§2 Notations

• Ordinary differential equations: one independent variable
• Partial differential equations: more independent variables
• Partial derivative:

  

  

• Order: order of the highest derivative
• Degree: highest degree of the dependent variable
• Linear: first degree
• Domain : the spatial region, i.e.
  • Plate (rectangle in the x, y-plane
  • Bar (line segment )
  • String (line segment )
• Boundary : the edges of the domain, i.e.
  • Perimeter of the plate
  • Ends of the bar
  • End points of the string