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Computer Software
8 January 2023
Here are some works of computer software
MATLAB
,
Julia Programming Language
,
Maxima
and
Mathematica
,
and some notes on elementary topics.
Some elementary topics in mathematics
Lecture notes created by
MATLAB Live Script (*.mlx)
Lecture notes created by
Julia Programming Language
with
Pluto.jl
Numerical Solutions to ODEs (including the SIR model)
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https://rencho.me/julia/pluto/pluto_numerical_ode.jl
Convergence and Divergence of Fourier Series
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https://rencho.me/julia/pluto/pluto_fourier.jl
The Nyquist-Shannon Sampling Theorem and Aliasing
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https://rencho.me/julia/pluto/pluto_aliasing.jl
X-ray transform on \(\mathbb{R}^2\)
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https://rencho.me/julia/pluto/pluto_ct.jl
package: xray.jl
material grayscale image
Differentiability
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https://rencho.me/julia/pluto/pluto_differentiability.jl
Riemann integrability
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https://rencho.me/julia/pluto/pluto_riemann.jl
The Haar wavelet and multiresolution decomposition
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https://rencho.me/julia/pluto/pluto_wavelet.jl
material RGB image
Low rank approximation of an RGB image
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https://rencho.me/julia/pluto/pluto_svd.jl
material RGB image
Taylor series
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https://rencho.me/julia/pluto/pluto_taylor.jl
Lecture notes created by
Julia Programming Language
with
IJulia.jl
and
Jupyter Notebook
(*.ipynb)
Lecture notes created by LaTeX (*.pdf)
MATLAB
is a commercial numerical analysis software widely used
in the world except for Japan.
YouTube Playlist
Number Theory
Calculus
CSV
X-ray transform and reconstruction
2D wave front set (in progress)
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
Solving PDEs with FFT
Julia Programming Language
is a well-known free programing language.
Here are some outputs.
YouTube Playlist
Number Theory
CSV
X-ray transform and reconstruction
Low rank approximation of grayscale images based on SVD
Wavelet filters
Fourier analysis and multiresolution analysis of audio signals
Multiresolution decomposition of grayscale images
Multichannel images
Solving ODEs and systems
Solving PDEs with FFT
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.
YouTube Playlist
Number Theory
Green-Tao Theorem:
wxmx ,
pdf
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
Linear Algebra
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
Calculus
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 Analysis
Fourier transform and Fourier series:
wxmx ,
pdf ,
mp4 ,
YouTube
Gibbs phenomenon of Fourier series:
wxmx ,
png 1 ,
png 2 ,
mp4 ,
YouTube
A continuous but nowhere differentiable function:
wxmx ,
png ,
mp4 ,
YouTube
Weyl's equidistribution theorem:
wxmx ,
png ,
mp4 ,
YouTube
The Nyquist-Shannon sampling theorem and reconstruction formula:
wxmx ,
png 1 ,
png 2 ,
Mathematica
is a well-known commercial computer algebra system.
Here are some mathematica files and outputs used in my courses
on calculus, linear algebra and etc.
YouTube Playlist
Number Theory
Linear Algebra
Calculus
one-dimensional Fourier series:
equidustribuion of sequences on unit circle:
nb