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
Book Cover
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


General Information About the Book

Table of Contents

Index

Solutions and a Hint

Typos

Reviews


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

Table 2.1

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

Table 4.1

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

Figure 6.5


Chapter 7: Elastic and Viscoelastic Materials

Figures from chapter

Table 7.1

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