Intereting Posts

How can I choose the best algorithm to integrate ODE's numerically?
Action of a group on itself by conjugation is faithful $\iff$ trivial center
Is this map to a finite dimensional topological vector space an open map?
Random determinant problem
An inequality involving arctan of complex argument
How fundamental is Euler's identity, really?
Prove that this function is bounded
Is classifying one dimensional generalized quasicrystals worthwhile strategy to approach RH?
If $d$ is a metric, then $d/(1+d)$ is also a metric
Limit of a periodic function
Curvature of the metric $ds^2=y^2dx^2+x^2dy^2$
Help locating mini mandelbrots
Why does $A^TAx = A^Tb$ have infinitely many solution algebraically when $A$ has dependent columns?
Counting matrices over $\mathbb{Z}/2\mathbb{Z}$ with conditions on rows and columns
Alternative notation for exponents, logs and roots?

Is the following statement $$\frac{\partial^2 f}{\partial x \, \partial y}=\frac{\partial^2 f}{\partial y \, \partial x}$$ always true? If not what are the conditions for this to be true?

- Continuity of multidimensional function: $f_1(x,y)=\frac{x^2y}{x^2+y^2}$ and $f_2(x,y)=\frac{2xy^3}{(x^2+y^2)^2}$
- Find a plane that passes through a point and is perpendicular to 2 planes
- WolframAlpha says limit exists when it doesn't?
- Volume bounded by a sphere of radius $1$ in 4 dimensions
- Is the curl of every non-conservative vector field nonzero at some point?
- Multivariable Calculus Book Reference
- Surface Element in Spherical Coordinates
- Pointwise supremum of a convex function collection
- Really Stuck on Partial derivatives question
- Maximum value of $ x^2 + y^2 $ given $4 x^4 + 9 y^4 = 64$

Second order partial derivatives commute if $f$ is $\mathcal{C}^2$ (i.e. all the second partial derivatives exist and are continuous). This is sometimes called Schwarz’s Theorem or Clairaut’s Theorem; see here.

This is true in general if $ f \in \mathcal{C}^2 $. This has a name: symmetry. More formally, it is known as Clariut’s Theorem or Schwarz’s theorem.

- Help understanding Algebraic Geometry
- Subgroups of Abelian Groups
- Homology of $\mathbb{R}^3 – S^1$
- How to compute the following integral?
- Locus of intersection of two perpendicular normals to an ellipse
- Is the notation for '$a$ divides $b$' standard?
- Why isn't the gamma function defined so that $\Gamma(n) = n! $?
- Baker-Hausdorff Lemma from Sakurai's book
- Is there an example of an orthogonal matrix which is not diagonalizable
- Finding all invertible elements of $S^{-1}D$, $D$ is a Noetherian integral domain
- How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
- Can finite theory have only infinite models?
- Is there an axiomatic approach to ordinal arithmetic?
- Solve $\sin x = 1 – x$
- General question: What one can do to help students one is grading?