Best Calculus book before college

[Nathew]

I am looking for a calculus book to help prepare me for college next year.

Currently i am in AP calc AB but that class will end in about 2 weeks. Next year i will hopefully start in calc 2 if my credits transfer. I want to have mastered calc 1 and be at least most of the way into calc 2.

What book would you guys recommend for me to buy and work on the rest of the school year/this summer?
I looked through most of the calc books on here but i couldn't really find a good one? Plus i don't really know what calc 2 entails so if you could recommend me a book, what would it be, and what is covered in calc 2?

Thanks a lot!

 

[eumyang]

Plus i don't really know what calc 2 entails so if you could recommend me a book, what would it be, and what is covered in calc 2?

I'll assume you are in the US. The length of the calculus sequence of courses vary by school. The two most common are the three-semester sequence and the four-quarter sequence. I think most schools in my area (Maryland) offer calculus as a three-semester sequence, so for those schools, what constitutes "Calculus 2", in general, would be:
- applications of integration
- a little differential equations
- techniques of integration
- L'Hopital's rule
- infinite series
- parametric/polar functions

I am looking for a calculus book to help prepare me for college next year.

Currently i am in AP calc AB but that class will end in about 2 weeks. Next year i will hopefully start in calc 2 if my credits transfer. I want to have mastered calc 1 and be at least most of the way into calc 2.

What book would you guys recommend for me to buy and work on the rest of the school year/this summer?
I looked through most of the calc books on here but i couldn't really find a good one?

You say that you are currently in AP Calc AB. What book are you using?

I'm partial towards Larson - not only did I study from it when I took Calculus in high school (3rd edition), but I currently teach out of it (9th edition). I like the amount of exercises given. I like his exposition. I don't like how he skips multiple steps in his examples.

 

[Nathew]

Right now, we are using single variable calculus early transcendentals (fourth edition) by james stewart.

 

[Nathew]

Seriously, anybody? My course is about to end and I kind of want to get a book soon. Any books that have both calc 1 and 2?

 

[kostas230]

I would suggest Spivak's Calculus. It's easy to read and also serves as an intro to proofs.

 

[dustbin]

If you want rigorous/theoretical treatment, my recommendation is Apostol. You can get the international edition for less than $20 on abebooks. The first volume covers calc 1 and 2, plus some linear algebra. The second volume covers the rest of linear algebra, calc 3, and some numerical analysis/propability. Spivak is also an amazing book (I just prefer the former). Apostol will provide a nice blend of technique and theory.

If you want a more standard text (more applications and computation), then I suggest Thomas' Calculus. It will cover Calc 1-3. It touches on some of the theory, but focuses mostly on application. I hear Courant is excellent, treating theory thoroughly with a heavy emphasis on applications.

 

[MarneMath]

Well, Spivak and Apostol were named, but I only advise those two if you want to review calculus with an eye for detail. If, all you want to do is learn and be prepared for calc II, then stewart is a fine book to stick it or Larson. Gilbert Strang Calculus is free online and will cover the same material as those two books. Calc II tends to just be a lot of integration techniques (parts, trig sub, partial fractions, ...) and infinite series and perhaps some conics or polar/spherical coordinates to prepare for Calc III. The integration techniques and application, if I recall correctly, take most of the course up.

 

[jtbell]

Right now, we are using single variable calculus early transcendentals (fourth edition) by james stewart.

Judging from the table of contents on amazon.com, that book includes the usual Calculus 2 topics. If you're comfortable with it, you can simply keep on using it.

 

[eumyang]

I would suggest Spivak's Calculus. It's easy to read and also serves as an intro to proofs.

If you want rigorous/theoretical treatment, my recommendation is Apostol. You can get the international edition for less than $20 on abebooks. The first volume covers calc 1 and 2, plus some linear algebra. The second volume covers the rest of linear algebra, calc 3, and some numerical analysis/propability. Spivak is also an amazing book (I just prefer the former). Apostol will provide a nice blend of technique and theory.

If you want a more standard text (more applications and computation), then I suggest Thomas' Calculus. It will cover Calc 1-3. It touches on some of the theory, but focuses mostly on application. I hear Courant is excellent, treating theory thoroughly with a heavy emphasis on applications.

It sounds like the OP is a high school senior. If so, then I don't know if any of the suggestions above (besides Thomas) would be appropriate.

 

[Nathew]

Say i want to do Spivak, should i have enough knowledge to go through it and learn from it? or do i need to know more about proofs/have more mathematical "maturity"?

 

[ronboyd]

I wish I would have had this book before I took Calculus I in college, it would have made the process so much easier. Prof. E McSquared's Calculus Primer: Expanded Intergalactic Version is like a comic book explaining the language of Calculus. You must learn the symbolic notations.

 

[Nathew]

Yeah I know I've taken calc 1 in high school. Is that enough for this book?

 

[ronboyd]

Best thing you can do is get your hands on one of those in a bookstore and look inside of it. Amazon has a feature which let's you do a little of that, you can view the table of contents to get an idea about what the book covers.

 

[Nathew]

Yeah but not for that book. If I know the basics of calc do you think I should understand it?

 

[ronboyd]

Check it out at Barnes & Noble or Books A Million in your area. It's a comic book, so it should be easy to understand.

 

[Nathew]

I am so torn. As i look into each book more and more, I am not sure its for me. Spivak seems like it might be too difficult for me as of right now, apostol also seems like it is for a more mathematically familiar crowd, and stewart seems like it isn't quite deep enough. I CANT DECIDE! I am dying someone help

 

[Jorriss]

I am so torn. As i look into each book more and more, I am not sure its for me. Spivak seems like it might be too difficult for me as of right now, apostol also seems like it is for a more mathematically familiar crowd, and stewart seems like it isn't quite deep enough. I CANT DECIDE! I am dying someone help

Spivak might have a tough learning curve but it's very rewarding.

 

[kostas230]

I am so torn. As i look into each book more and more, I am not sure its for me. Spivak seems like it might be too difficult for me as of right now, apostol also seems like it is for a more mathematically familiar crowd, and stewart seems like it isn't quite deep enough. I CANT DECIDE! I am dying someone help

I learned calculus when I was in high school from Spivak. Stick with it and it will teach you how to actually do mathematics, rather than just using formulas...

 

[Nathew]

I learned calculus when I was in high school from Spivak. Stick with it and it will teach you how to actually do mathematics, rather than just using formulas...

What prior knowledge did you have before starting spivak?

 

[kostas230]

Algebra and trigonometry. Seriously, you don't need anything else to know to study calculus.