ABSTRACT
Frequently, a problem stated in terms of one set of independent variables or coordinates needs to be restated in terms of a different but equivalent set of independent variables. It then may be necessary to find relationships among partial derivatives involving the two sets of variables. Let the old set of variables be x, y, z, ... and let the new set be r, s, t, .... The basis for the desired relationships is the formula for the total differential: d T = ∂ T ∂ x d x + ∂ T ∂ y d y + ∂ T ∂ z d z + ⋯ . $$ dT = \frac{{\partial T}}{{\partial x}}dx + \frac{{\partial T}}{{\partial y}}dy + \frac{{\partial T}}{{\partial z}}dz + \cdots \,\,. $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315108858/f4dff3a2-1feb-457b-a709-022257f02721/content/math16_1.tif"/>
