Learn Calculus: Resources for Beginners

[Abscissas]

Hey I am trying to learn calculus and I don't know where to begin , I want to have a very firm grasp on it so if you could introduce me to some books on all different walks of calculus it would be appreciated. I have no prior calculus experience but do have algebra down for the most part and I think I am ready to keep advancing

 

[micromass]

Hello,

The best calculus book out there is written by Spivak, I highly recommend that you go through it. But not immediately. The book tends to be quite difficult, and you're supposed to be familiar with the concepts already.

A book that I recommend to study now is Lang's "First course in Calculus". It's pretty theoretical, but not too theoretical. And there is no lack of practical problems. The book only really deals with single-variable calculus though, but if you know that well than multivariable is a very easy extension.

 

[Abscissas]

Thank you I've heard of Lang's first course to much now so I will get it and I will definitely try out that other book thank you very much

 

[AdkinsJr]

I actually learned calculus from a book called "teach yourself calculus" by Paul Abbott. I had the 1992 version. I didn't go past Algebra II in high school, so I had a lot of work to do before college to major in physics. The book introduced me to some of the ideas of limits, derivatives, and integrals, and it omitted some of the difficult formalism, like rigorous definitions of limits and proofs. It allowed me to go through important topics of calculus quickly. I learned the more rigorous formalism later when I finally went and took a calc course my freshman year.

I would recommend studying some more topics in trigonometry ahead of time though, if you haven't already, understand functions as well as possible, their graphs, domains, ranges, and inverses...trigonometric (circular) functions are crucial too. I had to teach myself trigonometry as well.

 

[verty]

Don't forget about this: MIT OCW.

 

[AnTiFreeze3]

While AdkinsJr brings up valid points, in that you should have your prerequisites down, including trigonometry, you should know that Lang's A First Course in Calculus covers virtually all of the prerequisitse you might need, in the book itself.

For instance, the first two chapters cover basic properties of numbers, functions, exponents, and how to recognize, interpret, and graph different shapes, such as circles, ellipses, hyperbolas, and parabolas.

Additionally, right before the section that applies differentiation to sine, cosine, and tangent, Lang includes three preceding sections that, as he explains, will provide you with all of the knowledge you need to complete the rest of the chapter. For this reason, you shouldn't worry too much about your prerequisites, so long as you are planning on using Lang's book.

 

[Abscissas]

Thank you I've just ordered Lang's book and will be trying it out as soon as it gets here I'll give you guys feedback once I'm done with it.