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Given X(u, v) = (a () cos u, a () sin u, ) 1-v² 1-02' 1+v2 2av 1+v2 COS u, a %3D (x(u, v), y(u, v), 2(u, v)), a > 0. %3D 1. Show that a2+ y? + z? = a? ax 2. Calculate ax dv 3. Calculate the first fundamental form coefficients. 4. Calculate all the second derivatives of X.

Given X(u, v) = (a () cos u, a () sin u, ) 1-v² 1-02' 1+v2 2av 1+v2 COS u, a %3D (x(u, v), y(u, v), 2(u, v)), a > 0. %3D 1. Show that a2+ y? + z? = a? ax 2. Calculate ax dv 3. Calculate the first fundamental form coefficients. 4. Calculate all the second derivatives of X.

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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Given X(u, v) = (a () cos u, a () sin u, ) 2av 1+u2 COS u, a %3D 1+v2 1+v? (x(u, v), y(u, v), z(u, v)), a>0. a > 0. 1. Show that x + y + z 2 = a? %3D ax 2. Calculate ax dv 3. Calculate the first fundamental form coefficients. 4. Calculate all the second derivatives of X.
Transcribed Image Text:Given X(u, v) = (a () cos u, a () sin u, ) 2av 1+u2 COS u, a %3D 1+v2 1+v? (x(u, v), y(u, v), z(u, v)), a>0. a > 0. 1. Show that x + y + z 2 = a? %3D ax 2. Calculate ax dv 3. Calculate the first fundamental form coefficients. 4. Calculate all the second derivatives of X.
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