Question

Let \(f_1, f_2,f_3\) be continuously differentiable functions from \(\mathbb R^4\) to \(\mathbb R\). Give suffice conditions so that the equations \(f_1(x,y,z, t)=0\\f_2(x,y,z,t)=0\\f_3(x,y,z,t)=0\) can be solved for x,y,z in term of t.
Please, help

Answer 1

@SithsAndGiggles @amistre64 @phi @perl

Answer 2

i wouldnt even know where to start with this at the moment. srry

Answer 3

It's Ok. Thanks anyway. :)

Answer 4

http://www.owlnet.rice.edu/~fjones/chap2.pdf

Answer 5

@nincompoop Thanks but it is not the same as my problem. :)

Answer 6

My attempt: Let \(f_1,f_2,f_3:\mathbb R^4 \rightarrow \mathbb R\) .
Let \(f:\mathbb R^4\rightarrow \mathbb R^3\), \(f=(f_1,f_2,f_3)\) . Hence f is smooth function

Answer 7

The derivative matrix of f is
\[D(f)=\left[\begin{matrix}\dfrac{\partial f_1}{\partial x}&\dfrac{\partial f_1}{\partial y}&\dfrac{\partial f_1}{\partial z}\\\dfrac{\partial f_2}{\partial x}&\dfrac{\partial f_2}{\partial y}&\dfrac{\partial f_2}{\partial z}\\\dfrac{\partial f_3}{\partial x}&\dfrac{\partial f_3}{\partial y}&\dfrac{\partial f_3}{\partial z}\end{matrix}\right]\]

Answer 8

But I don't know where to go from this. :(

Answer 9

How about this @rational @zzr0ck3r

Answer 10

I have no idea either. I really hate analysis and much prefer topology.

Answer 11

I will take topology next semester, is it hard?? @zzr0ck3r

Answer 12

I don't think so. It is much more general.

Answer 13

I find it makes analysis easier, but we are not this far yet.

Answer 14

any recommendation for preparing for the course?

Answer 15

Munkres Topology

Answer 16

it's a staple

Answer 17

are they books? any site?

Answer 18

yeah it's a book. I don't really watch videos of lectures, I learn much more from the books.

Answer 19

You can readily find it if you google

Answer 20

for free even! The book is super old.

Answer 21

I will, thanks for the tips. :)

Answer 22

If you have any questions next term, tag me:) I love that stuff