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Jan
14
comment How to find the following derivative?
@GitGud Edited. By the way, if you use \arcsin x, you produce $$\arcsin x.$$
Jan
14
revised How to find the following derivative?
added 484 characters in body
Jan
14
answered How to find the following derivative?
Jan
13
comment Wave equation solution properties
@rlgordonma I'd say that the fact that $v_{\alpha \beta} = 0$ implies that $v(\alpha,\beta) = F(\beta) + G(\alpha)$ which, in turn, means that $u(x,t) = F(x-t) + G(x+t)$ (this can be ensured because the transformation $(x,t) \to (\alpha,\beta)$ is invertible), and given that the wave equation with initial conditions has a unique solution (provided $f$ and $g$ are in some space, details left to the OP), this has to be it. Finally, using the initial conditions, one can determine $F$ and $G$ in terms of $f$ and $g$, and derive d'Alambert solution.
Jan
13
comment Wave equation solution properties
For completeness: Question no. 2 hasn't been answered. An argument of unicity must be performed in order to ensure that every solution has the desired form.
Jan
9
awarded  Revival
Dec
21
awarded  Revival
Dec
10
comment Consider the wave equation
I believe you need to solve using the reflection principle, which means your soltution is valid in the triangular region given by $$T = \left\{(x,t) \in \mathbb{R}\,\big|\, t > 0\,,\,t < x+a,\,t<a-x\right\}$$ and then it has to be extended using the Rhombus Theorem with the reflection condition $f \to -f$ in the boundaries.
Dec
10
answered Rewrite the following differential equation in Sturm-Liouville form
Dec
10
reviewed Reviewed Spherical coordinates to cartesian coordinates.
Dec
10
comment How do I solve a PDE with a Dirac Delta function?
@DarrelWee I've added the complete deduction for the analytic solution. I don't have time to do the numericall algorithm, but the only thing you need to do is, supposing $x_m = 1$, substitute $u_{m+1}$ with $1 - u_m$ in the algorithm.
Dec
10
revised How do I solve a PDE with a Dirac Delta function?
added 2751 characters in body
Dec
9
revised Multiplication over $F_{2^{31}-1}$ by power of $2$
escaped code
Dec
9
reviewed Reviewed Multiplication over $F_{2^{31}-1}$ by power of $2$
Dec
9
suggested approved edit on Multiplication over $F_{2^{31}-1}$ by power of $2$
Dec
6
comment Separation of variables linear PDE
What's the domain, initial and boundary conditions?
Dec
6
reviewed Reviewed Operations and relations
Dec
6
comment Finding Derivatives Using Fundamental Theorem of Calculus
If you enclose the upper/lower limits with {}, Mathjax will render the properly, i.e. \int_{2x}^{3x} f(t) dt will produce $$\int_{2x}^{3x} f(t) dt$$
Dec
6
reviewed Reviewed How can I introduce complex numbers to precalculus students?
Dec
6
comment How do I solve a PDE with a Dirac Delta function?
@doraemonpaul Is exaclty the same thing. See my answer for details.