As a grad student I’m taking a stats and probability theory course which requires a decent bit of calculus. Unfortunately my basic calculus knowledge has been atrophying since high school, 8 years go. In undergrad I took several more calc classes but none used much of the nuts-and-bolts stuff of calc 1 and 2, so I’m really struggling with those sorts of problems. I.e. now I have lots of problems where solving them requires the recognition and clever manipulation of finite or infinite sums, or common integrals and derivatives.
But conceptually, I’m fine. For all of my practical recent experience, I’m just used to setting up relationships and letting a computer do all of the numerical work for me.
Does anyone have any suggestions for books or websites that I can use to relearn and practice standard calculus manipulations?
The standard Calculus textbook (at least in the 5 universities I’m familiar with through my family and myself) is Stewart’s. There are a bazillion copies of these books floating around the universe, given as how the guy puts out a new edition every six months and students keep buying the new one even if they own the old one. They are pretty much all the same. You can probably get an older edition for pennies off Amazon. It’s a pretty decent book, is likely very similar to how the concepts were originally introduced to you and having a good reference around is a good start.
Khan Academy is a pretty good online reference with videos covering how to solve all kinds of problems. I found it to be really valuable when reviewing the basics of Laplace Transforms a while ago, though I didn’t use it for Calculus. Have a look around and see if it helps you.
Pauls Online Math Notes - complete with missing apostrophe - was also a good reference online “textbook” for me when I needed to review some random “trick” that came up in some questions I was solving. The webpage layout annoys me, but the content is good.
And, of course, Wolfram Mathworldis very useful to have bookmarked!
In my case, I went back to school about 8 years after my last calculus class in order to do another undergrad degree. Instead of trying to teach myself this stuff, I just took a couple of calculus classes (not for credit) to refresh everything!
Good luck!
It sounds like what you want is a book with lots of worked examples, or problems and solutions that you could practice on. I found several books at Amazon that look like they might be what you’re looking for, but I have no direct experience with any of them:
Forgotten Calculus
Schaum’s Outline of Calculus
The Calculus Lifesaver: All the Tools You Need to Excel at Calculus
Calculus Problem Solver
Schaum’s 3,000 Solved Problems in Calculus