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Re: Several Variable Calculus \text{Two metrics }\rho\text{ and }\delta \text{ are said to be topologically equivalent}\\ \text{iff every }\rho\text{-ball contains a }\delta\text{ ball}\\ \text{and every }\delta\text{-ball contains a }\rho\text{-ball} \text{Two metrics }\rho\text{ and...

For ordinary graphing purposes, Desmos suffices. GeoGebra allows much more interactive approaches. I use GeoGebra when I feel there is a need to simulate something, not just graph it. And indeed, GeoGebra can also be used for Euclidean geometry, by extension.

Re: UNSW chit chat thread 2017 I forgot everything.

Re: Group Theory I know that. I just don't want to appear as though I am undoing a moderator action without permission.

Re: Group Theory I am well aware that group theory may not fall under the umbrella of 'linear algebra'. However, in my course (MATH2601), it is the first thing that they choose to teach, hence I set the thread up with that title. I would like my thread name back so I can reserve this thread for...

\text{Define an operation}*\text{over }\mathbb{Z}_n\text{ where }x*y=xy \mod n\\ \text{Proven earlier: This operation is binary, commutative and associative} \text{Let }p\in \mathbb{Z}\text{ be prime. Show that }\mathbb{U}_p=\mathbb{Z}_p - \{ 0\}\text{ is a group under the operation }*\text{...

Re: Several Variable Calculus Completely forgot about this haha

Re: Several Variable Calculus \text{Proven earlier: For a particle with velocity }\textbf{v}(t)\\ \text{If }\textbf{v}(t)\cdot \textbf{v}^\prime(t)=0\text{ then the speed }v=\sqrt{v_1^2+\dots+v_n^2}\text{ is constant} \\ \text{A particle of mass }m\text{ with position vector...

Re: Several Variable Calculus Strange... That's what I did so maybe there's an error in my computation. \text{The values for }(s,t)\text{ were }(1,-1)\text{ and }(0,0)\text{ and the latter easily worked} \\ \textbf{r}_1^\prime (t) = (2t-1,2t+1)\\ \textbf{r}_2^\prime (s) = (1+2s, 1-2s)...

Re: Several Variable Calculus Excellent. Makes sense. ________________ Find the angle between the two curves at the points of intersection. I'm having a dumb moment now. Which vectors are we taking the dot product of?

Re: Several Variable Calculus Oh. I'll work on that right now but why was it necessary to introduce a new variable?

Several Variable Calculus Marathon & Questions For some reason I lost the point of intersection (2,0): \text{Find the }\textit{two}\text{ points of intersection of the curves}\\ \textbf{r}(t)=(t^2-t,t^2+t)\\ \textbf{r}(t)=(t+t^2,t-t^2) I equated the relevant r1 and r2 components but only...

Re: HSC 2017 MX2 Integration Marathon I'm actually trying to remember what the question was. I can't recall it.

Re: HSC 2017 MX2 Integration Marathon \int_0^\pi t \prod_{\beta=1}^\infty \cos\left(\frac{t}{2^\beta}\right)dt

Statistics (thread merged) It's a geometric distribution but suppose we didn't know that \\\text{Find, via first principles, }Var(X)\\ \text{if }Pr(X=k)=\frac23 \left(\frac13\right)^{k-1}\, k =1,2,\dots \text{Proven: }\mathbb{E}[X]=\frac32

Re: UNSW chit chat thread 2017 They told you to get the ID cards before O-week

Re: UNSW chit chat thread 2017 Does anyone know about this lecturer "Jan Zika"? Heard he's new but curious anyway

The course outlines usually don't vary that much. What courses are you doing?

Wait till harder 3U.

Fixed. I forgot the word at the time.