For the purposes of constructing explicit solutions to second-order linear homogeneous differential equations on the Riemann sphere the Kovacic algorithm partitions the subgroups of SL(2,C) into four… (More)

Normal forms for vector elds and Hamiltonians at equilibria have a long history, an extensive literature, and a continuing appeal for researchers (e.g., see the references in [Mur1], [Sa1]). These… (More)

We define the differential Galois group of a linear homogeneous ordinary differential equation and illustrate the type of information about solutions packaged within. The initial format is classical;… (More)

Algebraic geometry is fairly easy to describe from the classical viewpoint: it is the study of algebraic sets (defined in §2) and regular mappings between such sets. (Regular mappings are also… (More)

This talk should be regarded as an elementary introduction to differential algebra. It culminates in a purely algebraic proof, due to M. Rosenlicht [Ros2], of an 1835 theorem of Liouville on the… (More)

In this talk we indicate how elementary number-theoretic results depending on unique factorization can occasionally be established by “differentiating” integers. The presentation is intended to serve… (More)