The simplest things are the hardest?

[morry]

Gday guys,

Just wondering if anyone has been in a similar situation to myself. I am a 2nd yr mech eng and I am finding that some of the things I have having trouble with relate to simple mathematics, rather than the concepts being taught.

For example, in dynamics of machines, the concepts are very simple, however what I find hard is the basics. Such as when youre given one angle and you have to find the rest in a system. Or when you have to find the position vector, which is a sum of several simple vectors.

Its like I am lacking intuition, something which I (think I) had in high school.

Anyone know what I am on about?

 

[russ_watters]

I have never considered math simple - I always had more trouble with it than scientific concepts.

But don't fret - while you may struggle through the math more than someone who has a natural aptitude for math, when you get into the real world and become a real engineer, a thorough understanding of the concepts will make you an outstanding engineer. What makes someone a good engineer is the ability to reason through a new problem, not to regurgitate complicated math from an old one.

 

[brewnog]

I've always had a lot more trouble manipulating mathematical statements than understanding the underlying concepts. While I think it's important for an engineer to have a good feel for numbers, most of the heavy mathematical stuff nowadays in real life is done by computer. Obviously, a good engineer needs to be able to use his intuition and maths skills to determine whether the computed output is correct, particularly with things like FEA where the wrong answer can often look like the right one. But generally, understanding the principles behind a problem is far more important than being able to spew out lines and lines of equations.

 

[FredGarvin]

I noticed with myself that I was spending so much effort on the concepts that the "easy" things seemed difficult. I found it just took getting used to doing whatever it was I was doing. Through practice you get used to doing the concept and the math at the same time. It may be relatively easy math, but when it is combined with a problem or put in a way you're not used to seeing, it's not so simple any more.

 

[Clausius2]

I've always had a lot more trouble manipulating mathematical statements than understanding the underlying concepts. While I think it's important for an engineer to have a good feel for numbers, most of the heavy mathematical stuff nowadays in real life is done by computer. Obviously, a good engineer needs to be able to use his intuition and maths skills to determine whether the computed output is correct, particularly with things like FEA where the wrong answer can often look like the right one. But generally, understanding the principles behind a problem is far more important than being able to spew out lines and lines of equations.

I have a very close friend who thinks the same as you. But I don't think as both of you. When I talk to him, I say: "The concept remain just at the bottom of the mathematical expression. If you want to understand completely the concept you must understand the mathematical derivations and all the previous assumpitions. The concept is just inside the equation. When I want to understand some concept I try to visualize it through the mathematical formula, giving the correct physical meaning to each term."
That's just my opinion.

 

[brewnog]

I think you're totally right Clausius. I always try to follow (and understand) the derivations which surround a physical concept, indeed these skills are needed to get a degree! I'm just not too hot at recreating them.

 

[Clausius2]

I think you're totally right Clausius. I always try to follow (and understand) the derivations which surround a physical concept, indeed these skills are needed to get a degree! I'm just not too hot at recreating them.

Maybe I misunderstood you. You know, we have some classmates who are proud of understanding the concept but when you request them to do some number or to handle the founding equation they are unable to do it. And they argue they understand the concept which is more important than handling equations. I do think the correct and unique secquence for truly understanding some concept is: being able to handle the mathematics of the stuff, understanding this mathematics involved, and lastly interpreting physically the equations. Then, and only then, you will have fully understood the concept.

 

[russ_watters]

The example I would give, Clausius2, is thermodynamics. Along side of teaching someone about the equation for efficiency of a cyle, you learn that there is a maxumum theoretical efficiency, but knowing why takes more than plugging the numbers into an equation. You have to know where the numbers come from.

Ie, if efficiency is related to compression ratio, why not kick the compression ratio up to 1000:1? Answering that question requires more thought/understanding than picking an equation from a list and calculating the efficiency of a cycle with numbers that are provided for you. Perhaps there is a way to get that same deeper understanding from the math, but it isn't something that you learn in college.

There is an intangible property of engineers called "engineering instinct" which is an intuition built from the understanding of concepts. In my industry - the HVAC industry - it is possible to run a successful HVAC design company without any engineering instinct. Ductwork design is simple: just use your software to calculate the air flow and use your slide rule and match the cfm and duct size. But that isn't really engineering and some engineers go their entire careers without really doing any engineering. Ask such an engineer to think outside the box - perhaps to solve a problem - and they are utterly clueless about how/why things actually work. As a matter of fact, those engineers hire my company, led by an engineer who never went to college! Knowing how to design a duct - which you can learn in college, from equations - doesn't help you to know best to arrange the ductwork or what type of system to use. That, you can't learn from an equation.

You know, we have some classmates who are proud of understanding the concept but when you request them to do some number or to handle the founding equation they are unable to do it. And they argue they understand the concept which is more important than handling equations.

I am such a person. I didn't get good grades in school because I was weak with the math. But here's why: on a test, I often could not remember what equation went where, but could reason through a problem - derive the equations even - and come out with the right answers. But that's time consuming and I almost never finished a test! Later in engineering when the profs acknowledge that in the real world, you don't need to memorize every equation and the provide an equation sheet, it got better, but it never ceased to be a problem for me. But beyond that, what happens when you get to the real world and the problem isn't a cookie-cutter test question?

 

[morry]

Thanks for the replies guys. I went to see my lecturer yesterday and he actually laughed at me. He thought it was pretty funny that it was the high school math I was struggling with. Not that I took offence to it, I thought it was funny too.

I think my basic maths skills have decreased since high school. Mainly because I hardly use them. 2nd year maths is easy enough. I think some revision could be handy. :D

 

[brewnog]

Don't worry. I had to remind myself how to differentiate ln(x) before a 3rd year mech eng exam yesterday.

 

[morry]

Don't worry. I had to remind myself how to differentiate ln(x) before a 3rd year mech eng exam yesterday.

haha. When I saw my lecturer yesterday, one of problems required the derivative of tanx. He looked at me and said "You know how to do this don't you?" I gave him a bit of a sheepish look and shook my head. He rewrote it as sinx/cox and said "Ok, now this should make it easier." I once again shook my head and said I forgot the quotient rule. Oops.

 

[Clausius2]

Very interesting comment, Russ. And it is more valuable maybe than mine one, because you are submerged into professional world and I am not.

The example I would give, Clausius2, is thermodynamics. Along side of teaching someone about the equation for efficiency of a cyle, you learn that there is a maxumum theoretical efficiency, but knowing why takes more than plugging the numbers into an equation. You have to know where the numbers come from.

Ie, if efficiency is related to compression ratio, why not kick the compression ratio up to 1000:1? Answering that question requires more thought/understanding than picking an equation from a list and calculating the efficiency of a cycle with numbers that are provided for you. Perhaps there is a way to get that same deeper understanding from the math, but it isn't something that you learn in college.

I was not only referring to know how to handle equations. If you request me some thermo math demonstration, maybe I am not able to do it. But some time ago I was able to do it, there are some ideas remaining in my brain when I caught the concept. A physical concept is made by Physical considerations and interpretations, but such considerations are built over Mathematics.

There is an intangible property of engineers called "engineering instinct" which is an intuition built from the understanding of concepts. In my industry - the HVAC industry - it is possible to run a successful HVAC design company without any engineering instinct. Ductwork design is simple: just use your software to calculate the air flow and use your slide rule and match the cfm and duct size. But that isn't really engineering and some engineers go their entire careers without really doing any engineering. Ask such an engineer to think outside the box - perhaps to solve a problem - and they are utterly clueless about how/why things actually work. As a matter of fact, those engineers hire my company, led by an engineer who never went to college! Knowing how to design a duct - which you can learn in college, from equations - doesn't help you to know best to arrange the ductwork or what type of system to use. That, you can't learn from an equation. I am such a person. I didn't get good grades in school because I was weak with the math. But here's why: on a test, I often could not remember what equation went where, but could reason through a problem - derive the equations even - and come out with the right answers. But that's time consuming and I almost never finished a test! Later in engineering when the profs acknowledge that in the real world, you don't need to memorize every equation and the provide an equation sheet, it got better, but it never ceased to be a problem for me. But beyond that, what happens when you get to the real world and the problem isn't a cookie-cutter test question?

I know what you are talking about. I will put you some example. I have different kind of professors. Some of them are deeply involved in scientific world, are somehow scientists-engineers. They have a great mathematical power. They do know all these academic issues which professional engineers seem to forget due to time going. Maybe they don't know too much about professional-practical tasks, but potentially they could gather their great analytical knowledge with a professional experience. I think such an engineer would be an ideal one. One guy who has very very solid physics principles founded over a very great mathematical base, knowing exactly why that stuff is so or not, in addition to the convergence to real world: is it possible practically?.

On the other hand, I have another kind of professors. They are involved in professional world. To say the truth, I am able to see their weakness when explaining a difficult concept: their physics seem to be oxidated. On the contrary, they do know very much about industry. Therefore, they are potentially unbalanced, and maybe won't develop their work properly.

By the way, I am not meaning about memorizing any equation. One never should have to memorize any equation. The only equations I have memorized are those which have not any physical meaning. Those which have it, are automatically impressed in your brain, because you watch how the movie is going on. Your method trying to obtaining the equations from the bottom is very valuable, and I think it is the correct way. Once you will have derived it some times and understood the concept, you will never derive it again, because you will recover the concept hidden in some place of your brain.

 

[Danger]

I've mentioned various aspects of this in a few different threads, but maybe this is a good time to put it all out there. Although I finished grade 12 without graduating, I have a grade 9 math level. This is because I never had a math teacher in my life who was fit to be one, and the only trouble that I ever got into in high-school was for assaulting a math teacher in the first month of grade 10. I never took the subject since. (I got just a 45-minute detention for it, because the principal agreed that it was justified.) When it comes to scientific stuff, I just seem to feel it. I have books with all sorts of formulae that I can plug into my calculator, as long as it's something that's built in as a function. I have, for instance, no bloody idea what an integral is, other than an old fart who helps run things around here.
When I design something, I always go for overkill regardless of what a calculation would say. I can be pretty sure that 4 standard 3/8" bolts will be adequate for an attachment, but I'll make it 6 of those or 4 1/2" buggers instead. I've learned over the years that (copyrighted Dangerism) Reality Never Conforms to the Blueprints. So far, at least, nothing that I've built has blown up (unless that was its purpose).

 

[minger]

I'll just chime in my two cents. I agree that many times the simple things are quite hard. I never paid much attention to math classes in high school, so while determining convection coefficients may not be a problem, I don't know my logarithmic identities, and I always forget integration and derivitave rules. Many times I've messed up tests because I've used sine instead of cosine or vice versa.

On the topic of teachers though. I think many professors here do exactly what they should. They present us with the material in order to learn us the material. In some ways, I think true engineering skill is almost inherent to the person. Engineers are problems solvers, and I think that is an ability that is developed very early on. I think being able to reason and solve problems is a skill that stays with you forever. Professors, try to get you thinking about how to apply your ability to solve problems to engineering situations.

Referring to memorizing equations, I definitely like understanding where the equations come from. Even it takes all class to derive an equation, and even if maybe I don't understand the entire thing, I will master the concept much more than if we just present the equation, then solve examples using it. The best professor I've had derived every equation we used. Knowing where that equation comes from gives you such a better understanding of how and why you are using it.

Anyways, just my two cents. In short though, yes, simple things stump me all the time.

 

[Astronuc]

"Use it, or lose it" - I find often that when I don't use some part of my knowledge, I lose it. Without recurrent practice, one can 'forget' even the simplest of mathematical concepts.

That is why PF is useful - it helps to review the oldest and simplest concepts. Especially for us older folk.