# 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.

# 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. - p. 247, line -7: A
_{3}should be A_{2}.

## 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

- 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.