Best calculus book for self study pdf
I believe that there is no better book to learn calculus from - especially a free one like this - than the book I'm going to present to you here. No, I didn't write it, and yes, it's completely free. It's written by someone who has spent decades honing his skills, both as a teacher and researcher of mathematics at MIT (Massachusetts Institute of Technology). MIT is of course known as one of the best institutions of higher learning in the world in general, but even more particularly it excels in more technical matters such as mathematics. Don't fret if you don't think you're MIT material and can't handle this book. The professor's knowledge of tripping blocks for students and his ability to convey the intuition behind calculus really shines through in this free pdf. It starts off gently, but if you're willing to work through it, you'll be able to master calculus and you'll have a very deep knowledge and working intuition of derivatives, integrals and the fundamental theorem of calculus (among many other wonderful things, we'll get to these later when we take a brief look at the table of contents). And best of all, you'll be able to apply this new-found knowledge, as applications are sprinkled throughout the book (pdf), so you'll get plenty of practice!
There are some things to keep in mind when working through books such as this, and if this is your first time learning more advanced mathematics, it's best to keep these in mind.
Don't read too fast
This is not a competition! Unless of course you really are competing with someone on who will learn calculus first, but I doubt it. I hope you're not. You should give calculus and this book the time that they both deserve. You're not going to learn faster by skipping over parts or trying to up your words-per-minute. If you don't understand something, slow down and ponder it! That's when the real learning happens. Even if you don't get it, it's important that you gave it some time. Now it's more imprinted in your mind, and you'll be much more likely to understand it at a later time.
Also, don't linger
I know, I know, I told you to take it slow. And I meant it. Don't rush this. Nevertheless, it's also important not to linger too long on a concept you can't quite understand or a problem you can't solve (by the way, there are solutions available to all of the odd-numbered problems in this pdf). As long as you give something your serious time and effort, it's generally okay to move forward without understanding everything. Perhaps make a mental note of what you didn't understand, and try to come back to it later? Learning doesn't necessarily progress linearly. If you notice yourself starting to understand fewer and fewer concepts as you go on, you might have to go back to brush up on the more basic stuff that the newer concepts are built upon. Or, you just might have to go more slowly - the material really just might be harder!
Do the problems
It's not enough for most of us to just read the text and skip to the next chapter when we're done. Mathematics is done and practiced - not read. The author has spent a lot of time and effort in formulating and picking out practice problems, so you should consider these an integral part of the book. Doing these problems is when you get to apply what you've learned and find out where your weaknesses lie and what you need to improve upon! You'll find solutions to all of the odd-numbered problems in the book here.
Here's the book
Good luck in learning calculus! With this book, 671 pages full of goodness, you can't really go wrong. And you'll be learning so much more than just calculus (not that that wouldn't be enough on its own!). I'll leave the table of contents down below so you can take a peek.
May I present to you, Calculus, by professor Gilbert Strang.
Table of contents
- Introduction to Calculus, p. 1-43
- Derivatives, p. 44-90
- Applications of the Derivative, p. 91-153
- The Chain Rule, p. 154-176
- Integrals, p. 177-227
- Exponentials and Logarithms, p. 228-282
- Techniques of Integration, p. 283-310
- Applications of the Integral, p. 311-347
- Polar Coordinates and Complex Numbers, p. 348-367
- Infinite Series, p. 368-391
- Vectors and Matrices, p. 398-445
- Motion along a Curve, p.446-471
- Partial Derivatives, p. 472-520
- Multiple Integrals, p. 521-548
- Vector Calculus, p. 549-598
- Mathematics after Calculus, p. 599-615