Introduction to the Foundations of Applied Mathematics
by Mark H. Holmes

 The Chapters Chapter 1 Dimensional Analysis Chapter 2 Perturbation Methods Chapter 3 Kinetics Chapter 4 Diffusion Chapter 5 Traffic Flow Chapter 6 Continuum Mechanics: One Spatial Dimension Chapter 7 Elastic and Viscoelastic Materials Chapter 8 Continuum Mechanics: Three Spatial Dimensions Chapter 9 Fluids Springer web page
 Contact Information Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute, Troy, NY 12180 USA holmes (@rpi.edu)

Page Last Updated: 12/23/2012

Chapter 1: Dimensional Analysis

 Table 1.1 Figures 1.2(b) and 1.3 Figure 1.9(b)

Chapter 2: Perturbation Methods

Figures from chapter

MATLAB Files The following are the MATLAB files used to generate the respective figure (directions). Note that I save the figures in eps format for the book.

 fig23.m Fig. 2.3 fig24.m Fig. 2.4 fig27.m Fig. 2.7 fig29.m Fig. 2.9 fig212.m Fig. 2.12 fig216.m Fig. 2.16 lbvp.m General solver for: y'' + p(x)y' + q(x)y = f(x) nbvp.m General solver for: y'' = f(x, y, y')

Chapter 3: Kinetics

Figures from chapter

MATLAB Files The following are the MATLAB files used to generate the respective figure (directions). Note that I save the figures in eps format for the book.
 fig34.m Fig. 3.4 fig35.m Fig. 3.5 fig36.m Fig. 3.6 fig39.m Fig. 3.9 fig311.m Fig. 3.11 fig316.m Fig. 3.16 fig318.m Fig. 3.18 fig34.m Fig. 3.4 fig3134.m Figs. 3.13 and 3.14 arrowhead.html This is used in one or more of the above programs

Movie Files
 Figure 3.9 The movie version (ep = 1) Figure 3.9 The movie version (ep = 0.1) Figure 3.9 The movie version (ep = 0.01) warning: 28MB file mm_mov.m The matlab file used to produce MM movies Figure 3.13 The movie version (ep = 1) Figure 3.13 The movie version (ep = 0.1) Figure 3.13 The movie version (ep =0.0 1) Figure 3.15 The movie version Figure 3.18 The movie version, version 1 (ep = 0.004) Figure 3.18 The movie version, version 2 (ep = 0.004) Figure 3.20 The movie version, version 1 (ep = 0.004) Figure 3.20 The movie version, version 2 (ep = 0.004) fn_mov.m The matlab file used to produce BZ movies

Extras
 kinetics.v2.mpl This is a Maple program that can be used to analyze reactions. The file should be saved as: kinetics.v2.mpl mm.mw This is an example maple session using kinetics.v2. It should be downloaded and saved as: mm.mw Manual This is a manual for kinetics (note kinetics.v2 is an updated version but works the same way as kinetics).

Chapter 4: Diffusion

Figures from chapter

Figure 4.1 The movie version
Ref: "Measurement of the Translational and Rotational Brownian Motion of Individual Particles in a Rarefied Gas,"
by J. Blum, S. Bruns, D. Rademacher, A. Voss, B. Willenberg, and M. Krause
Physical Review Letters, vol. 97, Issue 23, 230601 (2006)

MATLAB Files The following are the MATLAB files used to generate the respective figure (directions). Note that I save the figures in eps format for the book.
 fig42.m Fig. 4.2 fig42D.txt The html format puts blank lines between rows (these need to be removed) fig46.m Fig. 4.6 fig47.m Fig. 4.7 fig48.m Fig. 4.8 fig410.m Fig. 4.10 fig414.m Fig. 4.14 fig417.m Fig. 4.17 fig418.m Fig. 4.18 fig420.m Fig. 4.20 fig421.m Fig. 4.21 fig422.m Fig. 4.22 fig424.m Fig. 4.24 fig425A.m Fig. 4.25A cmap.mat This file needs to be downloaded and saved as cmap.mat fig425B.m Fig. 4.25B fig427.m Fig. 4.27 fig428.m Fig. 4.28 fig429.m Fig. 4.29 fig431.m Fig. 4.31 The html format does not display part of the file (it's there, use download if necessary)

Movie Files
 Figure 4.5 The movie version Figure 4.14 The movie version Figure 4.24 The movie version (N=40) Figure 4.24 The movie version (N=400) Figure 4.24 The movie version (N=4000)

Chapter 5: Traffic Flow

 Figures from chapter

Chapter 6: Continuum Mechanics: One Spatial Dimension

Chapter 7: Elastic and Viscoelastic Materials

Figures from chapter

MATLAB Files The following are the MATLAB files used to generate the respective figure (directions). Note that I save the figures in eps format for the book.
 fig79.m Fig. 7.9 fig711.m Fig. 7.11 The html format does not display part of the file (it's there, use download if necessary)

Chapter 8: Continuum Mechanics: Three Spatial Dimensions

Chapter 9: Fluids

Figures from chapter

Figure 9.5 The movie version
Ref: "Velocity Field in a Pipe," Experiment of the Month, Physics Department, Millersville University
http://www.millersville.edu/physics/experiments/067/

MATLAB Files The following are the MATLAB files used to generate the respective figure (directions). Note that I save the figures in eps format for the book.
 fig92.m Fig. 9.2 fig93.m Fig. 9.3 fig914.m Fig. 9.14 fig913.m Fig. 9.13 fig916.m Fig. 9.16 arrowhead.html This is used in one or more of the above programs