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6 results
Clear filtersHeat.deriv_exp_heatKernel
Plain-language statement
Derivative of the exponential term exp(-(x²)/(4αt)) with respect to x.
Source project: PDE
Person-level attribution pending.
Heat.deriv_sqrt_inv
Plain-language statement
Derivative of 1/√x at a positive point.
Source project: PDE
Person-level attribution pending.
Heat.hasDerivAt_heatKernel_t
Plain-language statement
The time derivative of the heat kernel ∂/∂t heatKernel(α, x, t).
Source project: PDE
Person-level attribution pending.
Heat.hasDerivAt_heatKernel_x_x
Project documentation
Auxiliary lemma: derivative of the first spatial derivative's formula.
Source project: PDE
Person-level attribution pending.
Heat.hasDerivAt_heatKernel_xx
Plain-language statement
The second spatial derivative of the heat kernel ∂²/∂x² heatKernel(α, x, t).
Source project: PDE
Person-level attribution pending.
Heat.integral_heatKernel_one_gaussian
Plain-language statement
Property 2: The heat kernel integrates to one over all of ℝ. This shows that the heat kernel is properly normalized and can be interpreted as a probability density function (specifically, a Gaussian distribution).
Source project: PDE
Person-level attribution pending.