## Abstract

We demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments are determined by the transformation functions between the two coordinate systems. By integrating out an original coordinate with a Dirac delta function, we replace the original coordinate with a new coordinate in a systematic way. A recursive use of Dirac delta functions allows the coordinate transformation successively. After replacing every original coordinate into a new curvilinear coordinate, we find that the resultant Jacobian of the corresponding coordinate transformation is automatically obtained in a completely algebraic way. In order to provide insights on this method, we present a few examples of evaluating the Jacobian explicitly without resort to the known general formula.

Original language | English |
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Article number | 035006 |

Journal | European Journal of Physics |

Volume | 42 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2021 May |

### Bibliographical note

Publisher Copyright:© 2021 European Physical Society.

## Keywords

- Dirac delta function
- Jacobian
- chain rule of partial derivatives
- coordinate transformation

## ASJC Scopus subject areas

- Physics and Astronomy(all)