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F(x, y, z)=ri+2yj + 3z k

F(x, y, z)=ri+2yj + 3z k

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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Advanced Math F(x, y, z)=xi+2yj+3z k be a vector function in the Cartesian coordinate system. Write the vector F in the cylindrical coordinate system (r, 0, z) system by defining x = r cos 0, y = r sin 0, and z = z. Note that the vector function in the cylindrical coordinate system is obtained as F (r, 0, z)= Fer+Foeo + Fez. The vectors er, eg, ez are the unit vectors in the cylindrical coordinate system. The relation between unit vectors in the Cartesian coordinate system and the cylindrical coordinate system is shown in the following figure. eo 0 V.F (r, 0, z)= er i Compute V F (r, 0, z) in the cylindrical coordinate system with the following definition. 10 (rFr) 10 (Fo) a (F₂) + + T Ər T 20 дz Hint: The value you obtained from this computation must be equal to the value you obtained from part (a). The divergence of a vector function does not depend on the coordinate system.
Transcribed Image Text:Advanced Math F(x, y, z)=xi+2yj+3z k be a vector function in the Cartesian coordinate system. Write the vector F in the cylindrical coordinate system (r, 0, z) system by defining x = r cos 0, y = r sin 0, and z = z. Note that the vector function in the cylindrical coordinate system is obtained as F (r, 0, z)= Fer+Foeo + Fez. The vectors er, eg, ez are the unit vectors in the cylindrical coordinate system. The relation between unit vectors in the Cartesian coordinate system and the cylindrical coordinate system is shown in the following figure. eo 0 V.F (r, 0, z)= er i Compute V F (r, 0, z) in the cylindrical coordinate system with the following definition. 10 (rFr) 10 (Fo) a (F₂) + + T Ər T 20 дz Hint: The value you obtained from this computation must be equal to the value you obtained from part (a). The divergence of a vector function does not depend on the coordinate system.
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