What's your "master blaster" strategy for solving problems?

[Moriarty]

We had a running gag in my tutoring center whenever someone has a problem with integration, we ask them if they've used the "Master Blaster" to solve it. It stems from my friend who, when we were in Calc BC, he would always use RK on an integration problem to see if it would work. We had a conversation about what everyone else' "Master Blaster" was. Mine is meticulously writing every variable down and what I know before I would tackle something. We actually starting compiling serious ways of tackling physics and math problems. We made a handout for our students and they seem to work well with it. I was sort of wondering what the internet has to say about more complicated problems though, since all our students are in middle and high school and I'm going off to college soon. The sad thing about my education currently is that my physics classes I'm in basically only challenge us to do plug and chug and I was wondering how you would tackle a problem where just knowing an equation and solving for a variable won't cut it, like the famous inverted pendulum in oil problem or proving Gauss' law without prior memorization or online/book resources.

In other words, what's your "Master Blaster" PF?

 

[AdityaDev]

In integration problems I look for the pattern. Like when we see $x^2+a^2$ I will try substituting $atan\theta$. It comes from practice. I don't know much formulas but for me experience works. After I solved 100-200 problems related to partial fraction method and UV method things became very easy. I don't have the habit of writing down all the variables.
So my technique: Practice.
For physics, I am able to solve irodov's problems in general physics and other high level books because I go by basics. No formulas. Whenever I have a conceptual doubt, I post it in PF.
For physics: Apply basics and one has to be good in basic calculus.

 

[Timo]

[x] Scatter plots and histograms. Don't know what to do with data? Make a scatter plot and/or a histogram and hope something sensible comes out.
Admittedly, this is not exactly the "Master Blaster" in the sense that it solves the problem but more like the hammer in "if your only tool is a hammer everything looks like a nail". But usually, hitting a fish with a hammer still gives some feedback that gets you further, even if it is "hammer does not help you here because ...".

 

[Chestermiller]

This is an extremely good question you have asked.

I've been around modeling physical systems for over 50 years now, and I've evolved to a strategy that I always use and I think will be helpful to you. In solving any problem involving a physical or chemical system, I always follow these four steps in order:

1. Articulation
2. Formulation
3. Solution
4. Presentation

Articulation: You need to be able to articulate (in words) the fundamental physical mechanisms that are involved in determining the response of your system. Basically, you have to say in words what is happening physically. If you can't do this, then you will not be able to solve your problem.

Formulation: After you have articulated the physical mechanisms, you need to translate these into the language of mathematics (equations). This means writing down the equations that describe the physical mechanisms mathematically, and that thereby capture the response of your system. Once you have completed this step, the conceptually difficult part is usually over.

Solution: This involves applying what you have learned in mathematics classes to solve the equations.

Presentation: This involves using the results of solving the equations to reach conclusions about the response of your system. The results are usually presented in the form of graphs. You need to be able to explain to others (such as decision makers) concisely, and in simple ways, the important results and conclusions you reached from your analysis. Without doing a good job at this, all the clever work you have done will be worth nothing, and people will end up having a low opinion of you. The importance of communication skills can't be overemphasized.

Chet