Maxima/MATLAB/Mathematica

• 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 X-ray transform and reconstruction 1, original data 1
    • an example of X-ray transform and reconstruction 2, original data 2
    • MATLAB "Fan-Beam 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
    • Multiresolution analysis based the Haar (Daubechies 1) wavelet, original RGB data
    • Multiresolution analysis based the Daubechies 2 wavelet, original RGB data
    • Multiresolution analysis based the Coifman 1 wavelet, original RGB data
  
  
• Mathematica and Maple are commercial computer algebra systems widely used in the world including Japan.
  
  
• 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
  
  
• 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