4. Elliptic cylinder r(u, v) = [a cos U, b sinu, u] 5. Paraboloid of revolution r(u, v) = [u cos v, u sin v, u²] 6. 'n the
4. Elliptic cylinder r(u, v) = [a cos U, b sinu, u] 5. Paraboloid of revolution r(u, v) = [u cos v, u sin v, u²] 6. 'n the
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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![1-8 PARAMETRIC SURFACE REPRESENTATION
Familiarize yourself with parametric representations of
important surfaces by deriving a representation (1), by
finding the parameter curves (curves u = const and
v = const) of the surface and a normal vector N = ľu x rv
of the surface. Show the details of your work.
1. xv-plots
2. xv-plane i
-.\ = (¹,_v) (thus ui + vj; similarly in
-
VistulatESTIU. 01
u sin vl
Cone
si, c]
4. Elliptic cylinder r(u, v) = [a cos v, b sin v,
5. Paraboloid of revolution r(u, v) = [ucos v,
u²]
6.
L
Jau cost
u]
u sin v,
in the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed5788d2-a0b4-4eb1-998c-a4248e13736e%2F58cab8b8-2ba3-4252-9779-415a6739812c%2Feyr4lb_processed.png&w=3840&q=75)
Transcribed Image Text:1-8 PARAMETRIC SURFACE REPRESENTATION
Familiarize yourself with parametric representations of
important surfaces by deriving a representation (1), by
finding the parameter curves (curves u = const and
v = const) of the surface and a normal vector N = ľu x rv
of the surface. Show the details of your work.
1. xv-plots
2. xv-plane i
-.\ = (¹,_v) (thus ui + vj; similarly in
-
VistulatESTIU. 01
u sin vl
Cone
si, c]
4. Elliptic cylinder r(u, v) = [a cos v, b sin v,
5. Paraboloid of revolution r(u, v) = [ucos v,
u²]
6.
L
Jau cost
u]
u sin v,
in the
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