Calculus help!
Discussion
Not strictly science (or even at all), but I'm wondering if someone more learned than me can assist me here, with a calculus question I have on a paper, as part of my HNC.
I've gotten this one wrong and I'm not quite sure where I've messed it up, any help given would be appreciated!
http://postimg.org/image/6two7d7ot/
Please forgive my terrible writing, this back to work malarky doesn't suit me!
Cheers,
- Harvey
I've gotten this one wrong and I'm not quite sure where I've messed it up, any help given would be appreciated!
http://postimg.org/image/6two7d7ot/
Please forgive my terrible writing, this back to work malarky doesn't suit me!
Cheers,
- Harvey
The trick with calculus, well for us less that stellar mortals, is rote learning.
Don't try to understand it at first, just do it until you can apply the formulas in your sleep.
One of my final questions took 8 double sided A4 sheets to prove [fluid flow/mixes behind a closing valve].
Use a soft pencil as well BTW.
Don't try to understand it at first, just do it until you can apply the formulas in your sleep.
One of my final questions took 8 double sided A4 sheets to prove [fluid flow/mixes behind a closing valve].
Use a soft pencil as well BTW.
Edited by Mojocvh on Monday 5th January 20:34
Eric Mc said:
I am sure I would have understood calculus better if it had ever been explained to me what it was used for.
Good teaching is vital in maths and calculus is notoriously explained badly.The basic principle of calculus is extremely simple: it calculates rates of change. For example, the rate of change of an object's distance over time is its speed (e.g. "miles per hour"). So, if you have a formula describing an object's position with respect to time (i.e. x = 2t, where x = distance and t = time), you can use calculus to change the equation from one defining position (x) to one defining speed (or "dx/dt" as it's known, where 'd' just means 'small change’). The process of finding the rate of change using calculus is known as 'differentiation'. In the above example of x=2t, the speed is simply "2" (which would be 2mph if x is in miles and t in hours). So for example, if x=2t then after 2 hours the object is at 4 miles (2*2), and after 4 hours the object is at 8 miles (2*8) - it's going 2mph.
When the equations get more complicated, it's not so obvious what the answer is, and that's where knowing the rules of calculus comes in. For example, if x=2t^2, then the speed or "dx/dt" as it's known is = 4t. To get the “4t” or to differentiate anything there's just a simple rule that you use that every time. No matter how complicated the equation, you just use the simple rule and that’s the genius of calculus – life is complicated, but calculus simplifies it.
Obviously you can differentiate again to work out the rate of change of speed itself, which is acceleration, and you can also work back the other way, which is called integration, for which there's another simple rule (for example, if we know an object's speed dx/dt = 2, then it's position, x, is just 2t). Calculus has simple rules for all types of mathematical expressions, including trigonometric functions (many things in life involve those, for example anything that moves in a circle or oscillates).
The usefullness of calculus is that most things in life are changing and they're changing in a complicated way that can usually be defined by maths. If you know a Caterham takes an hour to go 60 miles, you can't just assume it's doing 60mph all the time - that would only be true if it went from 0mph to 60mph instantly at the start (impossible!) and stopped instantly at the end (sadly that is more possible!) - in fact using standard maths you'll only ever know its average speed between two points, no matter how close together those points are. Calculus breaks free from that quandary and allows you to deal with reality, where the Caterham's speed is varying all the time, and to work out the rate of change (speed in this example) at any point, not just the average speed between two points.
The explanation that most school teachers give of calculus is to dive right in with the "average between two points" bit in my last paragraph above, and I don't know about you but I switched off after a few minutes of that. I would instead just cut to the chase, as above. They also fail to give real world examples.
Edited by RobM77 on Wednesday 23 September 15:40
I just want to get on with programming my PLC's and building/designing instrumentation and control circuits.I bought a friend a copy of Newton's Principia for Christmas. Absolutely staggering what Sir Isaac was doing when the rest of the population could barely write their own name. I can't get beyond the title but I'm sure 'gravity' is in there somewhere.
Equally O/T, I heard that the reason why the Romans never got very far in maths was because they used letters for numbers - hence no calculus x/y thingies. But they were jolly good with spears, and spears beat x/y thingies - as the Greek Empire would concur!
NB Eric - do you need calculus to fly a spaceship? Just land the f
ker without bending it!
Equally O/T, I heard that the reason why the Romans never got very far in maths was because they used letters for numbers - hence no calculus x/y thingies. But they were jolly good with spears, and spears beat x/y thingies - as the Greek Empire would concur!
NB Eric - do you need calculus to fly a spaceship? Just land the f
ker without bending it! Gassing Station | Science! | Top of Page | What's New | My Stuff