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Steady state temperature and the Laplacian

Time-independent heat distributions where the Laplacian vanishes, on a wire and on a rectangular plate, splitting the boundary data side by side.

Notes on Diffy Qs: Differential Equations for Engineers, Steady state temperature and the Laplacian

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2 exercises

Exercise 101

In the region described by $0 < x < 1$ and $0 < y < 1$ , solve the problem

Exercise 102

In the region described by $0 < x < 1$ and $0 < y < 2$ , solve the problem

Adapted from Notes on Diffy Qs © 2008–2026 Jiří Lebl. Licensed under CC BY-SA 4.0. Source: Notes on Diffy Qs: Differential Equations for Engineers. Imported at revision 658bcae.