Boost Your Calculus Skills with the Best Combined I/II Book

[iRaid]

(combined in 1 book)

What would be the best, easiest to use book for calc 1/2. Something like a supplement would be really nice, but I want some extra problems so that I can really understand the material. My book right now is "Calculus Graphical, Numerical, Algebraic" and I don't really like it because the problems are too easy compared to my tests and then I'm sol.

Thanks in advance.

 

[micromass]

If you want fun and nontrivialk problems, then go for Spivak or Apostol...

 

[Ivan92]

You can't go wrong with Calculus by James Stewart. x)

 

[eumyang]

(combined in 1 book)

Many calculus books contain material for Calculus 1/2/3 combined. The books with the title "Single Variable Calculus" would usually contain Calculus 1 & 2 only.

You can't go wrong with Calculus by James Stewart. x)

I disagree. I would go with either Larson or Anton.

 

[iRaid]

If you want fun and nontrivialk problems, then go for Spivak or Apostol...

I want to become better at calculus problems :p

But there's 3 different answers I really need the best 1 :(

 

[micromass]

I want to become better at calculus problems :p

But there's 3 different answers I really need the best 1 :(

There is no such thing as the best one, unfortunately. Choosing your math books is like choose your girlfriend, it's a very personal choice. The book I like will not necessarily be the book that you will like. Some people like a conversational and informal tone. Other people like hard and rigorous arguments that make them think. It's all about what style you prefer.

Spivak and Apostol are very similar, so you can choose either one. They are very rigorous books with very challenging/hard exercises.
Stewart is another book (that I personally didn't like), but you'll find a lot of nice exercises in there.

I'd suggest you look those books up in things like "google books". Read the first chapter and choose whatever you like best.

 

[USN2ENG]

I used Stewart for Calc1 and liked it a lot, I am using Thomas now for calc2 and absolutely can't stand it. But oh well, I have a lot better professor this time so it evens out.

 

[brocks]

Choosing your math books is like choose your girlfriend.

OK, so who has bigger boobs, Anton or Stewart?

But he's right, OP --- if everybody agreed on the best book, there wouldn't be so many.

Spivak and Apostol are a combination of calculus and analysis, and are very challenging --- too challenging for most students' first encounter with calculus, but you might enjoy seeing what you can do with them. At the next tier, it's just a matter of preference whether you like Stewart, Anton, Thomas, Smith-Minton, Gill, or many others. All are good (but I lean toward Thomas). All of them have more problems than a student taking a full load would ever have time to do, and all of their problem sets start out easy and end up hard (for a freshman).

If you want a lot of problems and a lot of different approaches to the material, get cheap used editions of several of them. A book 20 years old is just as good as a brand new one, especially if you're just looking for problems to do.

 

[mathwonk]

you can learn plenty of calculus from the 30-40 year old versions of thomas's calculus.

here is a long list of used copies available for as little as $1.

http://www.abebooks.com/servlet/SearchResults?an=george+b+thomas&sts=t&tn=calculus&x=0&y=0I do not especially recommend the newest one by Hass, Weir, Thomas (after Thomas had died).

 

[physiker_192]

My favorite calculus book is by Swokowski:

https://www.amazon.com/dp/0534435386/?tag=pfamazon01-20

 

[Mancuso]

I have to second the suggestion for Spivak. I pefer Spivak over Apostol because it is self-containted. Additionally, Apolstol starts with integration before differentiation, which although being historically correct, is not my preference. Either book will leave you with a much deeper understanding of calculus than door-stop-sized plug-and-chug volumes.

Before reading Spivak or Apostol, I highly recommend a book on proofs, such as How to Prove it, Velleman.

In terms of more modern reads, I'm a fan of Larson's Calculus. I also highly recommend his Precalculus with Limits book if you're rusty. An MIT prof. put it best - the calculus part is easy, remembering every piece of math from junior-high through HS is the hard part. This is where I find Larson provides good reference when I need something explained quickly for the more mechanical parts.

As another poster put it, different strokes for different folks. Check the books out at a local library (university library have stockpiles of the older books) before you purchase to make the best purchase.

 

[Dembadon]

...

I do not especially recommend the newest one by Hass, Weir, Thomas (after Thomas had died).

I am being forced to use that textbook for Calculus III. I don't like it at all; very uninspiring and the proofs are hideous. My professor actually makes handouts for our homework, so I'm not sure why we were required to purchase the book.

 

[QuarkCharmer]

What does the original poster feel is "too easy" and "unlike my test questions"? Perhaps he can show us an example of both the typical test question and an overtly simplistic problem.

Personally, I used Stewart with Spivak. Stewart has a really great problem set. There are about 100 per section, and they range in difficulty from easy, moderate, difficult, very difficult, and a few annoyingly tedious tossed in for good measure.

Spivak's book is hard. Much of it will be completely unlike your course, unless you are using Spivak's book. The problems in his book are either insanely easy, or very difficult. There is virtually no in between, and much of it requires further external resources to learn the tools to solve. I finished all the problems in the first 2 sections (the part that hasn't even got to calculus yet), and a good portion of the formal chapter 3-4 problems, but I could honestly only do a hand full of the total problems and most were completely unlike the "typical" single variable calculus questions that most people see and are prescribed.

If you like, I'll scan a few problems from Spivak's in whatever section you are in and you can see first hand what I mean.

 

[deluks917]

I like calculus made easy

 

[autodidude]

I like Kline's book for intuition and Spivak's book for rigor

 

[deluks917]

I disagree with quark charmer that Spivaks problems require anything outside of the book to solve. Over a summer I solved about 70% of the problems in chapters 1-24 of Spivak Calculus (I randomly chose problems and tried to solve them I didn't try to solve all of them and only get 70%). I agree the problems were hard. On average I took about 2 hours per problem. Some I could not do even after 8-10 hours of work (I then looked in the solutions manual). I think it was worth it though. I learned a huge amount about how to do analysis which gave me a strong base in more advanced courses.

 

[Vinay Hebbar]

How many months do u guys usually take to solve a calculus text like stewart/spivak/apostol? I am yet to start.. Need approximation..

 

[Vinay Hebbar]

And forgot one thing.. Do we get solution book for Tom.M.Apostol textbook for calculus?

 

[Mmm_Pasta]

Are you self studying? Do you have other classes to take? Calculus I and II takes a full school year with other classes and other non-school things going on.

 

[deluks917]

spivak took me like 3 months.

 

[Perturbator]

I am going to disagree Strongly with Apostol recommendations and (begrudgingly) with Spivak. I love Spivak, but when you are first starting, it is too hard to keep motivation when you are consistently getting stuck. I suppose you could argue I was a weak student, but I don't care.

I am currently working on a PhD in math and nearly failed calc I (did fail calcII) when I first took it. The book I learned the absolute most from that kept me motivated and excited was Calculus the elements by Michael Comenetz

https://www.amazon.com/dp/9810249047/?tag=pfamazon01-20

It sounds corny, but this book changed my life, and hardly anyone seems to know about it. Pick it up, you will not regret it (and you might end up like I championing it for folks in a situation similar to yours years ago).

 

[Vinay Hebbar]

Are you self studying? Do you have other classes to take? Calculus I and II takes a full school year with other classes and other non-school things going on.

Im an electronics engineering student who has affinity to become theoretical physicist.. To be one i came to know i need to take lots of math courses.. So its obvious that i have to self study all by myself.. I can dig it and get an answer.. Takes too long.. Not easy going.. So i thought of getting some helping hand like solution book for texts that is most recommended..

 

[Vinay Hebbar]

spivak took me like 3 months.

What courses did u had been through and what are u studying right now? Asking this as i can know some of the foundations needed for a perfect start..

 

[Vinay Hebbar]

I am going to disagree Strongly with Apostol recommendations and (begrudgingly) with Spivak. I love Spivak, but when you are first starting, it is too hard to keep motivation when you are consistently getting stuck. I suppose you could argue I was a weak student, but I don't care.

I am currently working on a PhD in math and nearly failed calc I (did fail calcII) when I first took it. The book I learned the absolute most from that kept me motivated and excited was Calculus the elements by Michael Comenetz

https://www.amazon.com/dp/9810249047/?tag=pfamazon01-20

It sounds corny, but this book changed my life, and hardly anyone seems to know about it. Pick it up, you will not regret it (and you might end up like I championing it for folks in a situation similar to yours years ago).

Dude the thing is, i have come across mathematics pertaining to eangineering subjects and the calculus was taught 2 years ago.. I have bits and peices of jigsaw puzzle.. I don't knw the perfect applications of it.. I need to understand that encountering standard texts.. The only problem is lack of time.. It has many problems and to solve some 20 to 40 problems in a page, you need a day.. In another 1 and half years I am out of my college with undergrad degree.. Before that i should have strong foundations in Calculus(SV and MV).. Differential equations(PDE and ODE),Algebra(abstract,linear), and geometry.. Now you got the time constraint and my problem? :)

 

[Woopy]

wouldn't you have to take calculus II as an electronic engineering major anyway?

 

[deluks917]

I had studied Rogawski Calculus in high School. I'm not sure it helped very much as the problems in Spivak (that I did) where all theoretical. I struggled a lot with Spivak. Next semester I am taking Graduate Complex Analysis, Graduate Pde, Quantum mechanics and computational Physics. I am a junior.

 

[Vinay Hebbar]

wouldn't you have to take calculus II as an electronic engineering major anyway?

Im not doing my major in electronics and communication btw.. Ya, i have to undergo calculus 2 analysis if i were to.. For now, i don't know much of calculus 2..

 

[Vinay Hebbar]

I had studied Rogawski Calculus in high School. I'm not sure it helped very much as the problems in Spivak (that I did) where all theoretical. I struggled a lot with Spivak. Next semester I am taking Graduate Complex Analysis, Graduate Pde, Quantum mechanics and computational Physics. I am a junior.

Good for you.. As i don't know your system there, are u taking all those courses for a single sem? period of 6 months?

 

[mathwonk]

try computing the volume of a 3 dimensional ball, and then a 4 dimensional ball. If you like, look near the end of my website notes from this past summer's "epsilon camp" for bright 8-10 year olds. (This can be done without calculus if you know as much as Archimedes did about volume and centers of mass.)

 

[SirIsaac]

I am going to disagree Strongly with Apostol recommendations and (begrudgingly) with Spivak. I love Spivak, but when you are first starting, it is too hard to keep motivation when you are consistently getting stuck. I suppose you could argue I was a weak student, but I don't care.

I am currently working on a PhD in math and nearly failed calc I (did fail calcII) when I first took it. The book I learned the absolute most from that kept me motivated and excited was Calculus the elements by Michael Comenetz

https://www.amazon.com/dp/9810249047/?tag=pfamazon01-20

It sounds corny, but this book changed my life, and hardly anyone seems to know about it. Pick it up, you will not regret it (and you might end up like I championing it for folks in a situation similar to yours years ago).

mathwonk's review of Comenetz's book is at
http://www.worldscientific.com/page/4920-review01