Nomenclature in Differential Equations

  1. Integral curve [Arn1, p.17, l.1-l.2]; integral surface [Joh, p.9, l.16].

  2. Variational equation: The key concept is first approximation [Arn1, p.94, l.9 & l.15].

  3. A formal definition may not reveal its real meaning when there is a story behind the nomenclature.
        The term "autonomous" means "time-independent". A nonautonomous system may occur because it is only a part of the whole system [Arn1, p.117, l.4-l.21].

  4. The wave equation: Pictures of waves [Sne, p.216, Fig.34; p.218, Fig.36].

  5. The terms "elliptic, hyperbolic, parabolic" for PDE's are adopted from figures in [Bir, p.125] because the classification of linear systems for PDE's [Pet, p.59, (3)] is similar to that of linear systems for ODE's.

  6. The Riemann P-function
        For the symbolic form given in [Inc1, p.162, l.5], [Inc1, p.162, l.7] calls it the Riemann P-function, while [Wat1, p.206, l.-10; Guo, p.69, l.-5] call it the Riemann P-equation. We should judge for ourselves which terminology is more appropriate rather than blindly follow the authority. Since the symbolic form is used to represent the solution of a differential equation, the former terminology is more appropriate.