Where Can I Find a Proof for the Wronskian Formula?

zaybu
Messages
53
Reaction score
2
Can anyone point to a proof for the Wronskian formula:

W[v,v*] = v'v* - vv*' = 2iIM(v', v*)

Thanks
 
Physics news on Phys.org
What do you mean by 'IM(v', v*)'?
 
W= s z^{*}- s^{*}z
s=a+ib
z=c+id

W= (a+ib) (c-id) - (a-ib) (c+id)
W= ac -i ad +i bc -bd - ac -i ad +ibc+bd
W= -i ad +i bc -i ad +ibc
W= 2i bc - 2i ad = 2i (bc-ad)

sz^{*} = ac + bd + i (bc-ad)
so
Im(sz^{*})= bc-ad

The proof is already seen
 
Thanks
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
View full post »

Similar threads

I Determining linear indepedence/dependence of a set of functions
Replies
11
Views
3K
What is the connection between the Wronskian and linear independence?
Replies
2
Views
2K
Fundamental matrix vs Wronskian
Replies
2
Views
2K
I Difference between Wronskian and other methods
Replies
8
Views
2K
Understanding Wronskian of solutions to homoeneous 2nd order linear DE
Replies
2
Views
1K
Linearly independent functions with identically zero Wronskian
Replies
1
Views
1K
How does the Wronskian determine uniqueness of solution?
Replies
2
Views
2K
MHB Use Wronskian to show only 2 indepndent solutions of 2nd order ODE
Replies
4
Views
2K
Question about independance of functions and wronskian
Replies
8
Views
7K
I Energy of moving Sine-Gordon breather
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top