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A hyperbolic PDE in (x, y) can be written in canonical form, Pen = f(n. 0.03, Pn) by using the characteristic curves as the transformed coordinates (x, y) and n(x, y). That is, we let =y-λ₁x n=y=λ₂x apxx + boxy + covy + dox + eoy + fo = g(x, y) (2.32) (2.33) (2.18a)

A hyperbolic PDE in (x, y) can be written in canonical form, Pen = f(n. 0.03, Pn) by using the characteristic curves as the transformed coordinates (x, y) and n(x, y). That is, we let =y-λ₁x n=y=λ₂x apxx + boxy + covy + dox + eoy + fo = g(x, y) (2.32) (2.33) (2.18a)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 33RE
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Derive the canonical form for hyperbolic equations (Equation 2.32) by applying the transforma- tions given by Equation 2.33 to Equation 2.18a.
Transcribed Image Text:Derive the canonical form for hyperbolic equations (Equation 2.32) by applying the transforma- tions given by Equation 2.33 to Equation 2.18a.
A hyperbolic PDE in (x, y) can be written in canonical form, Pen = f (, n₂, 93, ¶n ) by using the characteristic curves as the transformed coordinates (x, y) and n(x, y). That is, we let =y-₁x=y=λ₂x a@xx + boxy + cyy + dox + e$y + fo = g(x, y) уу (2.32) (2.33) (2.18a)
Transcribed Image Text:A hyperbolic PDE in (x, y) can be written in canonical form, Pen = f (, n₂, 93, ¶n ) by using the characteristic curves as the transformed coordinates (x, y) and n(x, y). That is, we let =y-₁x=y=λ₂x a@xx + boxy + cyy + dox + e$y + fo = g(x, y) уу (2.32) (2.33) (2.18a)
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