Lectures for Math 537

1. Introduction (4-Panel) - Maple Commands (Maple .mw) - Maple System Plot (sys_plots.mw) - MatLab graphing template (graph_plot.m)
2. Linear Differential Equations and Scaling (4-Panel) - (powerfit.m)
3. Fundamental Solutions (4-Panel) - Maple Examples - eg1.mw (PDF), Maple_JFeg (PDF), jordan (PDF),
4. Power Series (4-Panel) -
5. Method of Frobenius (4-Panel) -
6. Perturbation Methods (4-Panel) - duff_plot.m, duff_tsplot.m, sec_duff_plot.m, duffDE.m,
7. Singular Perturbation (4-Panel) - MMesp_plot.m, MMespS_plot.m, MMspode.m, MMspxoode.m,
8. Method of Averaging (4-Panel) -
   

References

Notes for Math 337 are available on my website. The material for linear systems (2D Linear Systems A (4-panel), 2D Linear Systems B (4-panel), 2D Linear Systems Appl (4-panel)) should be of particular interest.

• V. I. Arnold, Ordinary Differential Equations, 1973, MIT Press
• William Boyce and Richard Diprima, Elementary Differential Equations, 2012, Wiley (early editions more on power series)
• Fred Brauer and John A. Nohel, Qualitative Theory of Ordinary Differential Equations, 1969, Benjamin
• Erwin Kreyzig, Advanced Engineering Mathematics, 2011, Wiley
• J. David Logan, Applied Mathematics, Fourth Edition, 2013, Wiley
• Lawrence Perko, Differential Equations and Dynamical Systems, 1991, Springer-Verlag
• Paul Waltman, A Second Course in Elementary Differential Equations, 1986, Academic Press

Fundamental Solutions

• Jordan Canonical Form - General Solutions
• Complex Jordan Canonical Form - Mark Schumaker (WSU)

Additional Resources

There is a Lab Manual (MATLAB and Maple) version, which will continue to be updated over the semester with detailed information for using MatLab and Maple on your written assignments.

Matlab:

• A practical introduction to Matlab (HTML, PDF)
• MathWorks - Getting Started and Overview links
• Other Overviews - University of Dundee,
• Matlab Help
• Matlab GUI for differential equations: dfield8 and pplane8. (Pplane may require a license file or should be downloaded directly from MatLab.)
• MatLab from Math 337 Lectures
  
• Basic MatLab (murder.m, murder_plot.m) - Introduction to MatLab
• MatLab Programming (lake2.m, lake_level.m, lake2_plot.m, fishdat.mat, sumsq_vonBert.m, vonBert_plot.m, powerfit.m, allo_plot.m, Hg_plot.m, sumsq_allom.m, sumsq_cubic.m, sumsq_Hg.m, sumsq_wtfish.m, wtfish.m)
• ODE Solvers (euler.m, im_euler.m, numeg.m, numeg_plot.m, numeg2.m, numeg2_plot.m, pop.m, pop_plot.m)

Maple:

• Maple Workshop notes
• Maple from Lectures
• Maple Commands - Introduction (Maple .mw)
• Maple Phase Plots (Maple .mw) and Maple Phase Portraits (Maple .mw)