<p>This is from Philip Morse’s textbook called Thermal Physics. It’s pretty old, the last edition was printed in 1968 or so. Pages 96-67 of the second edition.</p>
<p>As a note: (dX/dY)Z means the partial of X with respect to Y at a constant Z.</p>
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<p>So, we can see that maxwell’s relations are just like derivatives in that they’re a useful mathematical tool to help us figure out ways to get real work done.</p>
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<p>I think Fourier transform is to convert functions from the frequency domain to the time domain. Is that simple enough?</p>
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<p>Haha nice try but that is why there are group labs in engineering. Tests are used to test individual knowledge. Theoretically you could have a group where one person is able to get an A and everyone else would fail but because that one person gets an A everyone gets an A.</p>
<p>My dad actually told me about a few engineering classes he had in college where the final was a group final. There would only be 4-5 people in the class, so the professor would write the problem down for them, and they would have to divide the work of the problem up among the group. Professor would come back 2-3 hours later, look at what they all wrote on the chalkboards, how well they could explain their work, and would grade them based on that.</p>
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<p>It just starts to get a little confusing when you’re talking about reciprocal space and how certain vectors there are perpendicular to various vectors in real space and all the junk like that. I think if I had been introduced to fourier stuff in a math style instead of diffraction it might make a little more sense, but I always try to think of it in terms of diffraction now, and it’s just really weird. Like, I still don’t really get why when you’re performing electron diffraction of a crystal and there’s a little bit of a hole included in your beam, instead of seeing circular dots you wind up seeing half-moons for all the points. Like, there’s some sort of fourier transform of the shape of the hole being convoluted with the intensities based on where on the Ewald Sphere you are and then I get lost.</p>
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<p>Your second paragraph is spot on. The issue is not whether one can do the math. The issue is why should somebody do the math? That is, what exactly is the point of doing all that math? You said it yourself, I have never once seen a useful application of the M.R.'s. I asked once, and I’ll ask again: what the heck does it actually mean, in a real-world sense, to take the partial derivative of pressure with respect to entropy? How does that help me build a real-world engine (which was the whole reason why thermodynamics was invented: to explain engines)?</p>
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<p>I have no problem with TA’s who don’t know the material and yet are still trying to learn it. That’s clearly better than TA’s who don’t know the material and don’t care.</p>
<p>However, what I am saying is that it would be better if TA’s were to know the material before they became TA’s of that particular course. Or, in other words, you don’t select TA’s who don’t already know the material. Wouldn’t that be optimal? Unfortunately, often times, we don’t have that. Instead we have the blind leading the blind. </p>
<p>However, in this particular case, with the M.R.'s, it is probably impossible to get such a qualified TA, because like I said, nobody understands what the M.R.'s really mean.</p>
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<p>Uh, no, that’s false. That’s not what you’re doing.</p>
<p>That gets to what I’ve been saying. It’s all about being able to use thermodynamics. How do you actually use the M.R.'s to produce useful results? Nobody knows.</p>
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<p>Nope, I’m afraid it doesn’t work. </p>
<p>Look at it this way. What do you think would happen if you were to take that Morse book to a bunch of actual, real-world (bachelor’s degree level) engineers in industry and ask them whether they do any of that stuff described in Morse as part of their job. What do you think they are going to say? Be honest. </p>
<p>I think we can all agree that practicing engineers don’t do that as part of their job. They don’t go around manipulating Euler Equations or calculating partial derivatives. They don’t derive out pages and pages full of calculus. That’s not part of their job. </p>
<p>Which I think speaks to the real problem on the table. Engineering programs are hard because they don’t actually teach you much practical engineering. Instead, what they are really teaching you is how to become future engineering professors/researchers. Yet the fact is, most engineering undergrads will not become researchers. They’re just going to take regular engineering jobs.</p>
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<p>Dude, did you read anything from the excerpt I posted? The relations are used as a way to let you learn about the fundamentals of your system by turning those difficult/impossible-to-measure properties into things you can actually measure! One of the people in my lab was actually using these sorts of things to relate heat capacities and bulk modulus (another rather important thermodynamic quantity) to develop a new nondestructive testing technique to determine bulk properties of metallic glasses.</p>
<p>And I’m sure most of the engineers will say that they wouldn’t ever use Morse. I imagine they’d say my textbook on semiconductor processing is even more useless to them, though! In my field, at least, there are so many diverse career paths that are possible it seems ridiculous to me to try and teach to each and every possible job someone could get, and instead try to teach people the problem solving skills necessary to figure out the required knowledge for their field.</p>
<p>I agree there should be more business training of engineering students. I think it’s important that you learn how to do project management, learn about interviews (being on both sides), how to deal with company structures, and maybe even things like writing grant proposals. Engineering programs should really introduce a class or two on “soft” skills that will be required in any workplace.</p>
<p>And, also, if we’re complaining about things nobody actually understands, should we have any classes in quantum mechanics? ;)</p>
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<p>Dude, I read everything you posted. Did you read what I posted? </p>
<p>What you’re talking about is irrelevant, for a simple reason. The relevant question is whether most actual real-world engineers will ever do any of these things. I think you have conceded that they will not. See below. </p>
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<p>Yeah, * in your graduate student lab*. Again, how many engineers are ever actually going to work in a graduate student lab? </p>
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<p>I think you’re now coming around to the core issue. The real issue is: what skills do most engineers use? Schools should then concentrate most of their time on teaching those skills. If only a tiny percentage of engineers will use M.R.'s, then they should occupy only a tiny percentage of the curriculum. They certainly shouldn’t be a early-stage requirement, as is the case, where thermo is actually used as an early weeder. </p>
<p>I too believe in the development of problem-solving skills. But I think you would agree that these have to be actual problem solving skills, where the connection to actual real-world problems is made clear, not like what happens in many of your Caltech courses that you have complained about (i.e. that solid-state class of yours). Professors should be assigning problems in which you actually develop an intuitive feel for what is actually happening. Otherwise, you’re just doing math for the sake of math, which is something that I have heard you complain about before. </p>
<p>I seem to recall how you complained about having homework in which you had no idea what was going on, and had to resort to little more than handing in an incomplete answer set with a shrug of the shoulders, because it was the best you could do. Exactly what sort of problem-solving skills were you developing there? The skill to tolerate frustration? Exactly what did you mean when you warned that if you liked a particular subject, you probably shouldn’t take a class on it at Caltech? How do enthusiasm-draining classes like that actually help you to develop problem solving skills? They do not, and I think you know they do not. </p>
<p>Which connects back the OP’s question. Engineering is hard because many engineering courses force you to spend time on tasks that are not actually useful. You’re not really learning why you’re doing your assignments. Nobody is telling you how to use what you are learning. They’re just trying to use it as method to weed you out. </p>
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<p>Not for the people who don’t want to know it. Most engineers, in particular, will never need to know it. I’m still baffled as to why chemical engineers (at least at Berkeley) are forced to take an entire course on quantum chemistry. </p>
<p>I have no problem in offering specialized courses such as the above as electives for people who want to know. Hence, for those people who really want to understand how to use the M.R.'s, by all means, take an elective course on it. But what about the people who don’t care? What about those who just want to learn how to be regular engineers? Why are they forced to put up with courses they will never use, when there are plenty of other topics they could learn that they will use? Again, be honest, how many regular engineers out there will ever actually use the M.R.'s? </p>
<p>If the goal is to develop problem solving skills, then make sure that you are teaching relevant problem solving skills. You don’t just play games with math just for the sake of math. The math has to be shown to be relevant to tasks that real-world engineers *actually do *on the job.</p>
<p>It’s truth, all this math background is just it, math background. But in reality, when you go to work, you rarely use it. I never used Fourier Series and Laplace transform for nearly 30 years of working as an engineer. There are tools out there to help you do your job easier, like Matlab for example.</p>
<p>sakky, let me try again.
<nerdy stuff=“” alert=“”>
The partial of pressure wrt entropy implies to me that these quatities are related and it is a measure of their relationship when all other properties of the system are unchanged. Intuitively, it’s somewhat analogous to the relationship between time and distance travelled, in the domain of mechanics, and its derivative called the instantaneous velocity. This’s as intuitive as I can make it without explaining what pressure and entropy mean, which I won’t even try.
What Maxwell equations are saying is that – now I am being way off my base here, so I could be wrong – the pressure and the entropy are related in the same way as the internal heat is related to its friends. </nerdy></p>
<p>One practical application could be that, if you can measure the pressure and entropy (and some other stuff), you can figure out the internal heat. Or vice versa.
So, it sounds like a neat thing to know if you are trying to cook a mix of toxic chemicals that generate a lot of heat.
So, yeah, I believe it when you say the vast majority of chem engrs never use it. But that doesn’t mean it shouldn’t be taught. College is not just a vocation training. You learn some things because they explain why you do what you do. Say, you are a chem engineer fresh out of college with a BS degree working at a plant, and your boss tells you to do uh…something (I don’t know what chem engrs do. I just imagine them wearing a white coat and a gas mask pushing buttons and dialing gauges :)) wouldn’t it be nice to know why you are doing it?</p>
<p>Oh god damnit, the page just timed out after I wrote up my big response and the whole thing disappeared. I’ll summarize.</p>
<p>1) The MR thing was to show what they’re used for (which you said you never understood), not what they’re used for in industry.</p>
<p>2) The three most industry-oriented classes in my MSE undergrad program (semiconductor, metallurgy, and ceramic processing) were all heavily dependent upon thermo. The metallurgy class is actually joked about as being a higher-level thermo class where you finally learn enough to apply it to real systems. The class is also described as you to design a steel mill.</p>
<p>3) Stop bringing up my dissatisfaction with Caltech. 80% of my classes are in non-engineering departments, and those are the ones I haven’t been satisfied with. The three classes I’ve taken with the MS department have been pretty good, though, due to the nature of the school/department, they still have a very physics-y slant.</p>
<p>4) My comment on QM was a reference to Feynman’s line, “It is safe to say that nobody understands quantum mechanics.”</p>
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<p>I actually didn’t experience any weed-out classes at CMU (the only person that switched majors switched in to math. I imagine he didn’t do this because he found the math of engineering too difficult), yet my classes were still very difficult. I think the difference is I had professors that made classes challenging, yet still very understandable. I don’t feel what’s wrong is the material that’s being taught, I feel what’s wrong is the professors that do a poor job teaching. So if you want to say engineering is tough because teaching sucks, I’ll wholeheartedly agree. I’ll also say that the material on its own can be quite difficult.</p>
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I guess that you are also waiting for someone to explain the real world explanation to why potential energy + kinetic energy is constant in a conservative system?</p>
<p>The thing is, there is no explanation aside from the trivial one. Either you get it or you don’t, if you don’t get it is is just a mathematical equation which tells you nothing but you need to know it to solve the problems on the exams, if you do get it you understand that it is a valuable link between properties of a system that makes some things a lot easier to understand.</p>
<p>“The rate of change of blabla in tersm of bla = some ****” is the whole and only explanation of them, then it is up to each one to try to understand it but that is not something you can really explain, same with kinetic energy and potential energy, it is obvious when you understand the meaning of them, but how would you explain that to someone who do not understand it?</p>
<p>Or are you saying that we should stop teaching potentials just because it is an arbitrary concept and just helps with calculations? Or are you saying that since it is such an easy concept it should be taught while Maxwell relations are complex and therefore shouldn’t? But then where should they draw the line?</p>
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<p>It doesn’t surprise me at all to see that an outstanding researcher would admit that he would have struggled on some exams. It’s not humanly possible to do extremely well in engineering all the time. There’s too much material to master. I just wish that this was more acknowledged in the discussions about why US students drop out of engineering, causing the so-called “engineer crisis”.</p>
<p>[Don</a> Dodge on The Next Big Thing: 50% of US engineering students dropout - Why?](<a href=“http://dondodge.typepad.com/the_next_big_thing/2008/11/50-of-us-engineering-students-dropout---why.html]Don”>http://dondodge.typepad.com/the_next_big_thing/2008/11/50-of-us-engineering-students-dropout---why.html)</p>
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<p>Every US citizen can’t afford a private education, especially one that provides pre-college engineering training on par with the type of education Korean, Chinese, Russian, etc. students get.</p>
<p>I went to a public HS that was one of the highest-ranking in the US at the time I graduated. It provided a fairly seamless transition to university calculus and physics to some extent. OTOH, it lacked foundational material for computer science. But it could not have provided everything because (1) there were not enough funds, and (2) few if any on the HS faculty could have anticipated the importance of certain topics over others in computation.</p>
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<p>In countries like Korea, China, etc. those who are selected for an engineering preparatory education are getting a far more in-depth treatement of foundational engineering topics than what people get in a typical US K-12 program. This is by design. In the US, we have made conscious decisions not to preplan our children’s lives from such a young age. We feel it is more important for them to be well-rounded, at the expense of being immersed in engineering principles so they are more likely to outperform all other students on exams, etc. But there is a price to pay for this specialization - the students outside the US don’t get as much education in things it might be argued they need. For example, many come to the US with substantial English language deficiencies. I once had a TA for a compilers class that might have been a world-class researcher, but none of us who did not speak Chinese could benefit from him, because his English was very poor. It was so bad that many students complained to the department that he should not have been allowed to TA the class.</p>
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<p>No, but my point was that engineering was STILL hard even with all the really amazing advantages that I was fortunate enough to have, and plenty of people with similar backgrounds to mine have washed out of engineering, as well. I don’t think that we can point to a lack of secondary preparation as a reason why engineering is so difficult. I just don’t think it correlates.</p>
<p>It’s funny how some of us here think we can explain certain things.</p>
<p>A math equation is usually a model of some real world system. It’s one thing to understand the model (or equation) and another thing to understand the system it’s modeling.</p>
<p>Grammar? When will I ever actually need to know the difference between a noun clause and an adjective clause?</p>
<p>The difference between similes and metaphors? It’s not like I’m going to sit there analyzing why that persuasive speech/essay worked. If I ever have to write one, its persuasiveness most likely will not hinge on whether I used “like” or “as”.</p>
<p>Feudalism. Why do I care about lords and vassals? Does it affect my life now? This doesn’t include the argument that the reason I live under a president instead of a king is because of those lords… I don’t need an in-depth explanation of feudalism to understand that absolute power is bad.</p>
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<p>I realize this is a bit of a tangent, has nothing to do with math or engineering or M.R., and is probably the result of a misunderstanding.</p>
<p>Yet I feel it shows that this emphasis on stuffing useless stuff into our minds begins in elementary school.</p>
<p>While knowing the difference between a metaphor and a simile is not really important, knowing basic grammar is very important. It is also a skill many people (many engineers) seem to lack. </p>
<p>Anyways, much of our time in school is spent learning things we will forget. This all has to do with “learning how to learn” and that enough of that information will stick to give us a broad education. It also gives us an opportunity to find out what we enjoy. I’m sure English majors who took calculus or physics in high school feel that was a waste of time.</p>
<p>My husband dislikes English as much as the next engineer(he is a native English speaker). He thought he would be doing ok with just a Phd in Engineering. Guess what, as you move up even in technical world, not just management, you need to express yourselves very clearly. So don’t discount English and grammar rules. It’s how you communicate your ideas and thoughts to other people and the rest of the world. This is why I made sure my humanities child took Calculus in high school eventhough she never had any intention of majoring in engineering or any hard sciences.</p>
<p>You have no idea how much a well-rounded education will open doors for you. One-sided engineers stay in their cubicles. Engineers that can express themselves clearly, discuss music and art and culture, understand cultural and historical references, converse with clients, and market their abilities are the ones that are brought into the light by their superiors. Choose which you want.</p>