<p>I’ve never been particularly good in determining which formulas I should start with and then which formulas to use to get me to the answer.</p>
<p>Maybe I’m just thinking about the problems the wrong way but when you more gifted problem solvers [engineers or engineering students] work on problems, how do you approach it? What do you think of when you are given a few known information in order to get to an end result?</p>
<p>For example, how do you deduce what formula to start with when you are given many values that can go into various equations? Rather, how do you determine how to start?</p>
<p>Personally, I right out all the values I am given and what they represent (For example, i write k = 34.3 N/m) on the side of the paper so I can immediately determine what I have to work with. However, I am very inefficient with finding the right method to start the problems. It’s not a problem to manage numerous numbers but the problem is knowing which formulas I can use wit those numbers. This is especially a problem when I’m required to go through multiple formulas to get to a solution and when varous equations will allow me to plug in known information.</p>
<p>Besides practice, how can I improve my performance in math, physics and engineering courses? How can I, should I approach the problem the proper way?</p>
<p>Always think of it in terms of the relevant concept. Knowing or deriving the correct formula is pretty easy from there. </p>
<p>If you’re dealing with an object moving along another (ex: boat on a river), you’re solving relative motion. If you’re dealing with a falling object, you’re either dealing with kinematics or conservation of energy (your choice/depends on the problem). Understand what’s actually happening there, then you usually solve by using calculus with a bit of physics thrown in.</p>
<p>Formulas are useful for two things, really:
- When a relation isn’t that well understood but a formula can provide a “good enough” estimate for viable use (you will use these a lot in differential equations and fluid mechanics).
- When you already understand a concept well enough and they save you some time (doesn’t really happen much when you’re learning because you don’t understand yet).</p>
<p>I use mostly pattern recognition (trying to consider things I did in the past to solve a similar problem), and minor computations (try some stuff to see if the problem will reduce down to something simpler) when solving new problems, for computer science and math, at least. Also listing out what you know is good, because it’s easy to overlook an important piece of information you could use to solve the problem.</p>
<p>I spend a ton of time looking over past problems I know the solution of (from an answer key, etc.), and asking myself “if I changed step X of this solution, would I still get the right answer?” because if you can’t disprove the correctness of another approach to a problem, you probably don’t understand the problem well enough. I also contemplate other possible solutions, because there’s often many ways to solve a problem and prove/disprove whether they work.</p>
<p>By understanding what the equations that you’ve learned describe and where do they exist. I.e. understanding what a particular situation is and what physics can tell about it.</p>
<p>The way to practice this is to practice by doing several problems. You need to train an intuition for seeing the right things and for ignoring false clues and science that does not apply to the situation in hand. Same works for math and engineering projects. Practice makes perfect.</p>
<ol>
<li>What quantity am I solving for</li>
<li>What information do I have</li>
<li>What are some ways of solving for what I want</li>
<li>Is the information that I have sufficient, or do I need to break the problem up into smaller subproblems. If so, break it up and start from step 1 for each subproblem. </li>
<li>After solving all subproblems, combine solution</li>
</ol>