Once upon a time, I was an engineer. And in that environment, engineers would think it was insane to depend on a calculation, a computer program, or a sketch - without checking the result, and if possible, checking it in the simplest way possible.
Fast forward to now. You have calculating power in your hand that was beyond what I could do with a long computer program when I first entered an engineering career. Your problem is, you depend on it. The teacher gives you a problem and what do you do? You reach for the calculator.
So look: the human brain is infinitely more powerful than the best calculator you can put in your hand. Learn to reach for it first instead. Use it to set up your work, to help you understand why you're doing it, to help you recall how you did what you did, and to find out what it takes to do things right. THEN grab the calculator. Otherwise, the thing the calculator does best is give you the wrong answer fast.
I think I am done with my experiments. Whew. This summer I was able to run the test loop that my colleagues and I devised to investigate boiling flow in expanding microchannels. A mouthful, eh? True, but the data output is a rather a bigger bite. It's no Large Hadron Collider, but my four experiments ran to a 100 MB chunk of text data. What do you do with this? Well, certainly you write programs (in MATLAB) to organize it, do calculations, sniff through it, plot the parts you want, and so on.
But you look at all of it. And you don't delete. And you don't fudge.
This is not to say that you don't analyze it, or ignore the big spike where you turned power on, or even perhaps use a smoothing routine on the thermocouples (which are as noisy as undergrads), but if you do any of these things you say so. You work only from what the data confidently allows you to say, and the more layers of analysis lie between you and the data, the bigger the uncertainty becomes. You don't clip the...
I am a researcher. That is why I am pursuing a PhD, that is why I obtained a Master's, and that (at some level) is what I want my career to be when I am finished with grad school (where I tutor on the side).
Research is a business of trust. If I publish, I am asserting that this work represents the truth as far as I can carefully deduce. Others who may use my work rely on that assertion; why would you use, say, a heat transfer model prepared by a kook or a liar? Peer review is meant to guard the gates of academic literature from error, which is a tried and true, if not foolproof, method.
But what about undergraduates? They are not researchers. They are not publishing. They are, by and large, turning the crank on basic problems. So what if they share work, or hire an unscrupulous tutor? It's a victimless crime, right?
Let's pause and think out that line of thought. If I am a recruiter at General Electric, and a resume comes across my desk with a fabulous GPA from a school...
If you're anything like me, at times you've wished for an easy way to work math problems and get the answer in the back of the book.Of course, you probably tried just copying the book's answers on to your homework paper only to have that "unreasonable" teacher of yours refuse to give you credit for all those answers!... something about not showing enough work.
Well, you're in luck! I've taken a couple of math concepts from the internet,combined and refined them into a technique will take answer you have, no matter how wrong or bogus, and "transmogrify" it into the answer in the back using simple algebra which you can use to show full work. I call this technique The Correct Answer Algorithm (it's so simple it needs a really complicated name to make it sound sophisticated enough to impress your teacher.)
So here it is... the algorithm which will in short order transmogrify your answer into the answer in the back of the book:
Engineering and science are slow fields. Yes, you read about breakthroughs, revolutions, and the like, but those headlines are the fruit of years of labor. I acknowledge that all fields require planning, thought, and care, but the businessman can just go out and make a deal (perhaps a bad one) in a fairly short amount of time. You can't just go out and build a bridge (however poor) in an afternoon, or even a week. Enough anecdotes.
If you want to pursue an education, especially in the science/engineering fields, you must commit yourself to it for substantial periods of time. This is not easy. It is done at the expense of fun, friends, and even perhaps family. As a PhD student, I do not get to spend nearly as much time with my wife as I did when I was a practicing engineer. It is a very rare weekend when I can hang out with friends. A good education makes demands on you.
All this to say, if you are serious about learning, you will learn. If you are unwilling to give up...
I went to a lecture today, given by the president of the Illinois Institute of Technology. He was an engaging fellow, and spoke of his school's efforts to optimize both the aims and the means of undergraduate engineering education.
Following his lead, I should note that the engineering field (through the good offices of the American Society of Engineering Education) has routinely sought to improve the content, methods, and presentation of engineering education. Every few years, serious people take a serious look at it, asking "What can we do better?", and (as important) "What shouldn't we be doing?"
So, is the "standard American" model of undergrad engineering education a good one? This post will consider only two of the many options (just to keep it bounded).
Should there be a "core curriculum" with discipline-specific branches, as I experienced?
The upshots of this are that each student is armed with a standard,...
Richard Feynman once said: "The problem of how to deduce new things from old, and how to solve problems, is really very difficult to teach, and I don't really know how to do it. I don't know how to tell you something that will transform you from a person who can't analyze new situations or solve problems, to a person who can. In the case of mathematics, I can transform you from somebody who can't differentiate to somebody who can, by giving you all the rules. But in the case of the physics, I can't transform you from somebody who can't to somebody who can, so I don't know what to do."
This humble and frank assessment came from a man widely regarded as a fantastic teacher. It came in a review lecture available in "Feynman's Tips on Physics" (Feynman, Gottlieb, & Leighton; Pearson-Addison-Wesley; 2006), a supplement to "The Feynman Lectures on Physics", one of the most fascinatingly thorough digests of undergraduate physics. However, Feynman was...
There's an interesting concept in thermodynamics called "exergy". It's not one that comes up often in daily use, like energy (how much the molecules want to move), or even entropy (how much of that energy you lose and can't get back, per temperature). No, exergy is kind of an odd duck, because it's relative. Let me explain.
There was a problem I had in my homework with a car fueled by liquid nitrogen. An odd concept, for sure, unless you think about it in terms of "how different is my system from its surroundings?" For example, you can be at the top of the Space Needle, and if you were to, say, lower a weight on a rope that turned a generator, you'd get some work out, corresponding to the height of the Space Needle. Now, instead, imagine yourself standing on the ground at the mouth of a shaft mine with the same apparatus. You can still get work out, because you can still lower the weight. It all depends on the relative height of the start and end point, not...
Everybody knows what a rocket is, right? Rockets are the big white cylinders strapped to the sides of the shuttle gas tank, and they're the black nozzles on the back of the shuttle itself, right? Quite correct, but do you remember Deep Space 1? This long-range probe used an engine that looked and behaved quite a bit differently than you might expect.
After all, what makes a rocket? Is it the shape? The propellant? The use we put it to? Very simply, and perhaps boringly, a rocket is defined by the way we do the math. Let's look at Newton's second law in its general form F=d(m*v)/dt. If that doesn't mean anything to you, don't panic. All it says is that the Force on an object is equal to the time rate of change of the quantity (Mass times Velocity). So, force is related to how we change two things, mass and velocity, ok?
Many people (freshman engineering students) who use the second law just jump a few steps and say F=ma, where they've shortcutted by saying the mass is...