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Exercise 1. Consider the surface parametrized by X(u, v) = (u, v, u² − v²). Let a(t) = (t,0, t²) be a curve in the surface. Show that a is a geodesic by showing that atan 0. To do this, use the definition that a'tan = a" · (N×T). =

Exercise 1. Consider the surface parametrized by X(u, v) = (u, v, u² − v²). Let a(t) = (t,0, t²) be a curve in the surface. Show that a is a geodesic by showing that atan 0. To do this, use the definition that a'tan = a" · (N×T). =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 1. Consider the surface parametrized by X(u, v) = (u, v, u² − v²). Let a(t) = (t,0, t²) be a curve in the surface. Show that a is a geodesic by showing that atan 0. To do this, use the definition that a'tan = a" · (N×T). =
Transcribed Image Text:Exercise 1. Consider the surface parametrized by X(u, v) = (u, v, u² − v²). Let a(t) = (t,0, t²) be a curve in the surface. Show that a is a geodesic by showing that atan 0. To do this, use the definition that a'tan = a" · (N×T). =
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