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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<meta name="description" content="Physics Matlab, doing Physics with PYTHON / Matlab">
<meta name="keywords" content="python, Python, Physics, Matlab, Doing Physics with Matlab, Quantum Physics">
<meta name="keywords" content="Computational Physics, Matlab Physics, Physics Matlab, Quantum Mechanics">
<meta name="keywords" content="Hydrogen atom, Schrodinger Equation, Selection Rules, Hodgkin-Huxley">
<meta name="author" content="Ian Cooper">
<style> .s1
{
font-family:Calibri;
font-size:20px;
font-weight:10;
width: 960px;
color: black;
background-color: white;
align: left;}
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font-size:30px;
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color: blue;
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<style> .s3
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font-size:20px;
font-weight:600;
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</style>
</head>
<body>
<div class = "s2">
<img src = "Image1.gif" align = "left" />
<p> DOING PHYSICS WITH PYTHON / MATLAB </p>
</div>
<br>
<p style="font-size:24px">    <b>IAN COOPER</b></p>
<p style="font-size:24px">    Please email me any comments, corrections or suggestions</p>
<p style="font-size:24px">    email: matlabvisualphysics</p>
<p style="font-size:24px">    Many thanks to <b>Arora Dharam</b> for transferring files from physics.usyd.edu.au/teach_res/... to GitHub</p>
<p style="font-size:24px">    My Matlab licence expired and MathWorks would NOT renew it.</p>
<p style="font-size:24px">    So, I will use Python (it is free) for all future developments.</p>
<p style="font-size:24px">    Not that familiar with Python but not that different from Matlab.</p>
<br><br><br>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="https://github.com/barionleg/Doing-Physics-With-Matlab/tree/master/python" target = "blank" > <b>DOWNLOAD SCRIPTS PYTHON: GITHUB</b></a>
</li><br>
<li>
<a class = "s4" href="https://github.com/barionleg/Doing-Physics-With-Matlab/tree/master/mpScripts" target = "blank" > <b>DOWNLOAD SCRIPTS MATLAB: GITHUB</b></a>
</li><br>
<li>
<a class = "s4" href="https://drive.google.com/drive/folders/1j09aAhfrVYpiMavajrgSvUMc89ksF9Jb" target = "blank" > <b>DOWNLOAD SCRIPTS: GOOGLE DRIVE </b></a>
</li><br>
<br>
<br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s1">
<ul>
<li>
<a class = "s4" href="https://composarc.github.io/advschoolmaths/aboutT.pdf" target = "blank" > ABOUT</a>
</li><br>
<li>
<a class = "s4" href="https://aibolem.github.io/VisualPhysics/" target = "blank" > VISUAL PHYSICS ONLINE</a>
</li><br>
<li>
<a class = "s4" href="https://composarc.github.io/advschoolmaths/" target = "blank" > ADVANCED SCHOOL MATHEMATICS</a>
</li><br>
<br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>PYTHON</p>
</div>
<div class = "s3">
<p>COMPUTATIONAL OPTICS</p>
</div>
<div class = "s1">
<li>
<a class = "s4" href="pyDocs/op100.pdf" target = "blank"> Python: arrays, vectors, matrices</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/op001.htm" target = "blank"> Monochromatic plane wave animation</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/op002.htm" target = "blank"> Superposition principle </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/op003.pdf" target = "blank"> Interference: two coherent point sources </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/op010.pdf" target = "blank"> Numerical integration of [1D] and [2D] integrals</a>
</li><br><br>
<li>
<a class = "s4" href="pyDocs/op005.pdf" target = "blank"> Rayleigh-Sommerfeld diffraction: Rectangular aperture</a>
</li><br><br><br>
<br><br>
</ul>
</div><div>
<div class = "s3">
<p>QUANTUM MECHANICS</p>
</div>
<div class = "s1">
<li>
<a class = "s4" href="pyDocs/qm006.pdf" target = "blank"> Visible spectrum: create your own display, Balmer series spectrum </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm022.pdf" target = "blank"> Wave partilce duality: wave-like properties of particles </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmSun.pdf" target = "blank"> Blackbody Radiation: Sun, blue star, red star </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm001.pdf" target = "blank"> First and second derivatives as operartors </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm002.pdf" target = "blank"> Operators: expectation values and the Heisenberg Uncertainty Principle </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm004.pdf" target = "blank"> Schrodinger equation: Finite difference time development method </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm003.htm" target = "blank"> Free particle: Gaussian wavepacket spreading animation </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm005.htm" target = "blank"> Free particle: Gaussian wavepacket propagation animation </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm007.htm" target = "blank"> Free particle: Gaussian wavepacket confined within a parabolic potential well animation </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm020.htm" target = "blank"> Free particle: Gaussian wavepacket - scattering and tunnelling animations </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm030.pdf" target = "blank"> Free particle: Electron beam scattering from a step potential </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm033.pdf" target = "blank"> Free particle: Electron beam scattering from a square potential barrier </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmDS01.pdf" target = "blank"> FDTD: Conduction band of a semiconductor </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmDS02.pdf" target = "blank"> FDTD: Motion of an electron in an electric field </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm042.pdf" target = "blank"> Transverse normal modes of vibration for standing waves on a rod </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm042an.htm" target = "blank">       ANIMATIONS: Standing waves on a rod </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm040.pdf" target = "blank"> Bound particle: Eigenstates of a particle confined by a potential well (eigenvalues and eigenvectors) </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm043.pdf" target = "blank"> Bound particle: Finite and infinite square potential wells </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm040S.pdf" target = "blank"> Bound particle: Finite square potential well with a step </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm044.pdf" target = "blank"> Bound particle: Finite square potential well with a sloping floor (ramp potential) </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm045.pdf" target = "blank"> Vibrations and the harmonic oscillator: Truncated parabolic potential well </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm049.pdf" target = "blank"> Transitions between stationary states:Compound states, selection rules, lifetimes, EMR absorption and emisssion </a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm049an.htm" target = "blank">       ANIMATIONS: Compound states in a finite square potential well</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm050.pdf" target = "blank"> Vibrations of diatomic molecules HCl: Harmonic oscillator and anharmonic oscillator (Morse potential)</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm060.pdf" target = "blank"> Molecular spectra: Vibration-rotation states for the HCl molecule</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm061.pdf" target = "blank"> Central forces: Angular momentum and spherical harmonics</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmHydrogen.pdf" target = "blank"> Hydrogen atom: Solutions of the [3D] Schrodinger equation, a visual approach</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmHydrogenA.pdf" target = "blank"> Hydrogen like species: H+. Li++, Li</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmHydrogenB.pdf" target = "blank"> Hydrogen: selection rules, transition rates and lifetimes</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmCB.pdf" target = "blank"> Double well potentials: Covalent bonding</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm2Dfdtd.pdf" target = "blank"> Solving the [2D] Schrodinger equation with the FDTD method</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qm2DfdtdSC.pdf" target = "blank"> Time-dependent quantum-mechanical scattering in [2D]</a>
</li><br>
<br><br>
<li>
<a class = "s4" href="pyDocs/qmSM03.pdf" target = "blank"> QS: Probability distributions MB BE FD</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmSMS02A.htm" target = "blank"> QS: Molecular dynamics Maxwell-Boltzmann distribution</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmSM01.pdf" target = "blank"> QS: Probability distribtions, Maxwell-Boltzmann distribution</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmSM02.pdf" target = "blank"> QS: Maxwell-Boltzmann distributions</a>
</li><br>
<li>
<a class = "s4" href="pyDocs/qmSM08.pdf" target = "blank"> QS: Specific heat of crystalline solids</a>
</li><br>
<br><br>
</ul>
</div>
<div class = "s3">
<p>MISCELLANEOUS</p>
</div>
<div class = "s1">
<li>
<a class = "s4" href="mpDocs/cs_001.pdf" target = "blank"> Discrete dynamical systems with 1 degree of freedom</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cs_002.pdf" target = "blank"> CSI: MURDER - time of death</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pyChaos001.htm" target = "blank"> Logistic Difference Equation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cs_003.pdf" target = "blank"> Dynamical systems with 2 degrees of freedom: Pedator-Prey systems (Lotka-Volterra equations)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cs_006A.htm" target = "blank"> A chaotic dynamical system: driven damped pendulum (a comprehensive analysis)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cs_101.pdf" target = "blank"> Nonlinear [1D] dynamical system: fixed points, stability, bifurcations</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cs120.pdf" target = "blank"> Nonlinear [2D] dynamical system: fixed points, stability, bifurcations</a>
</li><br>
<br>
<br>
<li>
<a class = "s4" href="mpDocs/BIG_A.pdf" target = "blank"> The best mathematical model of the glucose-insulin regulatory system</a>
</li><br>
<br>
<li>
<a class = "s4" href="mpDocs/cs_008.htm" target = "blank"> Python tutorial X-Y plots: Projectile motion with animation</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>BIOPHYSICS         NEUROSCIENCE</p>
</div>
<div class = "s1">
<ul>
<H3 style = "color:#711C09">             Physics of neurons </H3>
<li>
<a class = "s4" href="mpDocs/pbs_001.htm" target = "blank"> A brief introduction to neural systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs_002.htm" target = "blank"> Neuron membrane as a capacitor</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs003.htm" target = "blank"> Neuron membrane: ion channels and gate variables</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs004.htm" target = "blank"> Neuron membrane currents and reversal potentials (Nernst Equation) </a>
</li><br>
<H3 style = "color:#711C09">             Single neuron models </H3>
<li>
<a class = "s4" href="mpDocs/pbs005.htm" target = "blank"> Geometrical methods of analysis of [1D] dynamical systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs006.htm" target = "blank"> The Fitzhugh-Nagumo Model for Spiking Neurons: Phase Plane Analysis </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/npHHA.htm" target = "blank"> Hodgkin-Huxley model for membrane currents and action potentials </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs007.htm" target = "blank"> Leaky integrate and fire model </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/ns801.htm" target = "blank"> Izhikevich model for action potentials and spike trains </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/ns802.htm" target = "blank"> Izhikevich quadratic model for spiking neurons </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cnsHindmarshA.pdf" target = "blank"> Bursting Neuron model using three coupled first order ODEs </a>
</li><br>
<H3 style = "color:#711C09">             Neural network models </H3>
<li>
<a class = "s4" href="mpDocs/ns803.htm" target = "blank"> Izhikevich models for networks of spiking neurons </a>
</li><br>
</ul>
</div>
<br>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>GETTING STARTED WITH MATLAB</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/matlabA.pdf">Matlab Basics</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/matlabB.pdf">XY Plots</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/matlabC.pdf">Advanced XY plotting techniques</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wav_shm_sine.pdf">Creating a simple GUI with input boxes: SHM and the Sine Function</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_beats.pdf">Creating and Saving Sounds: BEATS</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>APP DESIGNER: GUI SIMULATIONS</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/ad_001.pdf">OSCILLATIONS: Mass Spring System (free, damped, forced motion and resonance)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/ad_002S.pdf">OSCILLATIONS: Sinusoidal functions</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/ad_002.pdf">QUANTUM MECHANICS: Square / Sloping Potential Well (eigenvalues, eigenfunctions, expectation values)</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>DATA ANALYSIS and MATHEMATICAL ROUTINES</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/da_linear_fit.pdf target = "blank"">Curve Fitting: Least squares fit to a straight line for linear, power and exponential relationships </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/da_weighted_fit.pdf" target = "blank">Curve Fitting: Weighted least squares fit for uncertainties in the y-data</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_qe.pdf" target = "blank">Solving Quadratic Equations: GUI and Function call</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_turning_points.pdf" target = "blank">Stationary Points of a function: Function to find the points of maximima and minima of a curve </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVectors.pdf" target = "blank">VECTOR ANALYSIS: coordinates, vector algebra, dot product, cross product, [3D] rotation of axes </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemDifferentialCalculus.pdf" target = "blank">DIFFERENTIAL CALCULUS: 1st and 2nd derivatives; gradient; divergence; curl; Laplacian </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_integration_1D.pdf" target = "blank">INTEGRATION: Numerical computation of one-dimensional integrals </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_simpson_1D.pdf" target = "blank">INTEGRATION: Estimate the value of the integral of the function y = f(x) between x = a and y = b </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_integration_2D.pdf" target = "blank">INTEGRATION: Numerical computation of two-dimensional integrals - double or surface integrals </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/da_RK01.htm" target = "blank" >Fourth-order Runge-Kutta Method: Initial value problems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mec_chaosA.pdf" target = "blank">Runge-Kutta Method for solutions to the differential equations governing oscillating and chaotic systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_ODE_A.htm" target = "blank">ODE: Solving second order differential equations with the <b>ode45</b> solver (mass/spring system and van der Pol oscillator)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_sinc_function.pdf" target = "blank">SINC FUNCTION: Characteristics of the unnormalized sinc function</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/op_bessel1.pdf" target = "blank">BESSEL FUNCTION OF THE FIRST KIND: Fraunhofer Diffraction from a circular aperture</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_volume.pdf" target = "blank">SOLIDS OF REVOLUTION: [2D] and [3D] plots and an animation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/em_swe.pdf" target = "blank">Finite Difference Time Development Method: [1D] Scalar Wave Equation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/percolation.htm" target = "blank">PERCOLATION THEORY: A Matlab simulation of site percolation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_complex01.htm" target = "blank">Visualization of the phase of complex functions using COLOR</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mathComplex1.pdf" target = "blank">A Visual Approach to Understanding Complex Functions</a>
<p>John Sims Biomedical Engineering Department, Federal University of ABC, Sao Bernardo Campus Brasil</p>
</li><br>
<li>
<a class = "s4" href="mpDocs/maths_ft01.pdf" target = "blank"> FOURIER TRANSFORMS made easy (calculating a Fourier Transform has never been so easy)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mathComplex4.htm" target = "blank"> A VISUAL APPROACH: complex numbers and the Fourier Transform></a>
<p>John Sims Biomedical Engineering Department, Federal University of ABC, Sao Bernardo Campus Brasil</p>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscAliasing.htm" target = "blank" >Signal Analysis: ALIASING (Sergio Furuie, School of Engineering, University of Sao Paulo, Brazil)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/Laplace01.pdf" target = "blank">Solving ODEs with the Laplace Transform made simple</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/ODE_004.pdf" target = "blank">1st order nonlinear ODEs: slope (direction) field, nullcline, isocline, solution (integral) curve </a>
</li><br>
<br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>MECHANICS / MECHANICAL SYSTEMS</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/mec_friction_1.pdf">Horizontal Motion with Resistance: drag and viscous drag force</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mec_friction_2.pdf">Analytical and Numerical Analysis of Vertical Motion with Resistance: drag and viscous drag force, falling, drag coefficient</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mec_spring_energy.htm">Animation of a vibrating spring: time variation of KE and PE</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mec_slingshot.htm">Animation of the Slingshot Effect</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/osc_bungee.pdf">Physics of bungee jumps and bridge swings</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/m1FreeFall.htm">Animation of the free fall vertical motion of an object: trajectory, displacement, velocity and acceleration time graphs</a>
</li><br><br>
<li>
<a class = "s4" href="mpDocs/mec_satellite.pdf">Satellite Motion GUI used for inputs. Finite difference method used to calculate a detailed description of the satellite motion</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mecSatelliteA.htm"target = "blank">Satellites Orbits: Solving the equation of motion using ode45</a>
</li><br><br>
<li>
<a class = "s4" href="https://aibolem.github.io/VisualPhysics/mod5new/cg001.htm">Secrets of Computer Graphics and Animations</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>THERMAL PHYSICS</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/tp_conduction.pdf" target = "blank">Thermal Conduction: Temperature gradient and energy flux calculations through a composite rod</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/tpBlackbody.htm" target = "blank" >Blackbody Radiation: Sun and Earth, Hot Objects, Efficiency Incandescent Globe, Star Temperatures</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/tp_equilibrium.htm" target = "blank">Second Law of Thermodynamics - arrow of time: animation for the motion of gas molecules released from a corner of a room</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/tp_Newton.htm" target = "blank">Newton's Law of Cooling: CSI Murder - time of death / Coffee cooling problem / First Order Differential Equations</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/tp_LE_Maxwell.html" target = "blank">Live Editor:   Maxwell Distributuion of Speeds</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>A NUMERICAL APPROACH TO THE PHYSICS OF THE ENVIRONMENT AND CLIMATE</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/climateG.htm" target = "blank">The vertical profile of the atmosphere</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/atmDDP.htm" target = "blank"> Chaos in the atmosphere: Damped Drived Pendulum</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/solar01.htm" target = "blank"> Solar radiation modelling: Blackbody radiation</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>A COMPUTATIONAL APPROACH TO ELECTROMAGNETIC THEORY</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/cem001.pdf" target = "blank" > 1. VECTOR ANALYSIS: Coordinate Systems, Vector Algebra</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemDifferentialCalculus.pdf" target = "blank" > 2. VECTOR DIFFERENTIAL CALCULUS: derivatives, div, curl, Laplacian</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemCh3.pdf" target = "blank" > 3. VECTOR INTEGRAL CALCULUS: Integration: line, surface, volume; Green's & Stokes' Theorems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemCh4.pdf" target = "blank" > 4. VECTOR ANALYSIS: Problems with Matlab solutions</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemCh5.pdf" target = "blank" > 5. EM FIELDS: Visualisation of electric fields and potentials due to different charge distributions</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemB001.pdf" target = "blank" > 6. [2D] Surface Integration: Electrostatic potential along symmetry axis of a uniformly charged square plate</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemEDR.htm" target = "blank" > 7. GENERATING EM WAVES BY AN ELECTRIC DIPOLE: Graphical and animated analysis</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVEA.pdf">Electric Field and Electric Potential due to various charge distributions</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVEB.pdf">Electric Field and Electric Potential:     Line Integral of the electric field</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVEC.pdf">Electric Field and Electric Potential:     Method of Images</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVED.pdf">Electric Field and Electric Potential:     Gauss's Law and Electric Flux</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemVEF.pdf">Electrostatics:    Diververgence     /     Curl     /     Radial electric Fields</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemLaplaceA.pdf">Numerical solution of [2D] Poisson's and Laplace's equations: introduction and examples</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemLaplaceB.pdf">Numerical solution of [2D] Laplace's equation: Two concentric conductive squares</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemLaplaceC.pdf">Numerical solution of [2D] Poisson's and Laplace's equations: Examples using Dirchlet and Neumann boundary conditions</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/emCathodeSpot.htm" target = "blank" >Molecular Simulations of Cathodic Arc Plasmas (Cathode Spots)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/em_emf.htm">Animation: Electromagnetic Induction - induced current as magnet moves through a coil</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/em_motor.htm">Animation: DC Motor - Armature current, torque and rotation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/em_motorsSim.htm">Physics of DC motors - How a motor works in lifting a load</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/em_vBE.pdf">Motion of charged particles through magnetic and electric fields: Numerical and graphical analysis</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemB01.pdf">Electromagnetic Induction:    Faraday's Law     /     Mutual Inductance     /     Self Inductance</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/cemB03.pdf">Static Magnetic Fields:    Divergence     /     Curl     /     Biot-Savart Law </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/op1002.htm">ANIMATIONS: GIF and AVI FILES: POLARIZED LIGHT: Linear, Circular, Elliptical</a>
<p><b>John Sims</b>     Biomedical Engineering Department, Universidade Federal do ABC, Brazil</p>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_spectrum.pdf">Color plot of the visible spectrum for the wavelength range 380 nm to 780 nm</a>
</li><br>
<li>
<a class = "s4" href="https://emfieldbook.com/" target = "blank"> Engineering Electrodynamics: House of Maxwell's Electrodynamics (Vladimir Volman): link to an online textbook </a>
</li><br>
<li>
<a class = "s4" href="https://emfieldbook.com/blogposts/" target = "blank"> Advanced electromagnetism problem sets using Matlab (Vladimir Volman) </a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>DYNAMICS OF OSCILLATING AND CHAOTIC SYSTEMS / SIGNAL ANALYSIS</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/chaos23.htm "target = "blank"> Lorenz Attractor: chaos dynamics</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaosLogisticEq.htm "target = "blank"> Logistic Difference Equation</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wav_shm_sine.pdf">Creating a simple GUI with input boxes: SHM and the Sine Function</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/osc_bungee.pdf">Physics of bungee jumps and bridge swings</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/osc_string_driven.htm">Forced vibration of a string: RESONANCE - animations of a vibrating string due a vibrator</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscC001A.htm "target = "blank">COUPLED OSCILLATORS:> Part 1   Single Oscillator (Fourier Transform of Motion)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscC002.htm" target = "blank">COUPLED OSCILLATORS: Part 2   Motion of Two Coupled Oscillators (Fourier Transform of Motion)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscC00NA.htm" target = "blank">COUPLED OSCILLATORS: Part 3   N oscillators - [1D] monatomic lattice</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscC00NDE.htm" target = "blank">COUPLED OSCILLATORS: Part 4   N oscillators - [1D] diatomic lattice </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/osc_harmonic01.pdf">Modelling a Mass / Spring System: free oscillations, damping, force oscillations (impulsive and sinusoidal)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/atmDDP.htm" target = "blank"> Chaos in the atmosphere: Damped Drived Pendulum</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/mec_chaosA.pdf">Runge-Kutta Method for solutions to the differential equations governing oscillating and chaotic systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos07A.htm">    RIGID PENDULUM:   Free damped and forced motions, resonance, chaotic motion </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos01.htm">    DUFFING TWO-WELL OSCILLATOR:   damped and forced motions, resonance, chaotic motion </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos02.htm">    POINCARE SECTIONS   Duffing two-well oscillator</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos10.pdf">    PHASE PLANE ANALYSIS:   Linear Systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos10eye.pdf">    PHASE PLANE ANALYSIS:   Model of the retina: C-cell/H-cell negative feedback interaction</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/chaos11.pdf">    PHASE PLANE ANALYSIS:   Nonlinear Systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/pbs006.htm">    The Fitzhugh-Nagumo Model for Spiking Neurons: Phase Plane Analysis </a>
</li><br>
<li>
<a class = "s4" href="mpDocs/math_ODE_A.htm" target = "blank">ODE: Solving second order differential equations with the <b>ode45</b> solver (mass/spring system and van der Pol oscillator)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/oscAliasing.htm">Signal Analysis: ALIASING (Sergio Furuie, School of Engineering, University of Sao Paulo, Brazil)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/np001.htm" target = "blank"> Physics of Neurones: [1D] Nonlinear Dynamical Systems</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/Laplace01.pdf" target = "blank">Solving ODEs with the Laplace Transform made simple</a>
</li><br>
</ul>
</div>
<HR SIZE="3" COLOR="purple" WIDTH="96%">
<div class = "s3">
<p>WAVE MOTION</p>
</div>
<div class = "s1">
<ul>
<li>
<a class = "s4" href="mpDocs/wm_ttw.htm">ANIMATIONS: GIF and AVI FILES: [1D] Travelling Harmonic Transverse Wave</a>
<p><b>John Sims</b>     Biomedical Engineering Department, Universidade Federal do ABC, Brazil</p>
</li><br>
<li>
<a class = "s4" href="https://barionleg/Doing-Physics-With-Matlab/mpDocs/m31_wavesB.htm" target = "blank">WAVE MOTION ANIMATED GIFS: Travelling, Transverse, Longitudinal Waves</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_beats.pdf" target = "blank">BEATS: Superposition of two sinusoidal waves of slightly different frequencies: Creating and saving sounds</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_doppler.pdf" target = "blank">DOPPLER EFFECT: [2D] simulation for a moving source with sound effects and creation of animated gifs</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/p001.htm" target = "blank" >Travelling Wave Animations: Phase and Group Velocities</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_string_1.htm" target = "blank">Travelling waves along a string: Solving the wave equation for the transmission of energy along a string</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wmString.htm" target = "blank">Frequency spectrum of an excited string (wave equation & Fourier Tranform)</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/p002.htm" target = "blank" >Refraction: Animations of a plane wave incident upon an interface separating two different medium</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wm_Helmholtz.htm" target = "blank"> HELMHOLTZ EQUATION: Eigenvalue Problem: animation of standing waves on a rod</a>
</li><br>
<li>
<a class = "s4" href="mpDocs/wmRod.htm" target = "blank" >Transverse Normal Modes of Vibration of a Rod: Eigenvalues and Eigenfunctions</a>
</li><br>