Re-Learning Calculus 1 - Tips for Starting University

[key24]

Hello! I will be starting university in August and I plan on starting with Calc 2 and skipping Calc 1 to save myself some time. I received a 5 on my Calc AB exam but it has been awhile and I have forgotten a lot. The courses I will be taking my first semester require Calculus 1 as prerequisite so its crucial I have a solid understanding of the concepts. Also, I don't want to start Calculus 2 completely lost. What would you guys recommend to relearn and understand Calculus 1 at the college level? Any good textbooks/books out there or possibly online classes like MIT's OCW (but less confusing)? I found MIT's OCW extremely hard to follow for single-variable calculus. There was also Princeton's Calculus Lifesaver but it didn't have any notes to follow or problem sets (I like something visual to follow and a problem set to make sure I am getting it). Thanks.

 

[axmls]

There are a couple of free textbooks available at this Georgia Tech site: https://people.math.gatech.edu/~cain/textbooks/onlinebooks.html

I haven't used them, but maybe they'll work for you (just don't use the one that teaches calculus using infinitesimals).

 

[key24]

The book by Spivaks seems to have good reviews but a common complaint is that it is tough for beginners. Would this book be suitable since I have already taken Calc 1 and precalc (pre calc was 3 years ago)? I do plan on being a math major so maybe it will help in that sense too.

 

[axmls]

Spivak definitely requires some mathematical maturity. I'm in electrical engineering, and I worked through it last summer to complement what I had learned in Calc I and Calc II for my own personal enjoyment, and it was definitely difficult.

If you're looking to brush up on your calculus 1 so you don't do poorly in calculus 2 (and if you have a, say, physics course that requires calculus 1), then I would absolutely recommend against using only Spivak. That said, I would highly recommend reading Spivak's Calculus to anyone with an interest in math, and you should read if you can in addition to a more traditional Calculus 1 textbook (after all, the goal is to be ready for your other courses. You'll be exposed to more proof-based math eventually, anyway).

But it really depends. What topics would you say you aren't completely comfortable with from Calculus 1? What confused you about MIT OCW's single variable calculus course?

 

[key24]

@axmls i just found the course set up and instruction difficult to follow. When it come to calculus one I'm sure I could get my Barron's review book and within a few weeks be back at the five level. The problem is that I'm memorizing, not understanding the concepts behind what I am doing. Like I know f(x) = logxB -> f'x = 1/( B ln x) but no idea why

 

[MidgetDwarf]

For the last part. You have to go back to the definition of logs(prooof of log functions). ie ln is the inverse of what function? How do we know ln(ab)=ln(a) + ln (b)? Then you build on these definitions and you will see how why the derivative of logs is the way it is.

Note: when doing this proof. The derivative of 2 functions is considered to be equal, if at most they differ by a constant c. ( you will need this idea).

pplease anyone correct me if I am wrong. I am going on from memory.

 

[key24]

Yeah that makes since once I started to think about it. I guess where I'm most uncomfortable with my skills is 1) cones/shells/cylinders, I never really understood those. 2) integreals where it is like 5x^6 + 17x^5 ... 20x +4 over (x+6)(2x^2+8)^2(4x^3+1)

 

[MidgetDwarf]

Hmm. Yes stewart, Larson or what Evers do a bad job explaining the why. Most of these ideas are studied further I an intro analysis course.

However, there is thomas 3rd ed with analytic geometry that does offer insight. Proofs are explained and derived. Get this book.

It will serve as a great reference for years to come. One thing that I failed to mention, thomas explanation of the chain rule for derivatives, epsilon delta, and parametric equations may not be extremely clear to a reader who does not know how to stare at a single page and analyze it. However everything else is good.

 

[mrg]

I'm a big fan of Lang's textbooks, and his book on Calculus I and II is great. It's rigorous in that it contains proofs and he explains where things come from, but it isn't over the top (the infamous epsilon-delta proofs are saved for an appendix, for example). The other really great thing about his book is that just about all of the answers are in the back, and some of the answers contain completely worked-out solutions.

https://www.amazon.com/dp/0387962018/?tag=pfamazon01-20

I also really like Sigurd Angenent's Calculus textbook (he calls them lecture notes but they're more than that, in my opinion). They're more rigorous, in my opinion, and sometimes leave out some key details. However, they are completely free and contain all the proofs and intuition you might be searching for. I wish he had more examples and included more answers in the back of the book, but it's definitely worth check out.

https://onedrive.live.com/redir?res...4743&authkey=!AHQnVVHuhvEc3c8&ithint=file,pdf
(You should be able to download the PDF from that link. Let me know if you can't.)

I haven't read Spivak's Calculus, so I can't comment on that.

Best of luck to you!

 

[CalcNerd]

Find out what text the Calc II course is using and BUY THAT, with a solutions manual. Chances are it is the same text used in their Calc I class (and will be the same text used in their Calc III class). Find out how far into the book they taught for Calc I and review that. That will provide you with EXACTLY what information you need to transition into their Calc II class.