Best Introduction to Calculus Book

[Mark]

Hey, I know this is not on the level of the regular posts here, but I just want your opinions, on a good book to be introduced to calculus

In my science classes I have been continually been intrigued by many things (one of which, Maxwell's 4 equations). I ask questions, which results in..."this answer involves calculus"...And i am sick and tired of it. I am fairly good at math, but I have no idea where to start in this subject.

Can anyone recommend an introductory book for a grade 11 student who wants to start this..?

 

[jammieg]

A good introduction is "Calculus made easy" by Silvanus P. Thomas and Martin Gardner St. Martin's Press, it's been around a long time and makes it fun to learn in my opinion.

 

[fourier jr]

Calculus: A Physical & Intuitive Approach - Morris Kline

 

[Theelectricchild]

DIv grad curl and all that.

 

[fourier jr]

DIv grad curl and all that.

for grade 11? that book is good but not for someone who hasn't seen any calculus before.

 

[fishys182]

what ever you do.. DO NOT get this book... it did not explain things well AT ALL. this was a college book, but yeah.. still not recommending it. it did not explain things well.. i was very dissappointed.. i wanted to keep a calculus book... the thing was 100 bucks.. but i decided to sell it back at the end of the term b/c i mostly learned from going into talk to the professor then that book. evil evil book
Calculus, Single Variable
By Deborah Hughes-Hallett, Andrew M. Gleason, Daniel E. Flath, Patti Frazer Lock, Sheldon P. Gordon, David O. Lomen, David Lovelock, Brad G. Osgood, William G. McCallum, Andrew Pasquale
Release Date: 06 July, 2001

 

[Mark]

Alright, my library has...

• Calculus Made Easy
• Div grad curl and all that

I also have yet to take a senior algebra course (3d vectors, matrix, proofs, etc.) how complicated is div grad curl and all that stuff?

Also..
How long do you think a book has to be, to give a decent explanation of calculus, Calculus:Intuitive and physical approach is over 900 pages...
In the other post the people are talking about Calc I, and Calc II, etc. to these books all only cover Calc I? or more..?

Thankyou so much for your suggestions so far, any other books?

 

[fourier jr]

Don't bother with Div Grad Curl & All That, it's for people who are in their 3rd calculus course. I like the one by Morris Kline.

 

[Math Is Hard]

Course companion book

Hi Mark,
My favorite "companion" book for a first calculus course is "How to Ace Calculus" (Streetwise Guide). It's fun to read and does a great job explaining concepts at an overview level - sometimes the textbooks are so detailed that you can lose sight of what you're trying to solve.
Anyhoo, you might want to check it out when start your calc studies.
p.s. I actually did "Ace" Calculus

 

[Theelectricchild]

Teeehehhehe I was kidding about Div Grad Curl and all that--- I am taking vector calc and I have trouble with that book.

 

[QuantumDefect]

I always thought that An Idiots Guide to Calculus was good.

 

[Math Is Hard]

Don't forget Calculus For Blondes

 

[fourier jr]

Teeehehhehe I was kidding about Div Grad Curl and all that--- I am taking vector calc and I have trouble with that book.

It was written by a physicist so maybe it would be better for a physics or engineering student? I thought it was good because I do better with intuitive explanations. Not everybody does though.

How long do you think a book has to be, to give a decent explanation of calculus, Calculus:Intuitive and physical approach is over 900 pages...
In the other post the people are talking about Calc I, and Calc II, etc. to these books all only cover Calc I? or more..?

I just have a thing for big huge math books I guess. Either big huge ones or tiny little ones. Example: my favourite math history book is also by Kline; it's 1300 pages. His calculus book covers single- and multivariable calculus, infinite series, polar coordinates, etc so I guess that would be all of calc I & calc II. He's also got a 1-chapter intro to differential equations at the end. It's so long because he's got so much explanation and discussion.

 

[Theelectricchild]

But seriously--- I thought that James Stewart Calculus Early Transcendentals was an excellent textbook... 4th or 5th edition it doesn't matter! CHeck it out if you can!

 

[franznietzsche]

Calculus of a SIngle Variable
Larson, Hostetler, Edwards

Its the one i first learned from freshamn year, very good. It has a nice format to it makes it easy to follow.

 

[Theelectricchild]

^^^

Ahh the book i used in high school! Excellent indeed, although I personally thought that going into series calculus (ch8) immediately after integration (ch7) was a bit of a jump, but other than that it was excellent.

 

[Jdo300]

Hey, I know this is not on the level of the regular posts here, but I just want your opinions, on a good book to be introduced to calculus

In my science classes I have been continually been intrigued by many things (one of which, Maxwell's 4 equations). I ask questions, which results in..."this answer involves calculus"...And i am sick and tired of it. I am fairly good at math, but I have no idea where to start in this subject.

Can anyone recommend an introductory book for a grade 11 student who wants to start this..?

Hi Mark,

I'm glad you posted this, I'm also in the 11th grade (just finished pre calc) and I was going to ask the same question. Thanks everyone for all the suggestions

 

[Gza]

Okay, I know all the hardcore math heads would tend to disagree with me on this, but I would say that stewarts calculus concepts and contexts book is excellent. There aren't a lot of proofs, but the book really helps a beginner start using calculus, and understanding it before getting to the nitty gritty. A few people I know have trudged all the way through Apostle's tome, and found they had to skip over entire sections reverting to stewarts book to tell them what the hell is going on intuitively. Plus another thing I like about stewarts is that if you're a nerd like me, not having the proofs allows you to derive them yourself, and then check either at the back of the book or another reference to verify your result. This has gone a long way in deepening my understanding of calculus. Hope that helps!

 

[e(ho0n3]

The book I used for Calculus I and II in college was Single and Multivariable Calculus by Hughes-Hallet et. al. Although I wouldn't say it's the best book, it did gave me enough knowledge to go on to Calculus III. The one thing I don't like about it is that it omits proofs (like why Taylor series work, etc.), but I don't blame it since some things can't be proved of the bat at that level. The book I used for Calculus III was a very nice, very cheap book published by Springer called Vector Calculus.

While I'm on the subject, I don't know why books have to include so many unecessary pictures, colors, examples, etc. All books ought to be like Springer books: small and cheap. If I was an author though, I would want my book to be as reasonably expensive as possible (so I could get huge returns).

e(ho0n3

 

[Theelectricchild]

Gza right on!

I am still using Stewart for my multivariable calc course and its great!

 

[honestrosewater]

For an introduction, I suggest you google calculus tutorial. There are some very nice ones out there. They are short & sweet, visual, interactive- it's a great way to introduce yourself to a topic.
Then go bury yourself in a tome ;)
Happy thoughts
Rachel

 

[chroot]

If you need a conceptual introduction to calculus, Berlinksi's "A Tour of the Calculus" is quite readable. If you need a practical introduction that will help you solve problems, you'll need a first-year textbook. I like Thomas & Finney's.

- Warren

 

[Zorodius]

Hi Mark,
My favorite "companion" book for a first calculus course is "How to Ace Calculus" (Streetwise Guide). It's fun to read and does a great job explaining concepts at an overview level - sometimes the textbooks are so detailed that you can lose sight of what you're trying to solve.
Anyhoo, you might want to check it out when start your calc studies.
p.s. I actually did "Ace" Calculus

I read this book and would second the recommendation. It skips over too much to be sufficient on its own, but the energetic and entertaining explanations make a great introduction to the subject.

 

[FlatlineLemon]

my helpful sidebook would be Calculus Demystified. its very general and not too detailed at all, but it will defenitely give you a good overview.

 

[speeding electron]

I've been teaching my self calculus, and started with Thompson's book, which is very good for self-teaching IMO. I've now gone through Div, grad, curl and all that, which is a fairly big leap from basic calculus, as it assumes a knowledge of multi-variable calculus. It does howoever introduce Maxwell's equations, which you mentioned as a motivation for learning calculus - these involve vector calculus, which is the subject of that book. I would definitely start with Calculus made Easy, because it breaks the subject down, and some introductory chapters provide a gentle learning curve to start.

 

[franznietzsche]

Okay, I know all the hardcore math heads would tend to disagree with me on this, but I would say that stewarts calculus concepts and contexts book is excellent. There aren't a lot of proofs, but the book really helps a beginner start using calculus, and understanding it before getting to the nitty gritty. A few people I know have trudged all the way through Apostle's tome, and found they had to skip over entire sections reverting to stewarts book to tell them what the hell is going on intuitively. Plus another thing I like about stewarts is that if you're a nerd like me, not having the proofs allows you to derive them yourself, and then check either at the back of the book or another reference to verify your result. This has gone a long way in deepening my understanding of calculus. Hope that helps!

i used that one in my second year of IB Math Higher Level to cover 3-dimensional vector geometry. I felt it was satisfactory. I don't think for that its that critical to be overly rigorous for Calculus 1. Its more important to get a firm intuitive grasp of what derivatives and intgegrals are because they are so important in all higher math, that a firm basis in the concepts and their motivations is important.

 

[doriang101]

What's with you people? All of these math/physics majors and not one person mention's Spivak's "Calculus". Probably the best book if you are planning on going into pure math/math-physics specialist. Ok I know, you're in gr. 11. In that case, realistically, Stewart's is probably the best. I used it for my first year. Might be pricy though.

 

[fourier jr]

What's with you people? All of these math/physics majors and not one person mention's Spivak's "Calculus". Probably the best book if you are planning on going into pure math/math-physics specialist. Ok I know, you're in gr. 11. In that case, realistically, Stewart's is probably the best. I used it for my first year. Might be pricy though.

I know of Spivak's book, and I didn't recommend it because I think it's just wayyy too rigourous for an intro. Yes it's good, but definitely not good for an introduction.

 

[theFuture]

Varberg, Purcell and Rigdon's Calculus. Covers the whole 3 semester calculus sequence. Might be a little dense but it's got good problems.

 

[NSX]

Here's my Grade 12 Intro Calc book: http://www.nelson.com/nelson/school/math/functions/default.html

It was pretty good: limits, all the different types of differentiation, optimization problems, some applications, natural log...
There's more, but those topics stand out in my head. :)

Here's another book [used by some of my district's schools]:

http://www.harcourtcanada.com/school/math/calculus/

The publisher of this book is the same as my that of my Geometry & Discrete Mathematics course in grade 12.

The material is different [b/t the Calc & GDM] but they are laid out in the same fashion. I noticed that the Harcourt is much more like my Calc I & II book [Larson's Calc book]; whereas the Nelson one was more like gr. 9 to 11 layout.

 

[decibel]

im going to be using the Geometry & Discrete Mathematics textbook next semester, :D. i heard it was a fairly hard course, but meh, I am going to be doing calculus this summer, I am attempting to learn it myself but this book http://www.mcgrawhill.ca/book+search/bookinfo.php?isbn=0070917094&pNumber=557985 isent that kinda book, but hopefully with time, i'll be able to get it done

 

[NSX]

hehe

Self-determination!
;)

 

[futb0l]

I have: Thomas/Finney 9th Edition Calculus, it's got all types of calculus, the first few chapters is good for a grade 11 student...

i am in grade 10 btw ;)

 

[Jamez]

I'm from australia, age 16, year 11 TEE student.
I use A.J.Sadler's book , it's easy to understand and i find it a good book for my year 11 TEE course, Introductory Calculus... It's probably set out for the Western Australian Sylibus tho, so i doubt u'll find it. Unless u live in Australia that is.

 

[futb0l]

Hey cool, I am from Australia, I am in Melbourne though ;)
and Btw, Thomas/Finney Calculus is also in colour and lots of practical examples :)

 

[StonedPanda]

Teeehehhehe I was kidding about Div Grad Curl and all that--- I am taking vector calc and I have trouble with that book.

Me too. Vector Calculus by Marsden and Tromba, right? The T.A said that it made things overly complex and didn't explain things enough. Alas, this is what our teacher uses =p

A pretty awesome introduction to calculus book, and it's also pretty definitive is Calculus by Anton. He later included some co-authors, Bivens and Davis. Anton is a legend in the calculus textbook writing world =p

 

[mathwonk]

what about an honors calc book?

I am teaching honors calc this fall and cannot find a good book. I do not mean Spivak or Apostol, those are too hard for my "honors" course. There only seem to be really weak books for non honors, or really hard books for super honors courses, Any good plain old intermediate honors books out there?

I don't want to be difficult but I also dislike heavy books, and space wasted on technology, or bundled CD's. I want clear explanations, some rigor, and a logical sequence of ideas, intelligently written.

I have considered the old Courant, but it looks a bit unattractive on the page for todays kids. I once liked Stewart, and Thomas Finney, but subsequent editions have been dumbed down.

 

[mathwonk]

You need to look at some books to see what you like. I suspect you are not going to learn about Maxwell's equations from "Calculus for blondes".

Calculus Made Easy, by Thompson was written by a fellow of the royal society of engineers, about 80 years ago for average people to learn methods of calculus, without theory [quote: what one fool can do, another can"]. What he says about calculus is correct, and I loved that book, but it was impossible for me to understand WHY what he said was correct from the presentation there. It is short and cheap, and light.

A book like Stewart, is a step up. it is a good standard, long, heavy, expensive, calculus book that hits all the bases, but without extensive theory. In my opinion it has deteriorated in quality as new editions come out, so i would recommend an old edition, like the second edition, as better and also cheaper used.

If you are a budding mathematician or theoretical physicist, a real no nonsense honors level book by a master, that really explains deeply all the ideas of calculus, is the book of Apostol (2 volumes). Many people will say it is too hard, but I used it successfully with a class of returned high school teachers, none of whom were mathematicians. One of them liked it so well, she decided to go into graduate school in math afterwards.

Probably the best overall calculus book on one and several variables, including physics applications and enough mathematical rigor for most people is the 2 volume set by Richard Courant. It is a classic, has been in print over 60 years and has never been surpassed. Go online at Amazon.com and read the raves about it from users to see for yourself.

To go straight to the several variables stuff you need for physics without waiting for years, there are cheap excellent books on the partial differential equations of physics, by excellent pedagogues that explain the ideas without the mathematical baggage.

I would not be afraid to look at Div Grad Curl and all that. As I recall it was written in the 60's by a physicist who wanted to help his students, possibly at MIT, get to the material quicker than they were doing in their math courses. The famous books by Feynman as I recall made using calculus seem easier than my math courses did.

 

[mathwonk]

I realize it may be way too late for the original questioner, but here is a great deal on the excellent 9th edition of thomas and finney:

THOMAS/FINNEY
CALCULUS 9TH ED BY THOMAS/FINNEY
0201531763*
ISBN: 0201531763
Bookseller Inventory #T8029-15
*


Price:*US$*3.90 (Convert Currency) Shipping:*Rates & Speed


Bookseller:*SUBtext, Student Union Building, University of Victoria,, PO Box 3035, Victoria, BC, Canada, V8W 3P3


That's right, only $3.90. The good thing here is that this edition is actually better than later editions, but is so cheap because of the policy of textbook publishers of releasing new editions every year to kill off the used book market.

You can't beat this. To find such bargains occasionally, look on the excellent used book site, ABEBOOKS.com.

 

[BobG]

I would second two previous suggestions for an initial introduction:

David Berlinski's "A Tour of the Calculus" - It does introduce Calculus, plus the info on different math legends is great.

Any Michael Kelley book, including "The Complete Idiot's Guide to Calculus". He also wrote a very readable "Master the AP Calculus AB and BC Tests". He even has a nice website - www.calculus-help.com . The highlight of site has to be Michael Kelley's hit song, "Quadratic Formula Song".