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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.
• Julia is a well-known free programing language. Here are some outputs.
• CSV
• Low rank approximation of grayscale images based on SVD
• 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 well-known 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 Nyquist-Shannon sampling theorem and reconstruction formula: wxmx, png 1, png 2,