Engineering Differential Equations: Theory and Applications, Springer 2010

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This page contains supplementary material for the book, Engineering Differential Equations: Theory and Applications, by Bill Goodwine. 2010, Springer.


Chapter 11 considers solutions to partial differential equations.

The One-Dimensional Wave Equation

Section 11.1 considers the one-dimensional wave equation.

Some movies:

The One-Dimensional Heat Conduction Equation

Section 11.3 considers the one-dimensional heat conduction equation.

Some movies:

The Two-Dimensional Heat Equation


Vibrating Membranes

Partial differential equations describing vibrating membranes in rectangular and polar coordinates are considered in Section 11.5.

Section 11.5.1 presents the two-dimensional wave equation in rectangular coordinates.

Some movies:

Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.

Some movies:


Chapter 6

  • p. 220, line -9: the superscript for the second term in the equation should be m-3.
  • p. 244, line -11: the first component of the vector on the far right should contain t, not tau.
  • p. 245, line 8: the matrix A7 does not have a set of n linearly-independent eigenvectors.
  • p. 247, line -7: A3 should be A2.

Chapter 8

  • p. 326, line -10:"Figure 8.8" should be "Figure 8.37".
  • p. 327: the pendulum in Figure 8.36 should indicate a length, l, for the pendulum.

Chapter 9

Chapter 11