-
Fourier series using SAGE
Detailed examples (with one exercise) of computing
Fourier series coefficients and plots of piecewise
polynomial functions.
-
discrete Fourier transforms using SAGE.
Detailed examples (with one worked exercise) of computing
discrete Fourier transforms using SAGE.
-
cool function plots.
-
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)
-
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).
-
Granville's (public domain) Calculus text
is being latexed.
- Computational Fourier Transforms class notes
(110 page pdf or html) for a
course taught spring 2007 using James
Walker, Fast Fourier transform, 2nd ed, CRC Press, 1996.
The first of these items uses Maxima extensively.
The last one has examples of DFT routines in SAGE.
All these notes are licensed under the
Attribution-ShareAlike
Creative Commons license. All SAGE code is licensed under the
GPL, version 2 or later.
up
David Joyner
Last updated: 2-5-2008.