Advanced Higher Maths 2011-2012 : Discussion and Help

I'm just about to go into 2nd year at university and I've chosen an outside course where you're supposed to have done Advanced Higher Maths. I left at the end of 5th year at school so only did higher.

So basically, I'm trying to learn as much of AH maths as I can within the next 2 weeks for the start of the course.

Any tips?

Oh and thanks for the resources in the OP- very helpful!

What's the course on? Do you know what kind of maths is involved?

Khanacademy

It's a course on Problem Solving in Physics. It's supposed to be a course for direct entry Physics students into 2nd year so they're expected to have AH maths and physics. I emailed the course organizer and she said it's basically applying Higher and Advanced Higher maths to solving physics problems. It's pretty maths-based. I did physics courses in my 1st year at uni but no maths.

Thanks for the link. I'll take a look. I guess I'll just have to try to quickly work through the AH course notes.

You should try PatrickJMT as well
http://adf.ly/2c7MH

Ah.

In that case, I'd focus on your vector work, your trig work and your calculus work. Although that's just what I'd imagine would be in there.

really stuck. Can you guys please help me on a couple of questions:

1) y= e^2t. show that d^2y/dt^2 - 2t dy/dt - 2y = 0


2) if y=x^2 lnx, show that dy/dx = x ln(ex^2)

thanks

That's a second-order differential equation. Not sure if you've learned those yet, since they're not until the end of the second unit. I haven't learned them completely, so I wouldn't want to make an arse of it.

2.)

$y=x^2lnx$

Use the product rule:

$f'(x)g(x) + f(x)g'(x)$

$2x*lnx + x^2*\frac{1}{x}$

$x(lnx+1)$

Which is equal to what you have to show it's equal to, but only for positive values of x.

Sorry, I've been away from school for a few years and I'm lost. Where does the 2 disappear from the second to last to last line?

Sorry, typo. Fixed now.

Aw good This is starting to ring bells again, and then I got to that bit and thought I'd missed something. Thanks

Does maths come back to you quickly? I don't want to study something that doesn't require much maths, and then forget everything I know. :c

I seem to have a weird memroy, I soak stuff up and it only takes a wee bit to remeber it. I hope I remember fast cause my course starts on Wednesday!

Can you remind me what the rule is for differentiating lnx again?

$\frac{d}{dx} lnx = 1/x$

Although I remember that because I remember that:

$\int \frac{f'(x)}{f(x)} = lnx + c$

And obviously differentiation is just the opposite of integration. c:

Wah. Where does the e come from them? (Sorry I'm being so thick)

Remember that ln e = 1. Using log rules, you have 2lnx + 1 = ln(x^2) + 1 = ln(x^2) + lne = ln(ex^2)

Remember that ln e = 1. Using log rules, you have 2lnx + 1 = ln(x^2) + 1 = ln(x^2) + lne = ln(ex^2)

Remember that ln e = 1. Using log rules, you have 2lnx + 1 = ln(x^2) + 1 = ln(x^2) + lne = ln(ex^2)