebra, I would suggest Hubbard/Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms", which gives a great balance between applications and rigorous mathematics. As for single-variable calculus, check out the mathematics section at your local library. I found several good readable texts at mine. After a good readable introduction that runs at your pace so you can get the mechanics and general gist of what calculus is about, you can check out more advanced "baby analysis" texts like Spivak, Apostol, or Courant.

 

[ronaldor9]

In all honesty, my background is limited calculus I am currently in a HS calculus class. However the pace of the class and the material covered is at a very slow pace. Thus, I have chosen to work at my own pace and at a more mathematically mature level. I am no math wizz or any of the sorts, but wish to gain a good fundamental introduction to calculus that will prepare me for stronger math books. I have read some section of apostol's text and altough i can understand the proofs, more or less, it isint ( for me, considering my background) a good text to actually learn how to apply and do calculus.

Unfortunately my library doesn't contain any of the recommended texts for calculus, which is why i have to resort to asking on the forums. After some research it seems as though, Langs calculus text would be a good start for myself with the suplement of Antins calculus.

All i want to know, is if this combination of texts is well. I especially want to know of the strength of serge lang's book, particularly since it appears to exclude some ( probably minor) aspects that other calculus texts seem to contain.

Thanks

 

[slider142]

Serge Lang's text looks like a very good introduction to calculus and its applications. You can always check out Newton's method in another text.

 

[ruecow]

I'm looking for an introductory calculus book. I am thinking about purchasing serge Lang's: A First course in Calculus.
Would this be a good self study book? Or would you suggest others. I am looking for a book with a good balance between proofs and examples. I want the exercises though to concentrate on applied math, so no proving in the exercises.

BTW. I looked through the table of context of serge's book and I could not find anything about Newton's method or le hopital rules, indeterminate forms etc. ( I don't know what they are but i just noticed that other textbooks seemed to contain these concepts) this brings questions about the comprehensiveness of the text.

Thus, which would you recommend:

A First course in Calculus Serge Lang
Calculus: A New Horizon by Howard Anton
Calculus and Analytic Geometry by George B. Thomas, Ross L. Finney

thanks

You can take this with a grain of salt, since it's been a million (well, 30) years since I looked at a few of Lang's undergrad books. (I browsed at least one of his calculus books and owned and read his linear algebra text.) Lang was very prolific, and unfortunately it was easy to see why: the books seemed to be written very quickly (they used to say at Yale that he would knock one off each summer), they had only very mechanical problem sets, and the calculus book didn't have many proofs. Also, the omitted topics you mentioned are standard for first year calc (at least L' Hospital's rule is). So I'd recommend skipping Lang and using either of the other two. But maybe my memory is faulty, and everyone has their own personal preferences about textbooks. Good luck, regardless of your choice.

 

[lurflurf]

You can take this with a grain of salt, since it's been a million (well, 30) years since I looked at a few of Lang's undergrad books. (I browsed at least one of his calculus books and owned and read his linear algebra text.) Lang was very prolific, and unfortunately it was easy to see why: the books seemed to be written very quickly (they used to say at Yale that he would knock one off each summer), they had only very mechanical problem sets, and the calculus book didn't have many proofs. Also, the omitted topics you mentioned are standard for first year calc (at least L' Hospital's rule is). So I'd recommend skipping Lang and using either of the other two. But maybe my memory is faulty, and everyone has their own personal preferences about textbooks. Good luck, regardless of your choice.

It is possible that some of lang could have improved some of his books if he spent more time. That said they are still better than any of the garbage books like Anton. Anton could not write a book half as good as lang given lifetimes. As far as any difference in topics, you object that lang does not copy every hack book? What would be the point in duplicating his lessers? Langs book covers central topics well instead of covering numerous unimportant topics poorly like usual books. The book is written for a particular type of reader (first year with weak background) who needs a light serving of theory and some mechanical problems, some people would benifit from reading the next book up in place of or in addition to the basic book.

 

[ronaldor9]

lurflurf Thanks for your insights, I have just purchased the book. I do agree with what you have said, after I reviewed some of the material in the book I already knew. Despite the fact that I have just begun reading it, It does a very well job explaining theory and provides unique insights, which would have never occurred to me.

Thanks for the help

 

[Bob S]

I used "Differential and Integral Calculus" by Bacon. First Edition, 1942. There is a newer second edition 1955. I liked it and it is still on my shelf. Amazon lists 3 used for $5.00 to $10.00