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[BasicAcid]

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[hobbitle]

Haha.

The short answer is a resounding yes.

Calculus, specifically differential equations, are arguably one of the most useful and necessary mathematical tools for almost every engineering discipline (with the exception of perhaps software engineering).  There is also a whole other world of more abstract mathematical theory that you learn at uni if you do engineering.  Differential Equations are also useful to life scientists (modelling population growth in an environment etc), and applied maths in general is heavily used in actuarial studies (statistics mostly), geology, oceanography... pretty much science across the board really.

Complex numbers perhaps are used less so, but my partner is a Mech Eng Masters student and he just submitted an assignment that was quite complex number heavy involving an analysis of air flow over an aeroplane wing (or something similar).  So they do get used.

Uh so yeah.  Resounding yes, IMO.

[b^3]

Well yes. Engineering, well the theory for a lot of engineering courses will involve a lot (I really mean a lot) of differential equations and such. Complex numbers can be used to simplify a lot of problems. For example, in electrical engineering they can simplify capacitor circuits and such, instead of doing 2 or 3 pages of working using only the real plane, you can take shortcuts and do the problem in a few lines, and a lot quicker. The same goes for solving certain differential equations. Some of the abstract stuff we learnt in Linear Algebra last sem (I'm talking uni lin alg, it's not as simple as straight lines, it's pretty bloody confusing actually), can actually simplify solving a few things a hell of a lot quicker and with ease. At first it seems useless, but later on you see it's uses.

Euler's approximation (and better variants of higher orders, i.e. 5th and 6th order approximations) are very useful for solving differential equations that don't have exact solutions, except later on in uni you don't really use it, rather you need to know how to program it, then get the computer to do 10,000 iterations with a small time step in a couple of seconds. (Although for an exam we had to do 15 iterations of a fairly annoying equation on a damn scientific calculator).

Most of what I'm talking about is more applications from what you lead onto doing at uni later on, not exactly what you cover in VCE. To be fair though, the content in VCE is pretty basic, but you need these basics to be able to do anything later.

Although, with all of this being said, this covers the theory needed for eng, I'm not out in the field yet and such, but nowdays a lot of the calculations aren't done by hand, there are better ways of doing it, or even approximating it. Computers can do things a lot quicker than we do. But, you still need to know and understand how the theory all works, otherwise when the computer spits out something that's wrong, how are you going to know that its looks odd, instead of blindly using it and letting something break. You don't want to be blindy using something without understanding how it works, you'll need the understanding to work out what to do if you do need to change an input, which way the output will go, and whether that is what you want it to do. Sometimes you will need to know the theory to be able to program the computer to be able to do and spit out what you want it to do. If you don't understand how this works, then you're not going to get anywhere. Although, this could be biased more because I'm in aero, talking to a postgrad student who did electrical eng, 'apparently' electrical and chem do more by hand, and aero do a lot with computers and approximations, I don't know how accurate that is though.

So yes, for engineering, of course you'll need them, different disciplines of engineering will need differing amounts, but it just depends how it's all applied. If you know your stuff you can do a quick approximation to determine if something should be tried or not, before going to computing power to do it.

EDIT: Take this with a grain of salt though, as I'm not working as an engineer yet, merely a student. Most of the above is just what we've heard from lecturers, tutors, postgrads and such. So if there is anything that's not entirely correct, then pick me up on it.

Also my post seems all over the place. I tried to organise it a bit better, but think I just made it worse.

[DisaFear]

Yes, maths is required in many places.

I mean, you might not see the 'physical' mathematical calculations, because we rely so heavily on software to do everything for us. But you'd need to understand how stuff works, to make sure everything makes sense, and maths does come into play there.

If you do Physics, Chemistry, Biology, there are equations that model a lot of stuff. How do they come about? What do all the parameters mean? Are there boundary conditions? If you differentiate something, what does that tell you? How does a relation change if you take the log of it? Maths does appear, rest assured.

[hobbitle]

I don't know in what context exactly the complex numbers were used, except that air flow was the general gist of the assignment material.  b^3 offered you a pretty good alternative example that was more specific.

I don't understand what you mean when you keep asking about when and how will we apply this to real life.  b^3 just posted an essay on where it is relevant in real life and I offered some examples also.  Maths is everywhere in many, many professions and whilst we might have computers to calculate a lot for us we still need to understand what we are asking the computers to do. 

[b^3]

And b^3, I see that you're talking about all the theory you learn in university and how it can be used on software, calculators, etc...
But when and how will we apply this to real life?
How does Euler's method help the way our world works?

Again, this is for engineering (and well science I guess, since they come up with technology that engineers then seem to go and put into practice).

How do you think the cars, trains and planes that you use were designed? How do you think the building that you're standing/sitting in were designed? How do you think the computer/ipad/whatever that you're using atm were designed? They weren't just thrown together with guesses, careful calculations go into it all. When you hit a bump on the road the damping/suspension system on your car will go through some oscillations, which can be modeled by diff equations, and then solved back to work out what you need to put in to damped it or stiffen it so that it will absorb energy or release it over a longer time period (it's a hell of a lot more complicated than that). Simplified beams can be analysed and determine where they are most likely to break or buckle, and so the thickness of the beam can be worked back depending on what load it needs to support (again really simplified look of it). How do you know that the laptop or computer you're using isn't going to overheat and melt it's insides? There's a lot more involved with the thermodynamics and heat transfer side of things.

What I'm getting at is that maths is a very valuable tool, without it we wouldn't be able to design a lot of what we rely on in this world. I didn't mean that it's just used in programming and software, I was more looking at more that the results of what this software can do then can go into designing a part or system. You need the maths to understand what is going on in your system, you can't just chuck something together and think it's going to work. You need maths to be able to relate and look at how a system or variable change depending on other variables or with respect to time.

With euler's method you can approximate the solution of a diff equ at a certain point, sometimes you'll come across a diff equ that would take a while to solve, or doesn't have a known exact solution, so you approximate the solution using some numerical method keeping the time step small so that the error is close to zero, i.e. eulers (well you'd use something a lot better than eulers method, but still). Then from that result, you use that as an input for another part of the system.

This can be extending to more than two variables, where you have a system where pressure, temperature and flow velocity all depending on each other and quantities upstream. Which is more moving into Computational fluid dynamics, but anyways.

[TrueTears]

Hey there.

As my title states, I'm wondering whether the maths (particularly calculus and imaginary numbers) is ever used/applied in real life on a regular basis?

By that I mean, are there engineers out there who actually get paid for applying differential equations and whatnot?

Apart from high school methods/specialist maths teachers/tutors, are there actually jobs that involve this abstract type of math on a daily basis?

I did a bit of Googling (only skimmed through a few pages though) and I can see that imaginary numbers can quite possibly be applied to electronics in some sort of weird way but apart from that, there's not much else.
And I also read that calculus is sometimes used in engineering. But I asked my dad (who's an engineer at Optus) and he says that he hasn't seen the variable x in over 25 years. Obviously he's not the only engineer in the world, but I find it hard to believe how 'second order differential equations' can help us in real life.


Is the maths we learn at school just in order to improve the way we think, the way our minds work with abstract values and organise ourselves logically?
Is it just to teach us methodical ways to look at and solve problems?
Is it just a subject that a lot of us choose cause it's relatively easy to score higher on and scales by 10+?
Or is there some actual usage behind it?

yes... maths is the language of science, without maths -> no technology.

[hobbitle]

But damn, I'm actually so sick of maths at the moment, and I'm planning on doing Bachelor of Science at Melbourne Uni and eventually going on do a Masters in Engineering... Lol...

Everyone gets sick of things sometimes.  I have mini tantrums about Linear Algebra on a fortnightly basis (if you do your B-Sci, you'll learn what I mean).  But yeah, if you pursue that path - you'll figure out very quickly why maths is necessary. :-)

[MJRomeo81]

[Alwin]

MY MONASH UNI MATHS TEACHER GAVE THE BEST EXAMPLE OF HOW WE NEED MATHS IN REAL LIFE

It goes like this:
You are trapped on an equilateral triangle shaped island and want to build your hut somewhere on the island such that the distance to the beaches is minimal so you can spend as much time surfing as possible.

Answer:

Spoiler

We can use Viviani's theorem, a proof without words, to prove that it can be built anywhere YAYAYAY

But in all seriousness, yes it is useful, esp in uni ^_^

EDIT:
Wanted to add this one, since your thread it about calc too,
So e^x and 1 are walking down the road. Across the road, walking toward them is a derivative. 1, suddenly in a panic, turns to e^x and says, "Oh no! I'm doomed! I cannot cross a derivative and survive!" e^x smiles and says, "Fear not! I will go over, tell the derivative leave, then return unscathed." e^x walks up to the derivative and says, "Hi! I'm e^x!" The derivative says, "Hi! I'm d/dy!"

And that another use of maths, you'll get all the lame jokes

[b^3]

MY MONASH UNI MATHS TEACHER GAVE THE BEST EXAMPLE OF HOW WE NEED MATHS IN REAL LIFE

It goes like this:
You are trapped on an equilateral triangle shaped island and want to build your hut somewhere on the island such that the distance to the beaches is minimal so you can spend as much time surfing as possible.

Answer:

Spoiler

We can use Viviani's theorem, a proof without words, to prove that it can be built anywhere YAYAYAY

But in all seriousness, yes it is useful, esp in uni ^_^

That question was on my last assignment.

* bcub3d  looks at burkard

[lala1911]

I guess it depends on your career path.

And personally, from what I've seen, strong math skills help people become active thinkers and improves problem-solving skills.

[Lasercookie]

What the, how can these numbers that aren't even supposed to exist (hence their name 'imaginary' numbers?) used for something like that!? I just completed a practice specialist exam and I cannot imagine how any of what I just did would actually help me in the future.

Imaginary numbers is a misnomer. You'll see the term complex numbers to be more common. Let's think about natural numbers, what does the number '1' mean? Certainly it doesn't exist in some physical form in real life, it's just some concept that's been invented and developed with time. Sure you can understand natural numbers to be representing the number of LEGO blocks you have and have some physical intuition for it, but the numbers themselves are just a concept.

Complex numbers are just as imaginary as your negative numbers, natural numbers, real numbers and so on.

Do you think there are applications of negative numbers in real life? In the 18th century a lot of mathematicians rejected them as meaningless. There's also a lot on the history of zero and how that developed. If you take the number 4 and add a negative number, -5: , you can understand that as moving backwards on a number line. Which you could also understand to be rotating that number line 180 degrees. You'd already be familiar with some of the applications negative numbers have.

What if we remove the restriction of only being able to move in the direction of 0 degrees and 180 degrees? That's how we can get the Argand Diagram for complex numbers. We understand negative numbers geometrically as moving backwards and we can understand complex numbers as rotation. That's something that you can easily understand to be represented by some physical object. If you take a rubber band and stretch it into a straight line, you can show multiplication by a positive number by stretching it in one direction. By a negative number you start stretching in the other direction. You can easily conceive of stretching it in any direction, which you could represent using complex numbers. .

[lzxnl]

If you can't see where VCE maths is going to be used in real life...you're a perfectly normal person who is thinking about what they are learning. VCE maths provides a very gentle brushing of the surface. To really know what the heck is the point of learning about complex numbers, you'll have to go to uni to find out.

Besides, engineering isn't the only discipline that uses maths. You'll have lots of maths in physics (general relativity and electromagnetism come to mind) and in certain parts of chemistry, like quantum chemistry and thermodynamics. Granted, as people above have said, you may not have to solve equations by hand, but without maths, the concepts won't really make too much sense.

[BigAl]

I'm guessing your dad is a telecommunication engineer or something...well there are some engineers going out there, checking signals or something, collecting data and so on...Well you have to present this data through maths although we do this with computers. Some astrophysicists run simulations which require solving 4 or pethaps more differential equation simultenously. Not only that, meteorologists analyse heaps of data so you can check the forecast for the next week. If any of the above reply isn't satisfying you, think about how you would shoot a rocket into space without calculating how much fuel it needs. Maths is everywhere.