# Difference between revisions of "Engineering Differential Equations: Theory and Applications, Springer 2010"

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*[[p. 348, line 6]]: the numerator for both expressions of G1 should be 10. | *[[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. 349, caption to Figure 9.16]]: the numerator for G1 should be 4 in the numerator for G2 should be 9. | ||

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+ | ==Chapter 11== | ||

+ | *[[p. 513, line 2]]: the coefficient is alpha^2, not alpha. |

## Revision as of 15:16, 16 February 2011

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

# Movies

Chapter 11 considers solutions to partial differential equations.

## The One-Dimensional Wave Equation

Section 11.1 considers the one-dimensional wave equation.

Some movies:

- 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.

Some movies:

- 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

Movie:

## 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:

- 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.

Some movies:

- 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

# Errata

## 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 A
_{7}does not have a set of n linearly-independent eigenvectors.

## Chapter 9

- 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.

## Chapter 11

- p. 513, line 2: the coefficient is alpha^2, not alpha.