This book explains recent results in the theory of moving frames
that concern the symbolic manipulation of invariants of Lie group
actions. In particular, theorems concerning the calculation of
generators of algebras of differential invariants, and the
relations they satisfy, are discussed in detail. The author
demonstrates how new ideas lead to significant progress in two main
applications: the solution of invariant ordinary differential
equations and the structure of Euler-Lagrange equations and
conservation laws of variational problems. The expository language
used here is primarily that of undergraduate calculus rather than
differential geometry, making the topic more accessible to a
student audience. More sophisticated ideas from differential
topology and Lie theory are explained from scratch using
illustrative examples and exercises. This book is ideal for
graduate students and researchers working in differential
equations, symbolic computation, applications of Lie groups and, to
a lesser extent, differential geometry.
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