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- A partial differential equation (PDE) extends ODEs by adding
one or more independent variables (usually spatial variables)
- For example, the wave equation for the ideal vibrating string adds one
spatial dimension
(along the axis of the string) and may be
written as
where
denotes the transverse displacement of the
string at position
along the string and time
, and
is the string slope:
(partial derivative of
with respect to
)
- The physical parameters in this case are string tension
and
string mass-density
- As we'll see, this PDE is the starting point for highly practical
digital waveguide models and finite difference schemes
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Download ReviewPM.pdf
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