by Maido Rahula (Tartu University, Estonia)

The main theme of this book is the geometrical interpretation of phenomena taking place in Jet spaces in connection with differential equations. This concise volume caters to all mathematicians who wish to deepen their acquaintance with the mathematics of differential geometry.

• Invariant Differentiation:
  • Vector Fields, Trajectories, Invariants
  • Lie Differentiation in a Non-Holonomic Basis
  • Some Applications
• Connection in the Bundle:
  • Translation of Fibres
  • Linear Connection, Morphism of Bundles with Connections
• Ordinary Differential Equations:
  • Operator of Total Differentiation
  • Prolongation of a Differential Equation
  • Shadows on Illuminated Surfaces
• Partial Differential Equations:
  • Multidimensional Time
  • Characteristics Vector Fields
• Higher Order Differential Geometry:
  • Differential Invariants of Mappings
  • Iterations of the Tangent Functor
  • The Highest Connections