Math refresher that covers several courses?

Question

This is my first post in Mathematics but I'm not new to these forums. I use stakoverflow as I'm in software as a professional. This is going to be long post - not to mention a lot of what may seem a lot of blah-blah so I hope you can sort it out and get to the bottom of what I'm projecting.

I took a short cut from junior college and signed up with a regional private university to earn my BS in CIS. Back in the day it was a good choice as classes were at night and I was going to be done in less than two years. Supportin a family of four - this was a good choice. Draw backs? Yes - Only one semester of Calculus and no Physics (Calculus based to be precise).

After twelve years of writing web bases code I decided to get a masters degree because I'm, as far as the pay scale goes. maxing out and expenses are increasing. Not to mention the hunger for more/different is stirring.

I've applied and was accepted at local state university. I mean they looked at my transcripts I would imagine some bright minds scrutinized them, and decided I have the prerequisites to continue in the master’s program. Which btw, is in IA. All of the classes I'm required to take, including all the electives have prerequisites that I really haven't met. The department said that it is at my discretion to decide if I can be successful in this program. The classes I am talking about are Calculus II and III, Differential Equations, and Discrete Math. I’m sure somewhere calculus based Physics will be required as well.

My first class is a Computer Architecture where some of the calculation so far included formulas with complex fractions so basically algebra - and I was struggling with these. Which makes me wonder how much more difficult this is going to get. There is cryptography class that has Calculus II for prerequisite as well.

So with this as a prelude to my question here is my dilemma. I've always operated on the bases of all or nothing, so I'm thinking I'll have to reenroll in at least in Pre-Calc and work my way up to Diff Equation, including Statistics (which I never took either). That's six classes at about 2K per class and two years of my time.

Is there an option for this? Or, if someone has a related experience how did it worked out for you? I mean back in the day I didn't want to take all these courses but now I think they're fascinating and for a longest time I've considered learning calculus physics, I mean just for fun.

So what I'm I do to? I need some kind of super refresher so that I can confidently continue in Calc II and III, and so forth. What is covered in Calc II and III that isn't covered in Calc I and how is Physics depended on Calc, and perhaps my cryptography class dependent on this?

And I apologies for posting this here even though it's no purely mathematical issue, and on the other hand it relates totally.

Thanks for listening...

Risho.

Answer 1

Unfortunately, the content in a Calc I, II, or III class is not at all regularized. If the university has the ordering Calc I, II, III, Differential Equations, then I suspect that Calc I is mostly differentiation and perhaps the Fundamental Theorem of Calculus, Calc II includes techniques of integration and Taylor Series, Calc III is multivariable calculus, and differential equations is exactly what we think it is. I'm going to base my answer on this idea -

I definitely think that it is possible to teach yourself Calc I-III and ODE if you're dedicated, spend some time, and have someone/something to check your progress every now and then. But it's not necessary to reinvent the wheel either. I'd recommend that you try to do a quick check of your some or your previous skills. While you could buy some set of books and just sort of see what happens, I'm going to recommend a different tack: use the MOOCs.

In particular, right now, there is a free MOOC on Calculus I through Coursera being taught by Dr. Fowler of Ohio State University. If you don't mind a little self-reference, I wrote a blog post checking up on the calculus MOOCs a while back, and I've been keeping up with them. I think that Dr. Fowler's course is a very good first-intro-to-calculus course. I would also say that it's important to have a firm grasp of one-variable calculus in order to approach multivariable calculus (which is what I bet Calc III is) and ODE, and I think this would be a great way to attack it.

One good thing about that course is that it has an inbuilt and free textbook. An alternative free textbook is David Guichard's textbook. I'd like to add that there is absolutely no reason to buy an expensive calculus textbook.

Once you're set with Calc I, I recommend going through the second half (chapters 5-8) of David Guichard's textbook above. It covers integral calculus and Taylor series. I'd like to say that the material on Taylor series is a bit short and at the very end of the text, but it's a good start. Anytime that you feel like you need to know more about something, I'd recommend going to the corresponding Khan Academy video/lesson (also free). In particular, the Khan Academy has a good amount of material on Taylor Series.

I don't have any idea what sort of math you'll find that you need, so I don't know what to emphasize or de-emphasize. You said you have a degree in CIS (which I don't know what is) and you're getting a degree in IA (which to me means either Iowa or International Affairs, but I doubt both of these) - but I sort of doubt that Taylor series will matter here. But if you really get into calculus-based physics, Taylor series can be a really big help.

I don't have a good reference for physics, especially since neither you nor I know what you need. The Kahn Academy's physics section is lacking, I have not yet seen a good calculus-based physics MOOC (Udacity has a good algebra-based class though). But since I like open-source things when they should be open-source, I looked through a few of the free physics books out there and I liked what I saw in this one.

Calculus III is multivariable calculus, and is very different from the previous math courses. Khan Academy has reasonable videos and a few Georgia Tech professors wrote a free book. But multivariable calculus can be really confusing, and I highly recommend that you find either a teacher, professor, tutor, or another student to go through it with you.

That's enough to get you started. If you succeed at that, we can direct you further.

I'd like to end by saying that I highly suspect that you would be better-served to learn linear algebra than calculus-based physics. Everyone uses linear algebra, or could, if they wanted to.