Introduction to Perturbation Methods (2nd Ed)
by Mark H. Holmes

The Chapters
Chapter 1 Introduction to Asymptotic Approximations
Chapter 2 Matched Asymptotic Expansions
Chapter 3 Multiple Scales
Chapter 4 The WKB and Related Methods
Chapter 5 The Method of Homogenization
Chapter 6 Introduction to Bifurcation and Stability
Appendices
Answers to selected exercises (note that these are incomplete)
 Contact Information Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute, Troy, NY 12180 USA holmes (@rpi.edu) Author web page Springer web page

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Page Last Updated: 8/19/2017

Chapter 1: Introduction to Asymptotic Approximations
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.

 fig12.m Fig 1.2 fig15.m Fig 1.5 fig19.m Fig 1.9 fig111.m Fig 1.11 fig114.m Fig 1.14

Chapter 2: Matched Asymptotic Expansions
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.

 fig22.m Fig 2.2 fig24.m Fig 2.4 fig27.m Fig 2.7 fig29.m Fig 2.9 fig210.m Fig 2.10 fig214.m Fig 2.14 fig215.m Fig 2.15 fig216.m Fig 2.16 fig219.m Fig 2.19 fig221.m Fig 2.21 fig223.m Fig 2.23 fig224.m Fig 2.24 fig228.m Fig 2.28 fig228d.m generates data for fig228.m fig228dd.m generates data for fig228.m fig229.m Fig 2.29 parseArgs.m needed for fig229.m subaxis.m needed for fig229.m fig232.m Fig 2.32 fig234.m Fig 2.34

Chapter 3: Multiple Scales
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.

 fig31.m Fig 3.1 fig32.m Fig 3.2 fig33.m Fig 3.3 fig312.m Fig 3.12 fig313.m Fig 3.13 fig314.m Fig 3.14 fisher1.txt data for fig314,m fisher2.txt data for fig314,m fig317.m Fig 3.17 parseArgs.m needed for fig317.m subaxis.m needed for fig317.m

Chapter 4: The WKB and Related Methods
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.

 fig41.m Fig 4.1 fig42.m Fig 4.2 fig42data.txt data for fig42.m fig45a.m Fig 4.5a fig45b.m Fig 4.5b fig411.m Fig 4.11 fig415.m Fig 4.15 fig415data.txt data for fig415.m fig417.m Fig 4.17 fig417num,txt data for fig417.m fig417yl,txt data for fig417.m fig417yr,txt data for fig417.m

Chapter 5: The Method of Homogenization
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.

 fig52.m Fig 5.2 fig53.m Fig 5.3 fig54.m Fig 5.4 fig56.m Fig 5.6

Chapter 6: Introduction to Bifurcation and Stability
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.

 fig62.m Fig 6.2 arrowhead.m m file needed for Fig 6.2 fig69.m Fig 6.9 fig610.m Fig 6.10 fig611.m Fig 6.11 fig612.m Fig 6.12 fix_lines.m m file needed for Fig 6.12 fig613.m Fig 6.13 fig615.m Fig 6.15 arrowhead.m m file needed for Fig 6.15 fig616.m Fig 6.16 fig618.m Fig 6.18 fig619.m Fig 6.19 fig621.m Fig 6.21 fig624.m Fig 6.24 data_10000.txt data file needed for Fig 6.24 data_1.txt data file needed for Fig 6.24 burgers.f FORTRAN file used to create data for Fig 6.24 fig625.m Fig 6.25 parseArgs.m needed for fig625.m subaxis.m needed for fig625.m

Appendices
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.

 figb1.m Fig B.1 figb2.m Fig B.2 parseArgs.m needed for figb2.m subaxis.m needed for figb2.m

Extras

The following are MATLAB files I wrote to solve BVPs problems. A short explanation is provided at the end of each file on how to use that particular code. (directions)

 lbvp.m This code solves and then plots the solution of the linear BVP: y'' + p(x)y' + q(x)y = f(x), for x in (xL , xR), where a0*y(xL) + b0*y'(xL) = c0 and a1*y(xR) + b1*y'(xR) = c1 nbvp.m This code solves and then plots the solution of the nonlinear BVP: y'' = f(x, y, y'), for x in (xL , xR), where y(xL) = yL and y(xR) = yR sbvp.m This code solves and then plots the solution of the nonlinear BVP: ep*y'' = f(x, y, y', ep), for x in (xL , xR), where y(xL) = yL and y(xR) = yR