Asymptotic Wave Theory

The following sections are included:

• Wave Asymptotics and Approximate Symmetry

  • Eikonal Waves

  • The Local Fourier Transform

  • Stationary Phase, Laplace’s Method, and Steepest Descents

  • Eikonal Waves and Lagrangian Submanifolds

• WKB Theory and Asymptotic Equations

  • The Structure of First Order P.D.E.’s

  • Hamilton-Jacobi Theory and Symplectic Manifolds

  • Cotangent Bundles, Contact Spaces, and Jet Spaces

  • The Contact Bundle and the Conormal Bundle

• Limitations of WKB Theory