Computer Software

• Here are some notes on elementary topics in mathematics.
  • One-variable complex analysis and two-dimensional incompressible irrotational steady flow
  • X-ray transform on the plane and reconstruction formula: The principles of computed tomography
  • d'Alembert's formula for the one-dimensional wave equation
  • A first order system including the one-dimensional wave equation
  • The Euler kernels and one-dimensional Riesz potentials
  • A note on the Hermite functions (Japanese)
  • Fredholm integral equation (Japanese)
  • X-ray transform on the plane and reconstruction formula: The principles of computed tomography (Japanese)
  
  
• 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
    • Image Processing, Wavelet, Signal Processing, Deep Learning
  • CSV
    • websave, importdata, datetime, days, days, days
      COVID-19 in Japan
  • X-ray transform and reconstruction
    • Radon Transform, radon, iradon, para2fan, xray.m,
      square, double squares, half plane regular triangle, stomach
    • Fan-Beam Projection, fanbeam, ifanbeam, fan2para, phantom
  • Wavelet filters
    • Wavelet filters and their Fourier transforms
  • Multiresolution decomposition of audio signals
    • wavedec
      the Haar wavelet, the Daubechies 2 wavelet
  • Discrete Fourier transform and spectrogram of audio signals
    • Read and Write Audio Files, Fourier Transforms, spectrogram
      human voice, computer sound
  • Low rank approximation of grayscale images based on SVD
    • Singular value decomposition
      Marina Bay Area, Singapore, Eckhart, U of Chicago, flowers, shaved ice
  • Multiresolution decomposition of grayscale images
    • Continuous and Discrete Wavelet Transforms
      the Haar wavelet, the Daubechies 2 wavelet, the Coifman 1 wavelet
  • Multichannel Images
    imsplit, Display Separated Color Channels of RGB Image
    shaved ice, cactuses, fried hokkien mee
  • Solving ODEs and systems
    • ode45
      fluid flow, SIR model, SIR model for COVID-19.
  
  
• Julia is a well-known free programing language. Here are some outputs.
  • CSV
    • Plots, CSV, Dates, HTTP, DataFrames
      COVID-19 in Japan
  • 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
    • LinearAlgebra, Plots
      Wavelet filters and their Fourier transforms
  • Fourier analysis and multiresolution analysis of audio signals
    • DSP, Formatting, PyPlot, FFTW, WAV, Wavelets, FileIO, LibSndFile
      human voice, computer sound
  • Multiresolution decomposition of grayscale images
    • GR, LinearAlgebra, LowRankApprox, Formatting, ImageFiltering, Images, Plots, ImageMagick, Colors, TestImages, ImageView, ImageTransformations
      shaved ice, flowers.
  • Solving ODEs and systems
    • DifferentialEquations, Plots, Dates
      SIR model for COVID-19.
  
  
• 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
  • 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,