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Computer Software
11 January 2021
Here are some works of computer software
MATLAB,
Maxima,
Julia,
Mathematica
and
Maple,
and some notes on elementary topics.
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Here are some notes on elementary topics in mathematics.
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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.
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Toolboxes
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CSV
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X-ray transform and reconstruction
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Radon Transform,
radon,
iradon,
para2fan,
xray.m,
square,
double squares,
half plane
regular triangle,
stomach
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Fan-Beam Projection,
fanbeam,
ifanbeam,
fan2para,
phantom
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Wavelet filters
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Multiresolution decomposition of audio signals
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Discrete Fourier transform and spectrogram of audio signals
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Low rank approximation of grayscale images based on SVD
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Multiresolution decomposition of grayscale images
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Multichannel Images
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Solving ODEs and systems
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Julia
is a well-known free programing language.
Here are some outputs.
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CSV
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Low rank approximation of grayscale images based on SVD
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LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, PyPlot, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
Marina Bay Area, Singapore,
Eckhart, U of Chicago,
flowers,
shaved ice
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Wavelet filters
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Fourier analysis and multiresolution analysis of audio signals
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Multiresolution decomposition of grayscale images
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GR, LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, Plots, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
shaved ice,
flowers.
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Solving ODEs and systems
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Maxima
is a well-known free computer algebra system.
Here are some maxima files and outputs used in my courses
on calculus, linear algebra and etc.
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prime number theorem:
wxmx,
pdf
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RSA algorithm in cryptography:
wxmx,
pdf
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approximation of the base of the natural logarithm e:
wxmx,
pdf
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approximation of π:
wxmx,
pdf
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area of isoperimetric regular polygons:
wxmx,
pdf
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system of linear equations, determinant and inverse:
wxmx,
pdf
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eigenvalues, eigenvectors and normalization of square matrices:
wxmx,
pdf
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matrix exponentials of square matrices:
wxmx,
pdf
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LU factorization, QR factorization, singular value decomposition (SVD):
wxmx,
pdf
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l^p unit spheres on the plane:
wxmx,
pdf,
mp4,
YouTube
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differentiation,
integration,
Taylor's polynomial and quadrature:
wxmx,
pdf
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convergence and divergence of the Taylor series:
wxmx,
mp4,
YouTube
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the graphs of some functions of two variables:
wxmx,
pdf 1,
pdf 2
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successive integrations:
wxmx,
pdf
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planar vector fields and integral curves:
wxmx,
pdf
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complex numbers and residue:
wxmx,
pdf
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Fourier transform and Fourier series:
wxmx,
pdf,
mp4,
YouTube
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Gibbs phenomenon of Fourier series:
wxmx,
png 1,
png 2,
mp4,
YouTube
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Weyl's equidistribution theorem:
wxmx,
png,
mp4,
YouTube
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The Nyquist-Shannon sampling theorem and reconstruction formula:
wxmx,
png 1,
png 2,