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Maxima/MATLAB/Mathematica
18 November 2020
Here are some works of computer softwares Maxima, MATLAB and Mathematica,
and some notes on elementary topics.

MATLAB
is a commercial numerical analysis software widely used
in the world except for Japan.
This is a very important software for geometric tomography,
and HC is now studying how to use it.
Here are some examples of my outputs related with geometric tomography.

MATLAB
Image Processing Toolbox

MATLAB "Radon Transform",
radon,
iradon,
para2fan

an example of Xray transform and reconstruction 1,
original data 1

an example of Xray transform and reconstruction 2,
original data 2

MATLAB "FanBeam Projection",
fanbeam,
ifanbeam,
fan2para,
phantom

MATLAB "Singular value decomposition"

Low rank approximation of grayscale image based on SVD 1,
original RGB data

Low rank approximation of grayscale image based on SVD 2,
original RGB data

Low rank approximation of grayscale image based on SVD 3,
original RGB data

MATLAB
Wavelet Toolbox

Mathematica
and
Maple
are commercial computer algebra systems widely used
in the world including Japan.

Maxima
is a wellknown free computer algebra system.
Here are some maxima files and outputs used in my courses
on calculus, linear algebra and etc.

prime number theorem:
wxmx,
pdf

RSA algorithm in cryptography:
wxmx,
pdf

approximation of the base of the natural logarithm e:
wxmx,
pdf

approximation of π:
wxmx,
pdf

area of isoperimetric regular polygons:
wxmx,
pdf

system of linear equations, determinant and inverse:
wxmx,
pdf

eigenvalues, eigenvectors and normalization of square matrices:
wxmx,
pdf

matrix exponentials of square matrices:
wxmx,
pdf

LU factorization, QR factorization, singular value decomposition (SVD):
wxmx,
pdf

l^p unit spheres on the plane:
wxmx,
pdf,
mp4,
YouTube

differentiation,
integration,
Taylor's polynomial and quadrature:
wxmx,
pdf

convergence and divergence of the Taylor series:
wxmx,
mp4,
YouTube

the graphs of some functions of two variables:
wxmx,
pdf 1,
pdf 2

successive integrations:
wxmx,
pdf

planar vector fields and integral curves:
wxmx,
pdf

complex numbers and residue:
wxmx,
pdf

Fourier transform and Fourier series:
wxmx,
pdf,
mp4,
YouTube

Gibbs phenomenon of Fourier series:
wxmx,
png 1,
png 2,
mp4,
YouTube

Weyl's equidistribution theorem:
wxmx,
png,
mp4,
YouTube

Here are some notes on elementary topics in mathematics.