Using Rotation Matrices to Get ∇f and ∇• F in Cylindrical and Spherical Coordinates

Using Rotation Matrices to Get ∇f and ∇• F in Cylindrical and Spherical Coordinates

We show that the correct expressions for the gradient and divergence differential operators in cylindrical and spherical coordinates can be derived using rotation matrices. The method is intuitive and less strenuous than what is usually found in calculus textbooks.

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Veröffentlicht in:Mathematics magazine 2022-04, Vol.95 (2), p.137
Hauptverfasser: Lima, Fábio M S, Jordão, Pedro G F
Format: Magazinearticle
Sprache:eng
Schlagworte:
Algebra
Calculus
Cylindrical coordinates
Differential equations
Mathematical models
Matrix
Operators (mathematics)
Rotation
Spherical coordinates
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Beschreibung
Zusammenfassung:We show that the correct expressions for the gradient and divergence differential operators in cylindrical and spherical coordinates can be derived using rotation matrices. The method is intuitive and less strenuous than what is usually found in calculus textbooks.
ISSN:0025-570X
1930-0980
DOI:10.1080/0025570X.2022.2025708