# Difference between Larson's Calculus

1. May 9, 2010

### MushroomPirat

I'm looking to buy an undergraduate Calculus textbook, mostly for self-studying, since I'm currently in high school.
I've been looking on here and on amazon for some texts, and the books by Larson seem to be pretty good. However, there's two books which seem to cover almost the exact same thing: the book simply called "Calculus" and the one called "Calculus: Early Transcendental Functions". I was wondering if anyone knew what the difference was between these. I've seen some other calculus textbooks have this distinction as well.

If anyone's interested, here are the links to the google books version of these texts:

Calculus:

Calculus: Early Transcendental Functions:

Just by looking at the table of contents, they seem to have the exact same material, and even looking at the first few pages, they seem to be the same word for word.

EDIT: Oh, also, I was wondering if there are generally significant changes to the textbook in different editions. The older version is a lot cheaper, so I think I much rather get that one, rather than spend over a hundred on a new one if theres no new material. Sorry if these questions seem really basic; this is my first time buying a university level textbook. Thanks :)

Last edited: May 9, 2010
2. May 10, 2010

### Reedeegi

If I were you, I actually would not opt to purchase Larson's text if you wish to truly learn mathematics. Larson's book (as most high school and college texts do) focus on computation and application of mathematical concepts without devoting time to proofs and rigor, which is vitally essential to understanding mathematics. Instead, I'd recommend two rather inexpensive books to learn calculus from.

Elementary Real and Complex Analysis by Georgi Shilov (http://store.doverpublications.com/0486689220.html)

Introduction to Analysis by Maxwell Rosenlicht
http://store.doverpublications.com/0486650383.html

The former is more computational (while still devoting time to proof) whereas the latter is far more proof-based. Given that the two cost roughly $30 when bought together (a far better deal than buying the$110 books) and that they cover far more material than the run-of-the-mill high school calculus text, I recommend that you purchase these texts.

3. May 10, 2010

### MushroomPirat

Hey Reedeegi,

Thanks for your reply! I looked at the books you mentioned quickly on google books and I actually find them quite interesting. It really is a different approach than what I'm used to.

I'm not trying to learn calculus from scratch; I've done calculus up to about the AP Calculus AB level (if you're familiar with that), with more integration techniques like trig sub, partial fractions, and t-sub.

However, I think it would be interesting to re-learn what I do know with those two books you mentioned, with the theory with it. There IS one thing I was thinking about though. I'm planning to go into engineering once I get into university (mechanical or electrical). You mentioned that the "regular" calculus textbooks devote time to the applications of the mathematical concepts. Wouldn't that be important to have when going into engineering? Would learning math from this approach benefit as well?

Sorry if these questions sound really dumb. I'm really not sure how different approaches to math are used by different people.

EDIT: Oh, just thought I should mention. I started looking at calculus textbooks with the intent that I could brush up on Differential and Integral Calculus principles that I haven't covered at school, and then possibly using the same book to self-teach multivariable calculus. So, I'm not sure which direction to go here... To do some analysis and take a more theoretical (I think) approach, or keep going down the 'regular' path. Thanks.

Last edited: May 10, 2010
4. May 11, 2010

### jasonRF

I would actually recommend a more traditional approach of learning basic calculus before advancing to analysis. I am not familiar with Larson (but it is likely reasonable), but I am with Anton ("Calculus") and Thomas and Finney (now called "Thomas's calculus" I think). Both are good. Used copies of old editions are certainly the way to go. A 15 or 20 year old calculus book would be perfectly fine, and can probably be purchased cheap. For example, at Amazon a 1995 edition of Anton's book can be found for less than $5 if you include shipping; https://www.amazon.com/Calculus-Ana...r_1_11?ie=UTF8&s=books&qid=1273579853&sr=8-11 If it doesn't work for you, you are only out$5.

While the google books previews of Rosenlicht and Shilov lead me to guess that they are pretty good books, most of us mortals couldn't jump into a self-study of books at that level without even knowning any calculus ahead of time. The Rosenlicht book is still used at some universities for upper division (undergraduate) analysis courses, all of which require calculus as a prerequisite. They both discuss something called metric spaces before even addressing continuity and derivatives, which is quite the tough road to go. Of course, you can pick up one of those cheap as well and see how it goes, and again you won't be out much.

I am not a mathematician, but I have self-taught myself elementary analysis after I had already taken a fair amount of "easy" undergraduate math classes. In my personal experience, having an intuitive understanding of basic calculus and having experience with a broad variety of functions that a calculus background provides, makes the more abstract definitions and theorems in analysis possible to understand because I have the background to make up my own examples.

jason

Last edited by a moderator: Apr 25, 2017
5. May 24, 2010

### Pinu7

DO NOT LISTEN TO Reedeegi. Those are books on analysis, not Calculus. You should familiarize with the computational techniques in Calculus before touching Analysis

Most calculus books are the exact same, so authors like Larson, Antony, Stewart, or Thomas give more or less the same thing.

Somewhat slightly more advanced texts on Calculus includes Apostol, but that is currently out of print. I suggest using an "easy" book such as Kline for single variable calculus. After that, I would recommend a harder book for multivariable calculus(eg Advanced Calculus of Several Variables- Edwards).

6. Aug 28, 2010

### hitmeoff

May be a few months late here, but I agree with Pinu and jasonRF.

I learned from Larson's Calc text and have seen the other popular ones (Stewart's, etc). Yes they are all pretty similar and you would do well with any, but because I learned from Larson, I obviously am biased towards it. I just think its a super clear text.

If you are self studying and need a cheap calc book, go with Larson and get an edition thats one or two editions old for next to nothing.

If you try to jump right into an analysis text without having a real solid idea of HOW TO DO calculus then you are asking for a lot.

Chances are you have yet to touch a real, serious theoretic-axiomatic approach to math. Though beginning calc is not "axiom axiom theorem theorem proof" its also not just plug-n-chug like most of the math youve taken before. It does force you to think a little more critically about how to set up problems, break big problems down into manageable pieces, etc which are skills needed if you want to succeed at upper level math.

If you jump into analysis right away, you will be trying to learn calculus and learn how do proofs all without first developing your analytical and critical thinking skills. Possible? Sure. Hard? Definitely? My feelings are that this approach will not allow you to learn much "usable" calculus and most of the "analysis" will go over your head.

Get through Larson and maybe pick up an older edition of Anton's Elementary Linear Algebra (i suggest this because you will eventually have to take elementary linear algebra AND because Anton's book does a very good job at the "Elementary" part of Lin Alg, plus you will get introduced to writing proofs as well). From there go on to a solid Analysis text and maybe a more rigorous Linear Algebra book (Friedburg, Axler, etc).

As far as learning analysis for the sake of physics...you have to realize that most analysis, algebra and even linear algebra and ODE/PDE books are written for math majors. Which means not only are they heavy on proofs and light on computation, they also rarely touch on how to apply this more advanced math to other sciences.

I cant tell you how many times ive taken an upper dic math class or picked up a math book because the words "with applications" was part of the description, only to find out that by "applications" they mean applications to other problems in abstract math!

Certainly analysis, algebra, linear algebra, topology, ODE/PDE, differential geometry and so on have their applications in science, especially theoretical physics and chem. But usually you are taught the math you need in the science courses you need it in. I also dont like this approach and most "Math for Physicists" courses only cover that basics of higher level math. So finding a book or taking a course that teaches SERIOUS ADVANCED MATH for SCIENTIST (and not mathematicians) is something Ive been trying to find.