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Computer Software
31 March 2021
Here are some works of computer software
MATLAB,
Maxima,
Julia,
Mathematica
and
Maple,
and some notes on elementary topics.

Here are some notes on elementary topics in mathematics.

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 mainly related with
signal and image processing including geometric tomography.

Toolboxes

CSV

Xray transform and reconstruction

Radon Transform,
radon,
iradon,
para2fan,
xray.m,
square,
double squares,
half plane
regular triangle,
stomach

FanBeam Projection,
fanbeam,
ifanbeam,
fan2para,
phantom

Wavelet filters

Multiresolution decomposition of audio signals

Discrete Fourier transform and spectrogram of audio signals

Low rank approximation of grayscale images based on SVD

Multiresolution decomposition of grayscale images

Multichannel images

Solving ODEs and systems

Julia
is a wellknown free programing language.
Here are some outputs.

CSV

Low rank approximation of grayscale images based on SVD

LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, PyPlot, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
Marina Bay Area, Singapore,
Eckhart, U of Chicago,
flowers,
shaved ice

Wavelet filters

Fourier analysis and multiresolution analysis of audio signals

Multiresolution decomposition of grayscale images

LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, Plots, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
shaved ice,
flowers.

Multichannel images

LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, Plots, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
flowers,
hokkien mee.

Solving ODEs and systems

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

Newton's method of one variable:
wxmx,
pdf

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

The NyquistShannon sampling theorem and reconstruction formula:
wxmx,
png 1,
png 2,