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3.28 (a) In terms of the cylindrical coordinates defined by x = r cos 0, y =r sin 0. z = 2, show that a'u au au du 1 a'u au ay? az? r ar är ae la tormr ot the spherical coordinatcs definrd by =r sin e cos d, y = r sin e sin dd, z = r cos 8, show

3.28 (a) In terms of the cylindrical coordinates defined by x = r cos 0, y =r sin 0. z = 2, show that a'u au au du 1 a'u au ay? az? r ar är ae la tormr ot the spherical coordinatcs definrd by =r sin e cos d, y = r sin e sin dd, z = r cos 8, show

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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3.28 (a) In terms of the cylindrical coordinates defined by x = r cos 0, y = r sin 6, z = 2, show that a'u a'u du 1 a'u a'u it dx ду? az? r ar az (b) In terms of the spherical coordinates defined by x = r sin 0 cos d, y = r sin 0 sin d, z = r cos 0, show that du sin o du ди sin 0 ae 1 a dy az? àd sın e ad
Transcribed Image Text:3.28 (a) In terms of the cylindrical coordinates defined by x = r cos 0, y = r sin 6, z = 2, show that a'u a'u du 1 a'u a'u it dx ду? az? r ar az (b) In terms of the spherical coordinates defined by x = r sin 0 cos d, y = r sin 0 sin d, z = r cos 0, show that du sin o du ди sin 0 ae 1 a dy az? àd sın e ad
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