<p>Japher whats your major?</p>
<p>
[quote]
When you enter college and engineering programs you need to be reprogrammed to think ciritcally, analytically, and creatively. You are no longer expected to take what you're given and like it, you are now required to interpret, translate, and build upon the knowledge you are fed. Functions are not just definitions or interpretations or pictures on a graph they become tools to understand and utilize. It is not regurgiation any longer, and that is what you are used to doing.
[/quote]
</p>
<p>To that, I will say that I am still waiting for somebody to actually explain what the heck the Maxwell Relations and Bridgman's Equations of thermodynamics actually mean, in a real-world, intuitive sense. I have asked every engineer I know to explain, and to this day, I still haven't gotten a satisfactory response. Heck, even the people I know who went on to get PhD's from top engineering schools have admitted that they don't really understand what those equations actually mean. Invariably, whenever I show these equations to actual engineers, I get a smirk, a shake of the head, and an admission that they never really understood them when they were students and were just thankful to have passed the class. </p>
<p>I mean, seriously, what the heck does it mean for the partial derivative of temperature with respect to volume at constant entropy to be equal to the negative partial derivative of pressure with respect to entropy at constant volume, and for both of them to be equal to the double partial derivative of internal energy with respect to entropy and volume??? What does that translate to in plain English? *I don't know. Nobody knows! *</p>
<p>Bridgman's</a> thermodynamic equations - Wikipedia, the free encyclopedia
Maxwell</a> relations - Wikipedia, the free encyclopedia</p>
<p>Hence, it's still a great mystery to me why students are forced to take classes on topics that they won't understand, and the engineering programs know that the students won't understand. Was this just a matter of 'intellectual hazing'? Was it just a matter of simply intimidating the students? I don't know. What I do know is that there sure wasn't a heck of lot of 'understanding' going on during those classes. Like I said, to this day, I still can't find an engineer who actually understands that stuff.</p>
<p>It would be interesting to hear a professor's response to sakky's thoughts on the chemical engineering curriculum. Anybody ever ask? Anybody with a good relationship with chemE faculty want to ask?</p>
<p>I'll take another shot at it.</p>
<p>
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what the heck does it mean for the partial derivative of temperature with respect to volume at constant entropy to be equal to the negative partial derivative of pressure with respect to entropy at constant volume
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</p>
<p>If you change your volume during an an isentropic process you'll see a change in temperature that's equivalent to the negative of the change in pressure when you're changing the entropy in an isochoric process.</p>
<p>I think that's about as coherent an explanation as you'll see of anything involving any description of equations with a bunch of partials going on.</p>
<p>(I figured I'd give it a shot after you've made that same copy-paste post six times now.)</p>
<p>
[quote]
If you change your volume during an an isentropic process you'll see a change in temperature that's equivalent to the negative of the change in pressure when you're changing the entropy in an isochoric process.
[/quote]
</p>
<p>Dude, that's just a rewording of the mathematical equation!</p>
<p>I'm not asking for the math equation in words. I can solve the math. What I am asking for is what does it all mean, in a real-world sense? That is, let's say that I have a real-world car engine in front of me. {After all, thermodynamics was originally devised to understand engines.} How exactly do the Maxwell Relations and/or the Bridgman's Equations actually help me to understand what is going on with that engine? For example, what the heck does it even mean take the engine's double partial derivative of internal energy with respect to entropy and volume? I don't know! Nobody knows!. Even if you did know, how exactly does it help you design a better engine? </p>
<p>Now, don't get me wrong. I am not saying that all of thermodynamics is so inscrutable and, frankly, so useless. The 3 laws (actually 4 if you count the 0th law) of thermodynamics are extremely important, and the 2nd Law is arguably the most profound statement in all of science, for it helps you to truly understand what equilibrium really means. </p>
<p>The Maxwell Relations and the related Bridgman's Equations, on the other hand, are entirely different. As far as I can tell, and as far as the numerous practicing engineers that I know, they're not useful for anything. You never see any real-world engineers ever trying to calculate, say, the partial derivative of pressure with respect to entropy at constant volume. Heck, even if you did, nobody would understand why it would be helpful, or even what it would mean. </p>
<p>The point simply is that engineering courses often times relegate students to a state of nothing more than pure survival. You don't know what you're really doing. You don't know why. You certainly don't understand anything. All you can do is hope that you score enough points to pass the exams. That's all you can do.</p>
<p>Let me tell you this. I know one girl who's a brilliant engineer: she graduated with honors, and she stayed to get her PhD in engineering in just 3 years, and with 3 first-author publications and another 2 first-author publications under review by the time she finished her PhD. During her stint as a graduate student, the prof of the undergrad thermo class specifically contacted her, asking her to be the TA of that class (because she was a former student of the class who got a good grade). She turned it down. Why? I will always remember her reason. * She said that she wasn't comfortable being a TA for a class in which she didn't understand what was going on*. Think about that. If even she didn't understand what was going on, what does that say about the rest of the students?</p>
<p>
[quote]
The point simply is that engineering courses often times relegate students to a state of nothing more than pure survival. You don't know what you're really doing. You don't know why. You certainly don't understand anything. All you can do is hope that you score enough points to pass the exams. That's all you can do.
[/quote]
</p>
<p>Bessel J function, never used it, don't see myself using it.</p>
<p>I guess at some level there is unpractical stuff being taught in engineering courses.</p>
<p>
[quote]
I guess at some level there is unpractical stuff being taught in engineering courses.
[/quote]
</p>
<p>Well, in the case of the Maxwell Relations/Bridgman's Equations, they were taught in the second course of the (weeder) gateways that lead into the major (chemical engineering). I highly doubt that this was a coincidence: they deliberately chose to use concepts like the Maxwell/Bridgman's to weed people out.</p>
<p>The problem is that even those people who survived - like myself and, even more poignantly, that girl who ended up finishing her PhD in just 3 years - are also utterly mystified as to what exactly those concepts actually mean. The only difference between them and us (the weedouts) is that we were better at math than they were, and we were also luckier on the exams. But we certainly didn't have any intuition as to what was really going on or what the relations/equations actually meant. Nobody did.</p>
<p>check the papers posted on Olin, MIT Aero/asto and Webb websites. The amount of material to be taught in engineering school has increased 100 fold in the past 30 years, and so the schools have cranked up the workload to an impossible level. Result: TOO many students dropping out of engineer and a looming engineer shortage.</p>
<p>That is why MIT AERO/ASTO, Olin, and Daniel Webster have adopted entirely new engineering education paradigms. They focus on thinking, and problem solving rather then stuffing an impossible amount of info into students heads too fast.</p>
<p>The biggest difference between the College of Engineering and the College of Arts and Crafts at most universities is that in engineering the answers are either right or wrong and most engineering profs give little or no credit for understanding concepts if the answer is wrong. In the liberal arts your grade will often depend on whether you appear to agree with a professor's view of the world, which most manage to make an integral part of every course that they teach.</p>
<p>
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the College of Arts and Crafts
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</p>
<p>That made me laugh.</p>
<p>Heh, the humanities at my college was Humanities and Social Sciences, abbreviated H&SS. It was generally referred to as "H and Less Stress" by everyone.</p>
<p>Sakky, those equations are used in figuring out all of those properties about engines that everyone cared about. I mean, do you have an objection to teaching engineering students how thermodynamics works instead of just some results? Doing all of those crappy equations and stuff like that teaches you think critical thinking skills that's required of an engineering education (not to mention physics and chemistry, since it's not like they get to escape thermo). </p>
<p>Can you explain to me in plain words what Fourier transforms are without using anything "technical"? I was dealing with them in the first class of my materials major, and, even now as a grad student, I don't fully understand them. Does that mean they're not worth anything? Can you explain the meaning of Schrodinger's Equation without using the mathematical meaning? How about Fick's Laws? Can you describe how to measure the heat capacity without basically restating the mathematical definition for it?</p>
<p>PS: Isn't part of the point of TAing so you can learn in depth the things you didn't solidly understand before? I know I understand how a TEM works and what's going on much better now that I've had to learn it to the level where I could teach; why didn't your friend want to do the same thing for thermo?</p>
<p>
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Sakky, those equations are used in figuring out all of those properties about engines that everyone cared about.
[/quote]
</p>
<p>The problem is that they don't actually teach you properties of engines, or at least any real-world engines that anybody actually needs to know about or cares about.</p>
<p>As a case in point, the mechanical engineers at Berkeley (and presumably also other schools) don't have to learn the Maxwell Relations and certainly not the Bridgman's Equations. Don't get me wrong: they have to learn thermodynamics, but not these relations/equations. But why not? After all, I would argue that the mechanical engineers are arguably the most likely of all engineers to actually work on real-world engines. Granted, they can choose electives where they can learn all about these relations/equations. But they don't need to make that choice.</p>
<p>
[quote]
I mean, do you have an objection to teaching engineering students how thermodynamics works instead of just some results?
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</p>
<p>But that's precisely my objection. You don't actually learn how thermodynamics "works". Why? Because you don't know what's going on, and you don't have time to find out. All you have time to care about is passing the exam. That's it. That's all you can do. What's actually happening? You don't really know. </p>
<p>See below and I think you will understand what I mean.</p>
<p>
[quote]
Can you explain to me in plain words what Fourier transforms are without using anything "technical"? I was dealing with them in the first class of my materials major, and, even now as a grad student, I don't fully understand them. Does that mean they're not worth anything? Can you explain the meaning of Schrodinger's Equation without using the mathematical meaning? How about Fick's Laws? Can you describe how to measure the heat capacity without basically restating the mathematical definition for it?
[/quote]
</p>
<p>Again, the issue is not about whether to use mathematics. In fact, I even said that the one saving grace for me in thermo was that I could actually do the math, and other students could not. </p>
<p>But just because I could do the math doesn't mean that I actually understood what I was doing or why I was doing it. That's the part that was missing. I could derive and manipulate the mathematical equations all day long. But that shouldn't be the goal. The goal is to understand why you're doing it, and in particular, how to actually interpret the end results. When you can't do that, then all you're doing is simply playing games with math. </p>
<p>Again, see below. </p>
<p>
[quote]
Doing all of those crappy equations and stuff like that teaches you think critical thinking skills that's required of an engineering education (not to mention physics and chemistry, since it's not like they get to escape thermo).
[/quote]
</p>
<p>I find this to be an ironic statement, coming from you, for I seem to strongly recall you complaining about your courses at Caltech, i.e. something along the lines of how a group of you struggle to do the homework and then are forced to hand it in with a shrug because it's simply too difficult. You don't know what's going on. I also seem to remember you saying that if actually enjoy a subject, don't take a course on it at Caltech, for doing so will squelch that enjoyment. Hence, given your experience, I think you know exactly what I'm talking about. </p>
<p>Look, I have no problem with teaching engineering concepts, nor do I have a problem with doing so rigorously and quantitatively. But there clearly is some point at which you're overcomplicating the subject, such that nobody really understands what's going on. For example, when even somebody like John Prausnitz - one of the storied pioneers of chemical thermodynamics and a member of the NAE since 1979 - admits that even he probably couldn't have scored more than a 50% on a particular thermo exam, that indicates that that exam is far too difficult for an undergrad class. </p>
<p>Which gets to a philosophical point. The whole reason why we use mathematics and rigor within science/engineering is to improve our understanding of the phenomenon. In other words, the mathematical equations are supposed to be used merely as a tool to explain empirical results. The math is supposed to actually mean something in the real world. You don't use math just for the sake of using math. But that is precisely what happens in many courses, like my thermo course and evidently many of your Caltech courses. </p>
<p>Which is precisely what I am pointing to as the problem with topics like the Maxwell Relations and Bridgman's Equations. How does knowing how to manipulate those equations actually contribute to helping me understand real-world phenomenon? For example, once you know the M.R.'s, what exactly is it about real-world engines that you didn't understand before that you understand now? That is the question that no actual engineer I have ever known has been able to answer. </p>
<p>
[quote]
PS: Isn't part of the point of TAing so you can learn in depth the things you didn't solidly understand before? I know I understand how a TEM works and what's going on much better now that I've had to learn it to the level where I could teach; why didn't your friend want to do the same thing for thermo?
[/quote]
</p>
<p>The reason is simple and actually speaks to the OP's point. She didn't want to have to (re)learn those topics because, frankly, she never uses it. Now, don't get me wrong. She obviously uses general knowledge about thermodynamics. But she has never found any use for the Maxwell Relations or Bridgman's Equations. Yet, clearly, she is a highly successful researcher. </p>
<p>Which gets to the whole point of why I brought this topic up in this thread. The fact is, engineering is hard because the programs often times force you to learn things that you don't really need to know. And even the term "learn" may be a misnomer, because at the end of the day, all you may have learned is how to manipulate a bunch of mathematical equations, but not actually understand what the point is. {RacinReaver, again, think back to those courses you took at Caltech.} In other words, engineering is hard because the faculty are deliberately trying to make it hard.</p>
<p>
[quote]
Can you explain to me in plain words what Fourier transforms are without using anything "technical"? I was dealing with them in the first class of my materials major, and, even now as a grad student, I don't fully understand them. Does that mean they're not worth anything? Can you explain the meaning of Schrodinger's Equation without using the mathematical meaning? How about Fick's Laws? Can you describe how to measure the heat capacity without basically restating the mathematical definition for it?
[/quote]
</p>
<p>I find this explanation of Fourier</a> series useful as a basis for understanding Fourier transforms. However, it's the sort of thing where to fully understand it one has to also understand everything else it depends upon. This might be more difficult for some than others depending upon their background and patience.</p>
<p>
[quote]
PS: Isn't part of the point of TAing so you can learn in depth the things you didn't solidly understand before? I know I understand how a TEM works and what's going on much better now that I've had to learn it to the level where I could teach; why didn't your friend want to do the same thing for thermo?
[/quote]
</p>
<p>Well, it certainly helps. However, I can see why the student might be reluctant to TA something she didn't feel she understood very well. After all, she wouldn't want to explain something poorly to someone who really needed a better understanding, e.g. to pass the class. Also, some people are good at things but don't have a good handle on why they're good at them. They have trouble coming up with alternate explanations, analogies, etc. I was fortunate when I was tutoring linear algebra that I had somewhat of a background in abstract algebra, so I could explain some of the "why".</p>
<p>
[quote]
After all, she wouldn't want to explain something poorly to someone who really needed a better understanding, e.g. to pass the class.
[/quote]
</p>
<p>Actually, I suspect that this may be part of the problem, at least in my thermo course, and also a general answer to the OP's question of why engineering is hard. You get TA's who themselves may not really understand the subject they are teaching but who may be using their teaching experience as a way to actually learn the subject, as RacinReaver said. That may be helpful for the TA, but that doesn't exactly do much for the undergrads. </p>
<p>Heck, we may even have the glimmer of an perpetual cycle of confusion here. The undergrad engineering class is TA'd by people who don't really understand the subject and hence are using the TA experience to finally learn what is really going on. Yet that means that the undergrads don't know what is going on because they don't have a TA that can help them. Some of those undergrads then go to grad school, whereupon they become TA's of that same undergrad class so that they can finally understand what is going on, but also contributing to that class's lack of understanding, etc. etc. in an ever-unfolding cycle of bemusement and stupefication.</p>
<p>sakky, i think your point makes some sense but doesn't account for the fact that the people who are getting PhDs probably did a lot better than the average person in the class at getting a good understanding of the material so they, even though they themselves may have had bad TAs, figured it out on their own/from the professor.</p>
<p>Sakky, you forget that I had mostly fantastic classes in undergrad at CMU and realize that it is possible to have a class that involves a lot of moving equations around but still learning what things are actually about. That's actually one of my biggest beefs with Caltech. The workload here doesn't correlate to the amount of learning you get from a class at all, while it almost always did at CMU.</p>
<p>I've actually really been enjoying this Quantum Chemistry course here I've been taking here because the professor is completely about learning the physical meaning behind all of the equations, solutions, and derivations in quantum mechanics. We still do our fair share of ::math::, but for a good part of it I have a physical understanding of what's going on. It's pretty much the complete opposite of my solid state physics class.</p>
<p>Personally I think the problem isn't so much the material that's taught as the inability of many professors to effectively communicate what's important. To me, we should be developing physical intuition on how to solve problems and what all of these things mean.</p>
<p>And, you're right, some of those equations might not be useful for heat engines, but they were essential to solution theory and the type of thermodynamics I was doing as a materials scientist. Being able to predict phase boundaries, stable phases, and all those sorts of things are results of Maxwell's Relations (I never learned those bridgeman relations, but looking at some of them I'm sure I had to derive a few). While I doubt I'll be using Maxwell's Relations very much in a day to day career, I'm sure there's a good chance I'll be using their results, and knowing where those results came from can only help me understand why they're useful results even better.</p>
<p>
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Yet that means that the undergrads don't know what is going on because they don't have a TA that can help them.
[/quote]
</p>
<p>Didn't we figure that the TA was finally learning this material solidly, so shouldn't they then understand it enough to teach it to undergrads? Personally, I can tell when a TA doesn't want to TA the course and doesn't have a good enough understanding of the course to be a good TA versus when they don't necessarily understand everything, but they're willing to try and work the things they don't understand out.</p>
<p>
[quote]
sakky, i think your point makes some sense but doesn't account for the fact that the people who are getting PhDs probably did a lot better than the average person in the class at getting a good understanding of the material so they, even though they themselves may have had bad TAs, figured it out on their own/from the professor.
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</p>
<p>I certainly agree that those who went on to get PhD's obviously understood the material far better than the average person in the class. </p>
<p>But that's not saying much. In fact, that's been my point all along: that even the best students in the thermo class didn't understand much about the Maxwell Relations or Bridgman's Equations. Sure, they understood more than the average student (who didn't understand anything), but they still didn't understand much. </p>
<p>As far as I can tell, in that thermo class, the difference between the better students and the worse students is simply that the former were able to do the math better. That is, they could manipulate and derive the equations faster and more accurately than the other students. I was one of those 'better' students. </p>
<p>But the point of manipulating mathematical equations in engineering is to actually contribute to understanding of the phenomenon. You don't manipulate math just for the sake of manipulating math. This gets down to a fundamental principle within the philosophy of science (and engineering): math is supposed to be a tool to help you to understand and describe actual real-world science/engineering results. In other words, math is supposed to be a clarification tool, not an obfuscation tool.</p>
<p>All this gets to the OP's question: why is engineering so hard? I think much of the reason is that engineering programs often times force students to learn concepts for which the connection to the real world is not made clear. Instead of producing true engineers, they're actually producing mathematicians. </p>
<p>For example, I'm sure the Maxwell Relations and Bridgman's Equations are useful for something practical. But to this day, I'm hard pressed to figure out exactly what that would be. I can do the math all day long, but what does it actually mean? *I don't know. Nobody knows! *</p>
<p>
[quote]
Sakky, you forget that I had mostly fantastic classes in undergrad at CMU and realize that it is possible to have a class that involves a lot of moving equations around but still learning what things are actually about.
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</p>
<p>And similarly, I too have had classes where I learned what things are actually about. That's why I'm not pointing at all my classes. I am talking about a specific class that I took in which I clearly did not learn what was actually going on, in a real-world sense. Nobody in the class did. </p>
<p>
[quote]
That's actually one of my biggest beefs with Caltech. The workload here doesn't correlate to the amount of learning you get from a class at all, while it almost always did at CMU
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</p>
<p>So I see that your Caltech experience is giving you insight into how classes can be unnecessarily difficult. </p>
<p>
[quote]
I've actually really been enjoying this Quantum Chemistry course here I've been taking here because the professor is completely about learning the physical meaning behind all of the equations, solutions, and derivations in quantum mechanics. We still do our fair share of ::math::, but for a good part of it I have a physical understanding of what's going on. It's pretty much the complete opposite of my solid state physics class.
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</p>
<p>Again, my problem is not about the math. I certainly agree that math has to be used in engineering courses. But math is supposed to be used as a tool to help you to gain insight into engineering. It's not supposed to be the end goal in itself. We're not mathematicians. We're not supposed to be doing math for the sake of math. It has to be clear why we're doing the math, and what's useful about the equations. </p>
<p>
[quote]
Personally I think the problem isn't so much the material that's taught as the inability of many professors to effectively communicate what's important. To me, we should be developing physical intuition on how to solve problems and what all of these things mean.
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</p>
<p>Right, and that's what I'm looking for. To this day, I have no intuition into what the M.R.'s actually mean. What do they mean, in a real world sense? I still can't find anybody who actually knows. </p>
<p>The best I can get is what I have already provided: a simple restatement of the equations in words. But I'm not just looking for the equation. I know the equation. I can do the math. I want to know what the equation actually means in a real-world sense. What does it mean? I don't know. Nobody knows! </p>
<p>
[quote]
And, you're right, some of those equations might not be useful for heat engines, but they were essential to solution theory and the type of thermodynamics I was doing as a materials scientist. Being able to predict phase boundaries, stable phases, and all those sorts of things are results of Maxwell's Relations (I never learned those bridgeman relations, but looking at some of them I'm sure I had to derive a few). While I doubt I'll be using Maxwell's Relations very much in a day to day career, I'm sure there's a good chance I'll be using their results, and knowing where those results came from can only help me understand why they're useful results even better.
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</p>
<p>Then that's an argument for making the course an elective. Let's face it. Most engineers, at the undergrad level, just want to know the results. They don't really care why the results are true. After all, they're not going to be researchers. They just want to know the results.</p>
<p>I'll give you an analogy. As an engineer, you don't need to know real analysis. That is to say, you don't really need to rigorously understand what a derivative or an integral truly means, from a theorem/proof standpoint. You just need to know how to take derivatives and integrals. Now, for those rare engineers who actually want to know that stuff, they are free to take upper-division and graduate level math courses. But most engineers just want to know the results, without having to worry about why. </p>
<p>
[quote]
Didn't we figure that the TA was finally learning this material solidly, so shouldn't they then understand it enough to teach it to undergrads?
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</p>
<p>Yeah, they're learning the material solidly...during the course. Hence, after the course is over, they probably do know the material solidly. But that obviously doesn't help the undergrads while the course is going on. After all, the fact that my TA is going to know the material well 4 months in the future doesn't help me as an undergrad understand the material right now, and my grade is based on what I understand* right now*. </p>
<p>What might work is if the TA actually took the entire course over as a (auditing) student, and only then, in a subsequent term does he finally become the TA for the course. But that's not what happens. Instead, you end up with the blind leading the blind. </p>
<p>
[quote]
Personally, I can tell when a TA doesn't want to TA the course and doesn't have a good enough understanding of the course to be a good TA versus when they don't necessarily understand everything, but they're willing to try and work the things they don't understand out.
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</p>
<p>Yeah, but so what? How does knowing that help you? After all, if there is only 1 TA for the course (which is often the case), then knowing that he is bad and doesn't want to be there is not useful information to you. After all, there is no other TA anyway. There's no other place to go. Even if there are 2 TA's, if both of them don't want to be there, then once again, you're screwed. {That's what happened to me: I had 2 thermo TA's, and both of them didn't really want to be there.}</p>
<p>sakky, you are a whiner. lol. I know nothing about chemical engineering, and the Maxwell stuff doesn't look so bad to me. I mean, it says what the math says. If you understand the concepts of temperature, volume, entropy and internal heat (I don't), the equations seem to tell you something about how their changes are related.
Maybe, you just haven't seen a useful application yet. If it's something every chem engineering student learns, I am pretty sure it's useful to some engineers somewhere.</p>
<p>Sakky, what I mean about the TAs caring is that you shouldn't condemn all TAs that don't already know all of the material. I mean, the TAs I know that care do the homework as soon as possible so they fully understand what's going on and can explain it to their students. They don't wait until the end of the course, they try to get a little ahead and learn those little things they missed or didn't realize they didn't know completely the first time they took a class.</p>
<p>It also seems a little weird that you're arguing that engineering students don't need to get an understanding of what derivatives exactly are and how they work, they just need to be able to use them as a tool. That's exactly how they're teaching Maxwell's Relations! It's one of those things you learn as a tool to be able to use thermodynamics (much like partial derivatives). If you really want to learn what MR's are, then you can take some extra graduate level courses and really get into the nitty gritty of what they can do for you.</p>
<p>I suppose the biggest argument is where do you draw the line as what sort of things are worth understanding the derivation to and what's not.</p>
<p>
[quote]
Then that's an argument for making the course an elective. Let's face it. Most engineers, at the undergrad level, just want to know the results. They don't really care why the results are true. After all, they're not going to be researchers. They just want to know the results.
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</p>
<p>I had always thought most engineers feel you're supposed to teach a man to fish and not to just give him one...</p>
<p>Also, I finally got off my butt and looked up in one of my texts that I remembered gave a good explanation for what Maxwell's Relations are useful for. I'll type it up in the following post so people that don't care can ignore me.</p>