<p>What are some amazing calclus textbooks out there? I want to self-study calc AB/BC this summer and next year, because I couldnt fit AB into my schedule. I will be majoring in mathematics in college too. Also, I don't want to study the textbook for the sole purpose of the AP exam (although I will be taking the BC exam). I want to study this for my own knowledge and pleasure, because I love math. What are some textbooks that will get me through AB/BC stuff plus more?</p>
<p>stewart's single variable calculus</p>
<p>What about the Transcendental book? Are they any good? What is the difference between Early Transcendental and Late Transcendental books?</p>
<p>idk I've never used them- I know for a fact Stewart's is awesome though(having used it).</p>
<p>Definitely Apostol, Courant, or Spivak. Dont get those other crappy textbooks.</p>
<p>The Stewart's Single Variable Calclulus I've got says "Early Transcendentals" on it, so I'm pretty sure you (lil_killer and crosscurrent) are talking about the same book(s).</p>
<p>EDIT: I love it, by the way. Not that I have any experience with others. :P</p>
<p>What does "Early Transcendental" mean? I see Stewart's Single Variable Calculus in Barnes and Nobles. I also see Stewart's Early Transcedental Single Variable Calclus. Is there a difference? Which is better?</p>
<p>I guess I was wrong; looking at them I see both, too.</p>
<p>I searched the website, and here's what h ehas to say about the difference between the Calc book (red) and the Early Transcendentals book (blue):</p>
<p>"These best-selling texts differ from CALCULUS, Fifth Edition in that the exponential and logarithmic functions are covered earlier. In the Fifth Edition of CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions."</p>
<p>Why hasn't anyone mentioned Swokowski? Or Anton?</p>
<p>Swokowski is my favorite.</p>
<p>I just bought myself a copy of Stewart's Single Variable Calculus. All I have to say is that this book is the $hit. It's totally awesome man!</p>
<p>Spivak is great, although it's pretty advanced, especially for studying on one's own without an introduction to calculus in the classroom. Everything is proven and the problems introduce as much content as the written stuff. I'm just starting it, and it's the best textbook I've ever seen.</p>
<p>Are you attempting to study Spivak on your own? Are you using any other books as a quide?</p>
<p>I took Calc BC during the school year, but I don't have much experience with proof-writing outside of geometry so it's all fairly abstract to me. I haven't gotten to derivatives or limits or any of that in this book yet, but it seems like it'll be learning the proofs beneath the stuff I learned last year. The later chapters go into calculus with complex numbers and stuff like that too though.</p>
<p>Did you use any review books? Would you recommend PR for someone self-studying BC with no prior knowledge on calculus whatsoever?</p>
<p>you said you're not so much worried about the ap exam as about learning real mathematics, so my recommendations are tailored with this in mind:</p>
<p>leithold is good times for single variable calculus if you can get a copy of The Calculus 7. It's old, but it's a classic. It's a killer book to self-study out of because the exposition is so clear, and it covers all the BC topics to boot.</p>
<p>now for the beyond part:</p>
<p>if you're really planning to be a math major, it's really important to learn some abstract algebra; math majors aren't worried very much about computational methods. "vector calculus, linear algebra, and differential forms" (isbn: 0130414085) provides a really nice integrated treatement of multivariable calculus and linear algebra. sheldon axler's "linear algebra done right" is a fantastic resource to explore more linear algebra from a pure mathematics perspective.</p>
<p>if you'd like a treatment of differential equations, there are a multitude of approaches you could take, but my favorite applications of diffeq's are in dynamical systems. "differential equations, dynamical systems, and linear algebra" by hirsch and smale is a favorite of mine. note that this isn't the "orthodox" way of learning differential equations, but it's a really cool way to do it if you get this far in your summer studies.</p>
<p>that should keep you busy for a while :)</p>
<p>For Calc I studied from the textbook we had in class, but for most of my other tests I used Princeton Review. For the AP test I would suggest using one of the textbooks recommended above and reviewing the material in the Princeton Review book a few weeks before the test. Print all the resources you can find at collegeboard.com and work through the multiple choice and written problems. Good luck!</p>
<p>this isn't exactly a calculus textbook but I found it to be a very interesting read:
e - the Story of a Number by Eli Maor</p>
<p>Apostel is the book of choice for those wishing to truly master calculus. It might be a little intense in its formalism for an AP course or someone's first exposure to calculus, though.</p>