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pasmith replied to the thread I Non-orthogonal bases.

A lot o numerical analysis involves dealing with spaces of polynomials of degree at most $$N$$ on $$[-1,1]$$. There are various families...

Yesterday, 12:59 PM
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pasmith replied to the thread Family of lines that are at a distance of 5 from the origin.

The equation of a line in ##\mathbb{R}^2## can be written as $$\mathbf{n} \cdot (\mathbf{x} - \mathbf{x}_0) = 0$$ where ##\mathbf{x}_0##...

Sep 9, 2025
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pasmith replied to the thread Modeling a graph that shows age in relation to depth of an ice sample.

You can use linear interpolation between the data points. Between z_i and z_{i+1} that gives you \int_{z_i}^z \frac{1}{\lambda(z)}\,dz =...

Sep 2, 2025
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pasmith replied to the thread I Can one find a matrix that's 'unique' to a collection of eigenvectors?.

Yes, where D is a Jordan normal form, ie. the expression of the map with respect to a basis of (generalized) eigenvectors \{v_1, \dots...

Jul 28, 2025
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pasmith replied to the thread A Should the boundary condition have to satisfy dimensional consistency?.

For the purpose of this exercise, does it make a difference to the mathematical analysis if the boundary condition is the dimensionally...

Jul 24, 2025
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pasmith replied to the thread A Show positivity and boundedness of a non-linear system.

Can you find a Liapunov function for the system?

Jul 13, 2025
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pasmith replied to the thread Solve the first order linear differential equation.

I would assume the first, since the second would have been written as y \ln x. But the first leads to a non-linear, non-separable...

Jul 6, 2025
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pasmith replied to the thread I Homemorphism in quotient topology.

A graphical description is not really a rigorous proof, although it might help you to find one. Ultimately, showing that X/\sim is...

Jul 2, 2025
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pasmith replied to the thread I Homemorphism in quotient topology.

It should not be difficult to get from a graphical description to a parametrisation. For example, for the Mobius strip one can take a...

Jul 2, 2025
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pasmith posted the thread Bug '\epsilon < 8' renders as a "Misplaced &" error in Feedback and Announcements.

\epsilon < 8 renders as \epsilon < 8. Originally discovered in my post at...

Jun 30, 2025
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pasmith replied to the thread Limit of piecewise function using epsilon delta.

You haven't told us the definition of f. You can assume \epsilon < 8 (a \delta which works for such an \epsilon will also work for any...

Jun 30, 2025

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