Hey CD!!! Haven’t been here in a while, but figured I have a question that the other online hivemind has not really answered quite well (at least what I would have hoped for), and CD might fair better.
Long story short: 78/100 on my first exam in second semester calc-based physics :ahh:, primarily due to small mathematical errors. My first semester prof did not care much for them as he knew if we laid the groundwork, we would have the problems nailed. The current prof though is a fresh piece of work, and he does not bend too easily (which is in all likelihood, A GOOD THING). Problems I have are like the following:
*I forgot to leave some variables alone in doing partial differentiation (w.r.t. z: 3yz^2 I took to 6z instead of 6yz OR w.r.t. y: 2y^2z^2 I took to 4yz instead of 4yz^2).
Another problem I ran into was that I took 10^-5 to be like 10E-5 on a regular calculator, which among a mess of *[other] *scientific numbers could be a bad habit.
*
Seeing I am transferring to UMich after this semester, this problem, which has been recurring over the years, needs a fixing. I was thinking that some form of RSS feed that blasts daily problems (exercises) from pre-calc to calc III would be in order, yet you might have a better solution. It is obviously a problem that will not go over night, and not one that I can just fix by telling myself this is the way it is (simply because it has not worked over time).
Your advice would be awesome, and I greatly appreciate any. Many thanks!!!
Unfortunately, I don’t personally know of a website. One thing you consider is going back to your text books and just pulling questions out for practice. Perhaps a few from each chapter. Each text book is different, but the one I used had basic questions like what you wrote in your post first followed by some word problems. It sounds like that first bit might be what you would want.
This is probably too time consuming, but you could make a website that does this relatively easily. Just a database with questions and their answers along with difficulty, level, and other metadata. Then, you could make a question submit box for adding additional questions. As admin, you could approve questions for the live site by testing them out, which gets you the practice and creates a potentially valuable resource for people with a similar issue.
Ok, I don’t know if all schools have these, but I’d go to the math assistance center. It’s a great place full of educated students who can really help review such things. In fact, I work at a MAC to help people and to constantly review things. That job is the reason my strengths are algebra and geometry. Sure I can do calc, but I prefer to constantly review the basics.
Also, I’m glad you noted that its a good thing your teacher nitpicks about such things. As I always tell people: if you build a bridge and can explain why it should be standing, it really doesn’t matter to the people who are in the river from when it collapsed. One moved decimal can be catastrophic in engineering, good luck with figuring this out.
On habit to get into if you haven’t already, when working with physical problems, put the dimensions on every number (assuming it isn’t dimensionless and those are rare). Then you have two problems, one to carry through the math on the numbers and get a numerical answer. The other is to manipulate the dimensions and arrive at the dimensions for the answer. If the dimensions don’t come out, it’s usually a good sign that you’ve left something out or otherwise set up the problem wrong. This includes all the conversion factors needed to make all the values conform.
Also, learn to quickly at least figure out the order of magnitude the answer should be and if your final answer isn’t in the ballpark, something is rotten in Detroit.
