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Calculus Refresher?
zagdrob
Registered User regular
Registered User regular
I've signed up for a Differential Equations and Physics II w/ Calc course in this coming semester to finally finish up my degree. Unfortunately, it's been almost a decade since I took Multivariable Calc (III) and Physics I w/ Calc. I did well in those classes at the time, but I haven't really used Calculus since then.
While I assume I'll be able to catch up pretty quickly I don't want to start out behind and not be able to catch up. I've seen several Calculus refresher courses out there, but I didn't know if there are any that come highly recommended or - especially - offer a small sample of problems from Calc I / II / III so I can judge where I'm at / what areas I need to put the most effort into refreshing.
I am looking for something relatively short and sweet that will let me evaluate if I need to do some more in-depth review.
Also, I assume the TI-89 is still the standard for a Calculus / Physics calculator? Is there something newer / fancier that kids these days are using? I would guess most courses don't just let people use an app on their phone (cheating and all) but just wanted to make sure.
While I assume I'll be able to catch up pretty quickly I don't want to start out behind and not be able to catch up. I've seen several Calculus refresher courses out there, but I didn't know if there are any that come highly recommended or - especially - offer a small sample of problems from Calc I / II / III so I can judge where I'm at / what areas I need to put the most effort into refreshing.
I am looking for something relatively short and sweet that will let me evaluate if I need to do some more in-depth review.
Also, I assume the TI-89 is still the standard for a Calculus / Physics calculator? Is there something newer / fancier that kids these days are using? I would guess most courses don't just let people use an app on their phone (cheating and all) but just wanted to make sure.
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I used them to brush up on basic math, they have practice tests and kind of "game-ify" the learning process.
https://khanacademy.org
-Indiana Solo, runner of blades
Do some khan academy bro!
https://www.khanacademy.org/math/differential-calculus
https://www.khanacademy.org/math/integral-calculus
https://www.khanacademy.org/math/differential-equations
https://www.khanacademy.org/math/multivariable-calculus
Also Wolfram Alpha can be invaluable for Calc stuff. They'll integrate and derive expressions and have step by step explanations. They're not the clearest but with some thought you can usually see what it's doing. You may have to give them a few bucks to get Pro access for a little while, I don't remember.
http://www.amazon.com/Texas-Instruments-TI-Nspire-Graphing-Calculator/dp/B004NBZAW0/
http://ocw.mit.edu/
also good places to look
It's primarily integration techniques like integration by parts mixed with some Matrix Operations you probably saw in Precalculus/Algebra.
I'm not much of a fan of Khan Academy, watching videos without actually reading about the subject and doing some refresher problems usually just instills a false sense of security, but I like this site: http://tutorial.math.lamar.edu/
Get a copy of an old edition the Stewart Calculus book or the Larsen Calculus book off amazon or something. (Shouldn't be more than a few dollars for an older one). Work problems in the Integration Techniques chapters and review the differentiation rules.
Your calculator isn't going to do much for you in DE. Its a different kind of course from the Calc sequence.
EDIT: I'm a College Math Instructor, if you've other general math questions PM me.
Prof 1
1) practicing derivatives and integrals, to whatever extent you feel you need to refresh what you did of those in Calc I and II
2) reviewing infinite series, particularly power series and intervals of convergence
3) practicing the introductory differential equations (In whatever Calc textbook the place you're attending uses), including the applications of those
Prof 2
(1) Integration: There is an entire chapter in the Calculus book on methods of integration. The main ones you will need are substitution, integration by parts, and partial fractions. The other methods show up occasionally.
(2) There are one or two sections on differential equations in the calculus book. The topics are separation of variables, first order linear DEs, and slope fields. This material, along with some new applications, will be the heart of Ch. 1 in the DE course.
(3) If you take the DE course at Ohlone, we use a small part of the chapter on series from Calculus II. If you get to this topic, you can restrict your review to geometric series, ratio test and alternating series.
(4) Polar coordinates and parametric equations will not be used at all.
(5) If the DE book you use has an application called Torricelli's law, take a look at the disk method for computing volumes in 101B. If you don't see Torricelli in your DE book, then I don't think you will need volumes.
This info might not be completely applicable depending on what your school covers in their Calc courses and what they expect you to know for DE.
I was able to spend a summer meeting with a tutor and going over integration methods and I finished with C in DE. I'm terrible at math though, so I'm sure you'll do ok. At the very least, DE was the most interesting math course I've taken.
I'm sure @lessthanpi can provide an opinion on what I listed.
Edit: Also, our graphing calculators were banned in my class for tests, so you may not even need the 89