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The Single First Order Equation

Part of the Applied Mathematical Sciences book series (AMS, volume 1)

Abstract

The first order equations, in general, present interesting geometric interpretations. It will be convenient then to restrict the discussion to the case of two independent variables, but it will be made clear that the theory can be extended immediately to any number of variables. We consider then equations of the form
$$ F(x,y,u,{u_x},{u_y}) = F(x,y,u,p,q) = 0 $$
(1)
where we have used the notation ux = p, uy = q. A solution z = u(x, y), when interpreted as a surface in three dimensional space, will be called an integral surface of the differential equation.

Keywords

Characteristic Equation Characteristic Curve Order Equation Parameter Family Tangent Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

  • F. John
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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