Engineering Differential Equations: Theory and Applications, Springer 2010
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.
- String of length 3 plucked at L=1 (modeling a guitar):
- String of length 3 that is impacted near L=1 (modeling a piano):
The One-Dimensional Heat Conduction Equation
Section 11.3 considers the one-dimensional heat conduction equation.
- The solution to the heat equation with inhomogeneous boundary conditions
- The solution to the heat equation with an insulated end
The Two-Dimensional Heat Equation
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.
- 1-1 mode for rectangular drum
- 2-1 mode for rectangular drum
- 2-2 mode for rectangular drum
- Rectangular drum impacted near a corner
Sections 11.5.2-11.5.4 presents the wave equation in polar coordinates. The prototypical example would be a vibrating drum head.
- 1-0 mode for a circular drum
- 1-1 mode for a circular drum
- 1-2 mode for a circular drum
- 1-3 mode for a circular drum
- 2-0 mode for a circular drum
- 2-1 mode for a circular drum
- 4-3 mode for a circular drum
- Circular drum that is impacted by a drum stick
- Another drum impact movie
- 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.
- p. 348, line 4: the numerator for both expressions of G1 should be 5.
- p. 348, line 6: the numerator for both expressions of G1 should be 10.
- p. 349, caption to Figure 9.16: the numerator for G1 should be 4 in the numerator for G2 should be 9.
- p. 513, line 2: the coefficient is alpha^2, not alpha.