Differential equations with SAGE
Draft version
The material added in this version is licensed under the
GNU Free Documentation License (please see the
FDL).
The latest version of the Differential equations and Sage book
is written with
Marshall Hampton.
The latest version is available as a
pdf (about 190 pages, 2.8M, 2009-9)
This new version is copyright
David Joyner (wdjoyner@gmail.com) and
Marshall Hampton (mhampton at d.umn.edu), and
is licensed under the GNU Free Documentation License.
The material below is an older version based on lectures by me in
a course taught at the USNA. I hope they are useful as is.
Lecture notes (hypertext pdf and complete latex source in a tarball)
on introductory differential equations using SAGE.
-
desolvers SAGE file which you can "attach" to
run examples code in the following lectures notes.
-
Introduction (complete tarball)
-
existence and uniqueness
-
IVPs (complete tarball)
-
Direction fields and isoclines
(complete tarball)
-
Numerical methods (complete tarball)
-
1st order ODEs, the separable and linear
cases
(complete tarball)
-
Application to falling body problems
(complete tarball)
-
Application to mixing/diffusion problems
(complete tarball)
-
Linear DEs, I (complete tarball)
-
Linear DEs, II (complete tarball)
-
undetermined coefficients
for 2nd order
constant coefficient ODEs latex
source)
-
Variation of parameters for 2nd order
constant coefficient ODEs latex source)
-
Applications to
spring mass systems, part I
(complete tarball)
-
Applications to
spring mass systems, part II
(complete tarball)
-
Applications to
spring mass systems, part III
(complete tarball)
-
Applications to
LRC circuits
(complete tarball)
-
Solving DEs using the
power series method, I
(complete tarball)
-
Solving DEs using the
power series method, II
(complete tarball)
-
Introduction to
Laplace transforms
(complete tarball)
-
Introduction to
Laplace transforms, II
(complete tarball)
-
Lanchester's equations
(complete tarball)
-
Introduction to Gauss
elimination/row reduction
(complete tarball)
-
Introduction to Eigenvalue/eigenvector method
for systems of 1st order DEs (complete
tarball)
-
Solving electrical networks
using Laplace transforms (complete
tarball)
-
Introduction to separation of variables for PDEs using the transport equation (complete
tarball)
-
Introduction to Fourier series, sine series
and cosine series (complete
tarball)
-
Introduction to the heat equation using
Fourier series (complete tarball)
-
Introduction to the wave equation using
Fourier series (complete tarball)
-
All these lecture notes in one 216 page
pdf
(complete tarball).
The existence of this
document owes itself primarily to some great open source projects,
including TeX/LaTeX and Sage.
More information on Sage can
be found at its website (http://www.sagemath.org).
Please email corrections, especially for the latest version, to
wdjoyner@gmail.com.
Created 2008-12-01. Last updated were updated 2009-9-7 by wdj.