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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 =...

Tuesday, 6:07 AM
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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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pasmith replied to the thread What does this equation mean?.

Most calculators will label it as "tan-1" rather than "arctan". In mathematics we generally measure angles in radians rather than...

Jun 19, 2025
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pasmith replied to the thread Melin transform of the floor function [x].

How do you define [z] for z \in \mathbb{C}?

Jun 16, 2025
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pasmith replied to the thread A How to Find Critical Points of function f(x,y,z).

There is a fundamental problem here: \nabla \times (y + 5, 2z, y) = (-1,0,-1) is not zero, so (y + 5, 2z, y) cannot be the gradient of a...

Jun 7, 2025

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