Cylindrical Coordinates

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Pre: Polar Coordinates

Introduction

Polar coordinates on x and y, Cartesian on z.

Note that we can change orientation if we wish

The Jacobian for Cartesian to Cylindrical

See Jacobian, determinant, Partial Derivatives

Definition

With :

(see determinant, Partial Derivatives, Pythagorean identities)

Equation

Remark

These equations assume that is the "Cartesian" part, but different orientations will require different Jacobians.

Additional

  1. Triple Integrals#Using Cylindrical Coordinates