Monash Maths thread

[Kanon]

I'm not really that great at maths, so I'm thinking maybe I'm going about it the wrong way.
How are you guys studying for university maths? I'm doing MTH1020 and it just seems that when I get a question wrong I make that mistake in the future again, any advice?

[EspoirTron]

I'm not really that great at maths, so I'm thinking maybe I'm going about it the wrong way.
How are you guys studying for university maths? I'm doing MTH1020 and it just seems that when I get a question wrong I make that mistake in the future again, any advice?

Hey Kanon, I am doing MTH1020 as well. I suggest that when you get a question wrong you identify why you got it wrong. Perhaps it was arithmetic or just forgetting to factorize properly? Often I find it is trivial issues rather than actually having a gap in your knowledge. As silly as this may sound working on exercises that just test simple skills like understanding surds, fractions and factorising can often really help you speed up you thinking and allow yourself to avoid making mistakes. Since I am doing MTH1020 if you ever would like to form a study group or something I am more than happy too since no one else I know actually studies much for this unit.

I was wondering if anyone here could tell me if Euler's method is actually used in later units to numerically solve differential equations? We spent about 20 minutes on but I am not sure if it is really important. Having a quick glance over the MTH1030 unit book Euler's Method is not mentioned, so if anyone could clarify that for me that'd be great!

[LaLaLouise]

Hey Kanon! When I did MTH1020 (a year ago already! haha) I just did heaps of practise questions and actually tested myself on them under pressure. Like Monsieur Kebab said if you got it wrong go back and find out why. Don't just move on because you will regret it in the exam! Also don't waste time doing questions you know you can do because they make you feel accomplished (I'm super guilty of this ) but instead study the ones you are not so sure on which will help in the long run!

Monsieur Kebab I'm doing MTH2010 atm and I don't think we use Euler's method (but I may be wrong). I did MTH1030 last year but I can't remember if it was used sorry!

Also I have a question for everyone, it's more of a wording issue I'm having then needing help with solving. So basically I have a cardioid and a circle and the question says I have to find the area of 'the region contained inside both the cardioid and circle'.
(Picture attached for reference)
So do you think this implies the entire region of both (green) or just the part where they both intersect (blue)?

[DisaFear]

I have not done 2021 so I'm not sure how it's laid out in the lectures. The basis B' looks like the "standard" basis for so finding the change of basis matrix isn't as hard as it could be .

I used the procedure here: http://www.math.hmc.edu/calculus/tutorials/changebasis/changebasis.pdf

For part a) you should end up with this matrix for the change of basis (I think):



Verifying: if you have a vector with respect to B then AKA .

Thanks you

[kinslayer]

So do you think this implies the entire region of both (green) or just the part where they both intersect (blue)?

It would be the region that is inside the cardioid and inside the circle. So the blue one on the left is correct.

np DisaFear!

[BigAl]

(Image removed from quote.)

I can do b), given a) - It will just be the inverse

I can't seem to grasp the process to figure out a) though. I've looked at my lecture notes, and I think he does it sort of intuitively. I'm not sure about whether which bit should be a column or a row. (Yea...basic math flaws )

If anyone could outline the steps I'd need to take for a), would be thankful

Lecture notes are bit vague...I had to watch couple of YouTube videos to do that question...but basically what you're doing is writing p as a combination of q1 q2 and q3 and write these coefficients as a column..for future reference

[Kanon]

fmllllll, so bad at dis.

Which of the following functions has an inverse for x > 2?
a. sqrt(x - 4)
b. |x^2 - x|
c. ln(x + 2)
d. |x - 3|

So I got that b and c have a function has an inverse for x > 2 but I also selected a which is wrong.

interchange x and y



Which can be defined for all x > 2? 

[EspoirTron]

fmllllll, so bad at dis.
So I got that b and c have a function has an inverse for x > 2 but I also selected a which is wrong.

interchange x and y



Which can be defined for all x > 2? 

Okay so sqrt(x-4) is only considering x>0 first off, since there is a positive sign in front of the square root. However, since we have a horizontal translation of 4 units in the positive direction of the x-axis, we are only considering x>4, since if x<4 f(x) would be undefined. I am just saying that f(x)=sqrt(x-4). Let's check the domain of the inverse by observing the range of f(x), well we can see that it is [0,infinity). So let's look at the question, it says all x>2. From our orginal function we see that x=3 is an undefined point and hence a is excluded as an option. Putting in x=3 would give sqrt(-1) which is undefined on the real number line, and hence, we say there is no solution.

[duhherro]

does anyone here have solutions to the tute questions for eng1091?

[mrb3n]

Hi yall,

This is quite a rudimentary question, but I need some help determining the range of this function analytically.

H(x)=1-√(x+1)

They are really pedantic about full sentence answers in ENG1090, so an explanation would be really appreciated.

Cheers

[EspoirTron]

I think if you want to really precise it's a good time to use limits. See what H(x) converges to as x approaches infinity. Also, find the minimum x for which it is defined, you could do that be solving what's under the square root =>0. Then you can add sentences like: 'as x approaches infinity H(x) approaches blah'. Although, I don't do ENG1090, we have to use similar explanatory statements in MTH1020 so I generally chose to explain the formula. Starting off with a nice sentence like: 'I shall use limits to determine what values H(x) converges to within it's domain', is always great too.

I hope that helped.

[mrb3n]

Thanks man I'll give it a go

[LaLaLouise]

Hey hope everyone's first week back was good
Looking to get the solutions to the tutorial questions for MTH2032 (particularly the first half of the course). So if anyone happened to save them and could send them to me I'd appreciate it a lot!
Thanks!
(Also I've still got the MTH2010 soultions if anyone wants them)

[m.Chemia]

Hey hope everyone's first week back was good
Looking to get the solutions to the tutorial questions for MTH2032 (particularly the first half of the course). So if anyone happened to save them and could send them to me I'd appreciate it a lot!
Thanks!
(Also I've still got the MTH2010 soultions if anyone wants them)

I have the solutions to the tutorial questions for MTH2032. PM me your email if you haven't got them already (solutions to Problem Set 3 is missing somehow, but you can always ask questions in this thread )

[emchun]

Hello,

I have a question I don't know how to do...so I'm hoping someone could help.

I have to prove this statement true or either counter-example to demonstrate it is false:

"For any function ."

Thank you!