Engineering 'one oh one.'

[Brett Nortje]

I decided to start 'studying' engineering about two years ago on the wikipedia. man that site is awesome! the way i see it, there are different ways to approach engineering, along with new ways of doing the maths for everyone. but, let's start my 'class' with the basics of engineering - 'what is engineering?'

Engineering is when you get a machine to do things for you. think of your body as a machine and your heart as the engine, pumping blood throughout the body. you want it to pump more blood with less fuel or food taken to do so. this means that things get better all the time.

Basically, you want to observe that engineering is about energy changing forms. if kinetic energy and potential energy are understood, then there should be a solid foundation for this 'field.'

You will also learn a little bit about physics in engineering, as mass has boiling points and conductivity. the thing is that they go into such detail for the degree that you never use the things you learn about! think of it now, do you really need to know field theory to work an engine or split an atom?

I will continue after you ask specific questions, that i will be glad to answer, that is, if you have any. otherwise, i will just continue to unravel the working of the universe at a rather slow pace, step by step, okay?

[adrianh]

I am experiencing Déjà vu....

....are you directly related to some dude living in Limpopo?

[Brett Nortje]

Engineering mathematics.

This is the easiest part! basically, you can work out your calculus by squaring the number in the brackets and subtracting itself from the total.

For trigonometry, you need to simply measure the angles, then find the ratio between them on a calculator. this can be done in four measurements and one calculation, think like a child approaching it, okay?

For functions you need to observe that;

The function composition of two functions takes the output of one function as the input of a second one.

So, don't worry about [g] and [f], as they repeat themselves, and [x] equals [x]. this equation or sum means that [g] times [f] is equal to [g] times [f], multiplied by [x], yes? so, you say [g] times [f] times [x] equals your answer for the two functions.

[adrianh]

Aye, who needs university if you've got Wikipedia...

@Justloadit: I am sure that you are enjoying engineering math 101

[irneb]

[ATTACH=CONFIG]5130[/ATTACH]

So, don't worry about [g] and [f], as they repeat themselves, and [x] equals [x]. this equation or sum means that [g] times [f] is equal to [g] times [f], multiplied by [x], yes? so, you say [g] times [f] times [x] equals your answer for the two functions.

I think you misunderstand what "function composition" means. I.e. the o between the g & f on the left. It's not like a multiply, it means you run the one function, get its result and then pass that as the input for the other function.

E.g. Say you have the following two algebraic functions:



Then:

Expands to:

Which in turn expands to:


So now when you pass an input value into the combined functions (i.e. you give a value for x) that last formula is actually calculated.

See this concept similar to a formula in Excel which takes as its input the value in another cell which has a formula of its own.

[irneb]

Actually this is one of the issues I have against the way we're taught Maths at school. The one thing which confuses some is that idea of short-hand notation for multiply. It makes for ambiguous notation - which is where your misunderstanding stems from.


There's 2 solutions to circumvent this ambiguous misrepresentation:

1. Never shorthand a multiply. So instead of writing you should always write the multiply out fully like this . But that makes for very verbose notation.
2. Use an alternative notation instead of the normal Infix notation. Something like Polish notation (also referred to as Prefix notation) would alleviate some of it including removing the need to group portions due to precedence of operators, as would Reverse Polish (postfix). Or even better would be to use something like Lambda calculus. Personally though I feel S-expressions would provide the most consistent, readable, unambiguous and comprehensive alternative.

[adrianh]

Actually this is one of the issues I have against the way we're taught Maths at school. The one thing which confuses some is that idea of short-hand notation for multiply. It makes for ambiguous notation - which is where your misunderstanding stems from.


There's 2 solutions to circumvent this ambiguous misrepresentation:

1. Never shorthand a multiply. So instead of writing [ATTACH=CONFIG]5138[/ATTACH] you should always write the multiply out fully like this [ATTACH=CONFIG]5139[/ATTACH]. But that makes for very verbose notation.
2. Use an alternative notation instead of the normal Infix notation. Something like Polish notation (also referred to as Prefix notation) would alleviate some of it including removing the need to group portions due to precedence of operators, as would Reverse Polish (postfix). Or even better would be to use something like Lambda calculus. Personally though I feel S-expressions would provide the most consistent, readable, unambiguous and comprehensive alternative.

...or you could simply say that a little knowledge when misapplied is far more dangerous than no knowledge.

[Brett Nortje]

I think you misunderstand what "function composition" means. I.e. the o between the g & f on the left. It's not like a multiply, it means you run the one function, get its result and then pass that as the input for the other function.

E.g. Say you have the following two algebraic functions:
[ATTACH=CONFIG]5133[/ATTACH]
[ATTACH=CONFIG]5134[/ATTACH]

Then:
[ATTACH=CONFIG]5135[/ATTACH]
Expands to:
[ATTACH=CONFIG]5136[/ATTACH]
Which in turn expands to:
[ATTACH=CONFIG]5137[/ATTACH]

So now when you pass an input value into the combined functions (i.e. you give a value for x) that last formula is actually calculated.

See this concept similar to a formula in Excel which takes as its input the value in another cell which has a formula of its own.

So, for your example, it goes to the last one once you have all the information. i guarantee you a seventh grader can do it like i explain it!

You can find x in any of those sums. i will expand on the second one, as x will remain x, then for the last one you don't need to do the part to the right of the equals sign. so;

X must be a positive number, as engineering works with things that are positive in terms of angles, seeing as how things that are built actually have a value, and, let's say that x is 3 because that is the minimum it can be to be have two subtracted from it, yes? then, you need to [1] / [27] = 0.0038 or so, yes? then, you can use logic to place the poitn somewhere on the equation where it makes sense, and, even a seventh grader can make sense of this.

Simply, you assign any value for [x] that you feel comfortable with, then you get the 'ratio,' then you adjust the point.

[adrianh]

I take it you have a masters degree in K-logic.

[HR Solutions]

Aye, who needs university if you've got Wikipedia...

Lol .......

[irneb]

Simply, you assign any value for [x] that you feel comfortable with, then you get the 'ratio,' then you adjust the point.

Exactly!

You could also see it as you provide a value for x, then run it through the innermost function (the last one in the string of combinators) to get a new value to pass to the next function in line (the previous function in the string of combinators) as its "x". This continues until you've reached the outer function (the first in the string of combinators) - which then gives the final result.

So you could have something like this:

Formula	X-Value	Result
	5.5	5
	5	0.024
	0.024	6.121728
	5.5	6.121728

[Brett Nortje]

I have been busy with this sort of thing for a while now, and, think there might be an easier way to introduce kids to it at primary school level. that of course would mean that they would have to learn algebra at like the fifth and sixth grade levels, but, i believe that is now possible thanks to my discoveries in mathematics.

So, all we got to do is explain to them what the maths does. if we were to explain that machines work with parts, and parts have angles that need to be worked out, i am sure they would understand. an explanation could be that 'it is like lego,' yes? maybe a technique model from germany for each class could be organized so they can see that sometimes all things do not fit, and, then they could find ways to overcome this problem.

Sometimes there are parts that fit together that make it harder for other parts to fit together, by getting in the way or making some parts too narrow for the others to fit into naturally. it could be explained to the kids that you may adjust parts to make them work better, or, you could redesign the machine.

I have always thought that mechanics is about mechanisms. mechanisms come in all shapes and sizes, and, then they do things when other things do things. if they were to liken this to a computer code, it would be, when 'this' do 'that.' seeing as how it is us that activate the machine or mechanism, then we will see that we are the ones doing 'this,' and the machine is the thing doing 'that.'

So, if some kids understand code, they could understand engineering better, yes? of course, if we were to want them to get a firm hold of engineering, we could explain that it is all 'slaves' that 'work' for us. all the little parts are slaves, and when we make them do something they will do that thing.

Some parts have multiple functions though, or, lots of stuff they can do. for now, let's look at how a light works? the light is powered by electricity, and, the switch closes the circuit [or bridge] to allow the little electricity people to go to work, to put the light on. it stays on because the circuit stays closed, like a bridge staying down for the little slaves to stay connected - imagine a telephone that gets answered - you can talk as long as both places are connected or closed on each other. think of a circuit as if it were a 'regulator,' not letting the 'mechanism' work until the circuit is closed, so you could say that the dorr is reversed - you can only go through the door when it is closed, okay?

Okay, that might confuse some kids. if they were to think of a blender, you can only use it when there is food inside, or electricity inside, and then the lid must be on so the electricity does not fly all over the place.

Do you think kids will understand this fundamental of engineering?

[HR Solutions]

I have just come from my sons graduation as a civil engineer - he studied at Wits tho, not wikepedia ....

[Brett Nortje]

I have just come from my sons graduation as a civil engineer - he studied at Wits tho, not wikepedia ....

Are you saying that kids will not understand the fundamentals of engineering, or, are you saying that this doesn't cover half of it? what did you expect?

[adrianh]

Brett, how many kids do you have?
How old are they?
How are they doing at school?