<p>I am dealing with Applications of Fourier series in partial differential equations and I have problem in understanding the proof behind it. Although I can understand parts of the proof, I really cant recall them without looking at the book.</p>
<p>c My question is: It is neessary to understand the proof in order to use a math equation?
How many of you here just simply use the equation without knowing how it came from?</p>
<p>Sorry for the bad grammar.</p>
<p>If you are merely going to use the equation in an applied sense, probably not. But if you are ever going to go beyond it, then probably yes. I can use an automatic transmission without understanding it, but I cannot go beyond mere use, and must rely on other people when I run into trouble.</p>
<p>It’s important to know what you’re doing and why. Understanding proofs helps you do that. Of course if you can get away with just being able to apply it, that will work, but like UT said above, you won’t get any deeper understanding and if you need that understanding sometime in the future it’ll take more work.</p>
<p>Of course, this is from a guy in physics, so we care about learning everything. Be a GOOD engineer and learn it, so that the physicists can’t make fun of you for being a gearhead or inferior or something (though it’ll probably happen anyway… 8) ).</p>
<p>If you can partially or on a higher level understand the proof BUT can apply it even better, then master the application without totally knowing the proof behind it FIRST, but…</p>
<p>Whenever you have ANY type of free time…it can be while waiting for someone or even in the bathroom, try to learn the proof behind it.</p>
<p>rico, to be fair, sometimes proofs in applied textbooks are kind of lame. Sometimes in order to present a non-confusing proof of a concept, you need to step back, and define some abstract crap and then the your old proof is actually a special case of a more general thing which is easier to show. This sort of approach is often impractical for applied classes.</p>
<p>It isn’t that big of a deal to not be able to provide the proof for math equations you use in engineering. What is more important is that you have a good intution about the equation and about what the solutions to it mean. </p>
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<p>Physics students don’t care about learning everything. Physics students use math that they would have no idea how to derive from first principles too.</p>
<p>Learning the proof is useful, but not strictly necessary if you don’t intend to improve or modify the equation. Understanding the derivation may also help you to develop an intuition for the assumptions underlying the equation and hence a faculty for knowing how it needs to be applied. </p>
<p>Consider calculus. All engineers use it, but unless the student is a math minor/major, they probably haven’t taken advanced calculus, where the theorems of calculus are rigorously proven.</p>
<p>Some proofs you can understand conceptually, others you can really only “understand” the steps of the proof one-by-one.</p>
<p>Sometimes a concept has more than one proof. Look in other books or on the internet for a better proof. Sometimes it really is that simple. My calc class used a textbook that used an awful proof (or a badly-explained good proof) for why definite integrals give you the area under the curve of a function. But I’d seen another proof, one that used a simple graph and a three-step squeeze theorem proof to show the same thing, and it was much easier to grasp. Same deal with proofs about integrals in polar coordinates, I had to hunt online for a proof that I could grasp because the one my book used was bad.</p>
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Not if you’re in theoretical physics. Experimentalists seem to care less about this though, so they have the same problem as engineers.</p>
<p>A good experimentalist is every bit as theoretically and mathematically competent as the theoreticians in that field. In practice that isn’t always the case, but it is true of a truly GOOD experimentalist.</p>
<p>That’s true. I probably should say that in theoretical physics, you’re required to understand things mathematically, though any good experimentalist (and engineer, for that matter) will be well-versed in the theory and mathematics as well.</p>