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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
15.1. Separation of Variables (Fourier Method) 1163
TABLE 15.1
Description of auxiliary problems for Eq. (15.1.4.1) and problems for associated
functions ϕ(x) and ψ(y) that determine particular solutions of the form (15.1.4.3).
The abbreviation HB C stands for “homogeneous boundary condition”
Auxiliary
problem
Functions vanishing
in the boundary
conditions (15.1.4.14)
Eigenvalue problem
with homogeneous
boundary conditions
Another problem with one
homogeneous boundary
condition (for λ
n
found)
Problem 1
f
2
(y) = f
3
(x) = f
4
(x) = 0,
function f
1
(y) prescribed
functions ψ
n
(y) and values λ
n
to be determined
functions ϕ
n
(x)
satisfy an HBC at x = x
2
Problem 2
f
1
(y) = f
3
(x)
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Publisher Resources

ISBN: 9781466581494