The purpose of this book is to provide core material in nonlinear
analysis for mathematicians, physicists, engineers, and mathematical
biologists. The main goal is to provide a working knowledge of
manifolds, dynamical systems, tensors, and differential forms. Some
applications to Hamiltonian mechanics, fluid mechanics,
electromagnetism, plasma dynamics and control theory are given using
both invariant and index notation. The prerequisites required are solid
undergraduate courses in linear algebra and advanced calculus.