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## #1 Help Me ! » Help with tensors? » 2016-10-25 20:51:09

mrpace
Replies: 0

From the transformation law for a Cartesian tensor αijk of order 3, prove that αijj is a Cartesian tensor of order 1.

Please note that the 'ijk' part above is meant to be in subscript but not sure how to do that.

Thanks for any help.

## #2 Help Me ! » Converting from Cartesian to spherical coordinates? » 2016-10-17 18:00:23

mrpace
Replies: 1

Convert

F(x,y,z) = k / (x^2 + y^2 + z^2)^2

into spherical coordinates.

Thanks for the help.

## #3 Re: Help Me ! » Find all distinct subgroups of <32> in <Z60, +60> » 2016-03-16 12:09:35

Nehushtan wrote:
mrpace wrote:

My answer is <0>, <12>, <20>, <32>
Is this correct?

Looks good to me. As a subgroup of the given group, <32> = <4> is cyclic of order 15, and a cyclic group of order 15 has precisely four subgroups.

Thanks mate.

## #4 Help Me ! » Find all distinct subgroups of <32> in <Z60, +60> » 2016-03-15 16:34:39

mrpace
Replies: 7

My answer is <0>, <12>, <20>, <32>
Is this correct?

## #5 Help Me ! » Proof involving a bijection. » 2016-02-29 16:42:27

mrpace
Replies: 1

Suppose that a, b, and y are all functions.
If ay=by and y is one-to-one and onto, prove that a=b.

This looked very straightforward at first then I realised that a and b are functions, not values. I am therefore stuck on what to do.
Any help is much appreciated.

## #6 Help Me ! » Series convergence in complex analysis. » 2015-10-07 14:03:03

mrpace
Replies: 1

For which values of Z do the following series absolutely converge?

∑ (Z+1)^n / 2^n

The sum is from n=0 to infinity.

Thanks for any help.

## #7 Help Me ! » The definition of ''or'' when sketching a set » 2015-09-20 14:12:12

mrpace
Replies: 1

z is the set where Re(z)<1 or Im(z-1) does not equal zero.

so my question is when they say ''or'', do they also mean the points that satisfy both sets or does ''or'' mean exclusive to one set?

## #8 Help Me ! » Complex numbers algebra » 2015-09-20 05:06:44

mrpace
Replies: 2

Show that,

|1 − zw*|^2   −   |z − w|^2 = (1 − |z|^2)(1 − |w|^2)

where z and w are complex numbers and z* is the conjugate of z.

Not very fluent with algebraic properties of these things so please help!!
Thanks.

## #9 Help Me ! » Simplifying complex numbers » 2015-09-16 19:10:29

mrpace
Replies: 2

So according to my textbook
|iz*/2 - i/2| simplifies to |z-1|/2

where z* is the conjugate of z.

I can't work out how they got that so could someone please show it to me.
Thanks.

## #10 Help Me ! » Prove this one?? » 2015-09-10 12:49:19

mrpace
Replies: 1

Suppose that f is continuous on the closed interval [a, b], a < b, and that f(a) =
A, f(b) = B, A < B.
Suppose further that f is strictly increasing on [a, b] (i.e. for any x1, x2 ∈ I, x1 <
x2, impliesf(x1) < f(x2)).
Let C be a number between A and B. Show that there is exactly one value of x in
(a, b) such that f(x) = C.

I used the bisection process to try to explain why this must be the case but i'm not convinced that's what they're looking for....any ideas???

## #11 Help Me ! » Proof by induction » 2015-09-09 19:42:56

mrpace
Replies: 1

Let X0 = 1, X1 = 1, and suppose that, for n ≥ 1,
Xn+1 = Xn + Xn-1(r^r)
where 0<r<1

prove by induction that....
Xn+1  ≤ (1+r)(1+r^2).......(1+r^n)

I've done several induction problems before, but this one has got me stuck.

Help is much appreciated

## #12 Help Me ! » Proof to do with supremums. » 2015-07-28 03:25:07

mrpace
Replies: 1

For any real number c and any set S ∈ R, we define c + S to be the set {c + x : x ∈ S}.
Prove:
If a set S ⊆ R, and c is any real number, the c + S has a supremum and
sup(c + S) = c + sup S.

Any help is much appreciated, thanks.

## #13 Help Me ! » Quick question on sequence convergence. » 2015-07-23 05:57:29

mrpace
Replies: 1

I understand that if a sequence converges to a particular value then we call that sequence convergent.
However, what if the sequence converges to 2 values?

For example the sequence 2/3, -3/5, 4/7, -5/9 approaches -0.5 from below and approaches 0.5 from above. Do we just say that the sequence diverges?

## #14 Help Me ! » Which of the following are subrings of C? » 2015-05-12 14:49:21

mrpace
Replies: 1

Z[√7] = {a+b√7|a.b ∈ Z}

2Z+iZ = {2a+bi|a,b ∈ Z}

Where C is the complex plane, Z is the set of real integers.

Any ideas? Thanks.

## #15 Help Me ! » Solve the following differential equation. » 2015-04-12 18:04:14

mrpace
Replies: 0

Solve:

2y∂u - 3x∂u + 2xyu = xy
∂x       ∂y

given that along Y^2 = (-1/2)x^2

u = 1/2  +  cos(x)e^(x^2/2)

Any idea?

## #16 Help Me ! » Find a permutation group isomorphic to.... » 2015-03-26 02:32:33

mrpace
Replies: 2

Find a permutation group isomorphic to U(16), X16
using the proof of cayley's theorem.

Any ideas?

## #17 Help Me ! » Question on isomorphisms » 2015-03-26 02:09:26

mrpace
Replies: 2

Let H be the subgroup of all rotations in Dn and let φ be an isomorphism from Dn to Dn. Prove that φ(H) = H

Any ideas on this one?

## #18 Help Me ! » Find Green's function for the problem... » 2015-03-22 12:20:47

mrpace
Replies: 0

Find the Green's function for the problem.

y'' - y = f(x)          x>0
y'(0) = 0              lim as x goes to infinity of y(x) is 0.

Any idea on this one?

## #19 Help Me ! » Differential Equations help please » 2015-03-20 15:51:55

mrpace
Replies: 1

Find all the real eigenvalues and eigenfunctions for the eigenvalue problems

y'' + λy = 0,
y(-3) = y(3),
y '(-3) = y '(3).

Not really sure on the process. Thanks for any help.

## #20 Help Me ! » Help with a fairly simple proof please? » 2015-02-24 21:53:32

mrpace
Replies: 10

Show that 5n+3 and 7n+4 are relatively prime for all n.

I'm fairly new at proofs and I think I've made decent inroads but can't seem to finish it elegantly.

Here is my attempt:

Show that gcd (5n+3 , 7n+4) = 1

let A=5n+3 and B=7n+4

if n is even then A is odd. If n is odd then B is odd. Therefore gcd cannot be even.

For an odd number (k) to divide A as well as B, the difference between A and B must be some multiple of k which can only be true if k equals 1.

That last line I don't think is sufficient but I don't know how to put it in more convincing terms. Help is appreciated.

## #21 Help Me ! » Critical points problem: Differential equations » 2014-10-13 17:35:13

mrpace
Replies: 1

Hey. I can find nothing on this material in my textbook and nothing online that's quite like it, so i'm hoping someone here can show me how to do this.

Consider the system

dx/dt  =  4x + 5y + xy

du/dt  =  x + x^2 - y^2

Discuss the type and stability of the critical point at (0,0)

## #22 Help Me ! » Differential equations problem » 2014-10-01 01:13:20

mrpace
Replies: 4

write the system

x'(t) = -3x(t) +y(t) +e^t + 1
y'(t)= 2x(t) - cost

In the matrix form x' = Ax + f

could this really be so simple as x' = {-3, 2}x +f ??
or is there more to it?

## #23 Help Me ! » Help with Laplace transform please » 2014-09-15 16:47:11

mrpace
Replies: 0

determine the laplace transform of f(t) of the following

f(t) =
e^(-t)   when 0 ≤ t ≤ 5
-1  when t > 5

I got my answer as simply 1/(s+1) when 0 ≤ s ≤ 5
-1/s when s > 5

I'm not sure if this is right though.

## #24 Help Me ! » Linear Transformation problem » 2014-09-11 14:06:37

mrpace
Replies: 1

Find all real values of a and b such that the following is a reflection

T:  X  =  aX + (24/25)Y
Y      bY + (24/25)X

Sorry for the lack of latex; I'm sure you can work it out.

## #25 Re: Help Me ! » Prove this limit » 2014-09-11 03:01:03

Agnishom wrote:

There is no need to factor it. You are confusing yourself by factoring it

Really? I'm trying with it not factored and not having any luck.. can you help?