<p>I'm an undergraduate student and my engineering textbooks many times spend pages upon pages to derive just one formula. How much time should I spend to try to remember all these derivations because I find that most of my test and homework questions ask me to merely find and manipulate the right formulas in order to get the right answer. I do however, spend a lot of time figuring out the conditions that certain equations can be used or not, but I'm getting into the habit of using equations I don't know the origin of. Is this bad? Are derivations necessary for successful engineers in industry?</p>
<p>Knowing when an equation does and does not apply is a pretty important skill. You might not have to know the entire derivation, but certainly you will have to know when it works and why, and when you have to do something different.</p>
<p>I don’t think you need to know how things are derived, but you do need to know when and how to use certain formulas. </p>
<p>Once you get out of school, the math you use will be practical, plug-n-chug applications. You won’t have to be deriving formulas or doing proofs unless you’re working at a university</p>
<p>@simba9 That is awesome…I can’t wait to get into industry then. Also, once out of school, do engineers usually use the same techniques over and over again with slightly different modifications for their work? </p>
<p>Well, it’s best to know derivations if you forget a formula. </p>
<p>^^^ No. If you forget a formula, you look it up. . </p>
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<p>For the most part, yes.</p>
<p>Understanding the derivations allows you to understand where and how the underlying assumptions break down. So yeah, you need to understand the derivations. </p>
<p>A model is only good when it applies. </p>
<p>I mean, I understand most of the derivations; it’s just that I usually throw them out my mind after reading them while still holding on to the conditions needed for certain equations.</p>
<p>My mind always went blank when a professor was doing a derivation or mathematical proof in class. Most of the things they drone on about you’ll never use in your career. What you learn in school is a superficial introduction to subject matter.</p>
<p>It’s through on-the-job practice and making mistakes that you learn when to use, and when not to use formulas, equations, processes, algorithms, etc. Only then do you start to really understand why certain things work and don’t work.</p>
<p>That’s why people who have just graduated are rarely given jobs with critical responsibility right away. They’re still at the point where they know just enough to be dangerous.</p>
<p>You need to understand the derivations, but understanding them does not mean remembering every step off the top of your head. However, it is an exceedingly bad idea to get “into the habit of using equations [you] don’t know the origin of.” This is tantamount to not knowing what assumptions are required for validity. So yes, you ought to know the origin of the formulae, though memorizing the steps is overkill.</p>
<p>Of course, once you actually sit down and understand the basics from which most of the equations originate, you will likely have no problem figuring out the steps even though you don’t remember them off the top of your head.</p>
<p>I try to derive the formula at least once, i think it’s important to know how you got from point A to point B. Often times it’s also an enlightening experience and gives you an appreciation of how smart the ppl who’s footsteps you follow in were. Don’t memorize every step tho, that’s a waste. </p>
<p>You need to understand the first principles (i.e. the starting point of the derivations). That will keep you out of a lot of trouble. I had more than one class where the exams were simple if you understood those, and almost impossible if you relied solely on the formulas at the end of the chapter. It’s also a good way to do a sanity check on a complex analysis. If you can say to yourself “Hey, fluid shear does not work like that!” when looking at a result, then you can catch a lot of mistakes.</p>
<p>You do need to understand the assumptions that go into the derivations so that you can know whether the formula that was derived applies or not. Understanding the derivation is also important for the same reason, but you don’t have to memorize that derivation. After all, you can always go back to your text and look it up as necessary. </p>
<p>Once you get out of school, you will find that there are handbooks and manuals that list all kinds of derived formulas. It will be up to you, the engineer, to know which formula applies and be able to stand behind the use of it. It will be your reputation and your liability on the line and it pays to get it right.</p>
<p>Some engineers work in a very small space within their field. They may use only a few formulas and they will get to know them very well. Others will have a more broad range of expertise. At this point you probably don’t know where the twists and turns of your career will take you. Pay attention to the derivations.</p>
<p>I find putting time into studying the derivations helps me really understand a equation (Why, how and when it works) which helps me figure out when I should use said formula.</p>
<p>What if I have a very inefficient textbook that goes from point A to point E and inaccurately assumes that I know how to do all the intermediate steps in between each step it lists, causing me to spend around half an hour every page of the book in order to understand everything in it? This is without teacher/peer help by the way; I would love to be able to have the skill to do things on my own instead of always relying on others for help. </p>
<p>The higher the math, the more assumption are made about what knowledge you possess at that point. You might have gaps in your mathematical foundation that prevent you from understanding the intermediate steps that connect point A to E. Do you think that might be the case?<br>
I do agree some textbooks will have convoluted explanations. It might be helpful to ask in the math forums or watch a video on the topic. It might be explained in a more succinct form.</p>
<p>Most of the times, when I don’t understand what the author or the professor is doing in lecture or in the textbook, it’s because he does not mention what techniques were used to get to a certain step. The math is usually extremely simple (expansion, factoring, multiplying, differentiating, adding two equations together) but because they are so simple, I think the author/lecturer skips them and instead puts “by inspection, you get this formula” or “clearly, this function equals 0.” I thus spend around 20 minutes every page because I get stuck in trying to figure out how everything connects but fail to do so because the author doesn’t bother to mention those crucial steps needed to get to a certain equation. And then it gets frustrating because I would spend an hour on “experimenting” with various mathematical tricks to try to figure out what it is that the authors were paid to explain. </p>
<p>When I’m with a tutor or with a professor one-on-one though, these issues are cleared up almost instantaneously but I cannot be with someone who knows more than I do in engineering all the time. Is there no way to reduce this frustration or do I just have to learn to deal with it? </p>
<p>Well the hope would be that once you’ve seen a trick a few times you’ll catch on and start trying similar things on your own without a tutor.</p>
<p>Yeah i get the feeling you fundamentals might be a little off base koalass. It really helps having a solid understanding of precalculus (factoring, trig, how graphs behave, how to manipulate them) and one of my calc professors once said, “what gets you in calculus isn’t calculus, it’s algebra”. Hope it helps</p>
<p>Yeah that does help a lot. I feel like I’m just complaining though haha. My professors did tell me that the best way to learn was to struggle and I am struggling a lot with this. The pace is slow but I’m getting the hang of things.</p>