Reputation
8,671
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
2 10 40
Impact
~169k people reached

Sep
3
comment Confusion with Euler-Lagrange Derivation
That is the chain rule.
Sep
1
comment Can I solve an Euler differential equation by using the Frobenius method?
In short, the Euler equation is a Frobenius method problem where only the indicial equation matters. Or, from my perspective teaching, the method of Frobenius is a generalization of the Euler ODE solution to other singular ODEs of the same managable (regular) singularity.
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
Exactly, sadly the stack exchange software is now scolding us for discussion of math here. I hope the added few lines are helpful as you study further...
Aug
31
revised Index of Summation Shift? Power Series and Differential Equations
added 742 characters in body
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
Honestly, what you need to do to solve things later is to make one summation which gathers all terms as possible at each order, so, the thing were looking at is just a step towards that eventuality.
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
Yep. Think of it as the author sweeping the dirt into two piles rather than leaving 4.
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
no it's not a mistake. The $n=1$ gives $[2(1)(0)+6(1)+2]a_1x=8a_1x$ and $n=0$ gives $[2(0)(-1)+6(0)+2]a_0=2a_0$ so those exceptional terms get put into the right sum by starting $n$ at $0$ rather than $2$.
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
to answer my question: yes, yes we can.
Aug
31
comment Index of Summation Shift? Power Series and Differential Equations
Yep. I think I know what you mean, the lumping in the $n=0$ and $n=1$ terms is a bit slippery.
Aug
31
answered Index of Summation Shift? Power Series and Differential Equations
Aug
31
reviewed Approve approximation tag wiki
Aug
31
reviewed Approve hamiltonian-path tag wiki excerpt
Aug
31
reviewed Approve approximation tag wiki excerpt
Aug
31
reviewed Approve hamiltonian-path tag wiki
Aug
30
revised Sine-Gordon Equation application
edited tags
Aug
27
comment Definition of the principal symbol of a differential operator on a real vector bundle.
Thanks! I'm trying to cipher Cartan For Beginners at the moment and it would be helpful to have a better sense of what they are trying to generalize...
Aug
27
comment How hard is it to endow a $\textit{Spin}^{c}$ structure on four-dimensional manifolds?
I was browsing Friedrich's book earlier today. I think Branimir's comment is worthwhile. If you haven't looked at that yet it's probably worth a few minutes.
Aug
23
comment Solving a wave equation: $a^2\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial t^2}$
The case depends on the boundary conditions. Different boundary conditions give you different $\lambda$ contributing nontrivial solutions. So...
Aug
23
comment Solving a wave equation: $a^2\frac{\partial^2 u}{\partial x^2}=\frac{\partial^2 u}{\partial t^2}$
seems like you're missing the boundary conditions and perhaps an initial condition or two...
Aug
19
reviewed Approve Solution in terms of Lambert $W$ function