Warm-up Assignment #6 responses

I’ve finished reading your great questions on Warm-up Assignment #6. I apologize it took me so long to process them, but I think you’ll find the discussion worth the wait! Below, I’m pasting in anonymous responses that I received, followed by my commentary for each.

“I'm currently taking Calculus 2, so my question for you is are we going to be using derivatives and integration alot during physics? I'm pretty good with derivatives but I'm not that strong yet with integration.”

A great question, especially since we haven’t done too much calculus yet!

PHYS 151 assumes that you’re in Calculus II right now. That means our textbook and assignment problems assume that they can throw derivatives your way without having to give you a refresher. (That may be a bad assumption, so see the links in response to the student quote below!) The textbook uses a lot of derivatives in its mathematical manipulations—for example, in turning Delta x / Delta t (the average velocity) into dx/dt (the instantaneous velocity). The problems will use derivatives in a more subtle manner. For example, a number of problems are going to ask you for “the least amount of force necessary” to accomplish some goal. When you see “least,” you should think “minimum,” which should lead you to a first (and likely second) derivative test to find the minimum. (What should you be differentiating with respect to? That depends on the problem…)

The assumption that you’re in Calculus II right now also means we’re not doing integrals—yet. We’ll first introduce integrals in our unit on energy (coming in October), which gives you lots of time to solidify your understanding of integrals.

PHYS 152, on the other hand, will use integrals a lot!

“I'm a little foggy when it comes to all the rules of derivatives.”

Aren’t we all! I’ve found a number of helpful resources at

http://www.mathwords.com/d/derivative_rules.htm (see also the links at the bottom of this page)

http://en.wikipedia.org/wiki/Differentiation_rules (contains some good explanations; be sure it matches what you know, though, as Wikipedia can be edited by anyone!)

http://math.arizona.edu/~calc/Rules.pdf (short and sweet!)

http://www.math.brown.edu/help/derivrules.html  (contains interactive sample problems and explanations; click on the “+” buttons to view the hidden information)

The rules that I see students missing the most are the product rule (some of you missed this in the damped harmonic motion functions in the most recent Graphing Project) and the chain rule (just keep taking derivatives until you multiply by dt/dt).

“I dont have any misunderstandings, just still trying to adapt to physics and what each means, like velocity is position over time and so and so forth. I am very new in this material and trying to kick my butt to do good in this course.”

That is a difficult transition to make! There are lots of study techniques you can use to help you internalize the meanings of physical properties. Some students keep a running equation list of the most important equations in the textbook so that they can view the most important concepts at a glance. Other students like to transcribe their notes to another notebook or electronic file after each class meeting to make their notes more organized and to reinforce the material in their minds. Many students also find it helpful to form an out-of-class study group with classmates to meet weekly over pizza/coffee/ice cream/a favorite TV show to work problems, check each other’s work, and ask each other questions.