Here is a listing of my mathematica notebooks. The most recent of any of these notebooks can all be obtained from my github Mathematica repository.
The Wolfram CDF player can also be used to view a number of these notebooks after download.
Figure illustrating projection and rejection.
One parameter differential figure.
Two parameter differential figure.
Oriented areas of different shapes representing bivectors.
Overlapping parallelograms with fixed areas. Figure: parrallelogramsFig1.eps.
This is the notebook for two rotation figures. One is for a rotation of a vector lying in a plane (but that plane is viewed from a 3D vantage point), and the other is for a rotation with respect to a plane through an angle, and applied to a vector out of the plane.
Some messy evaluation of integrals that end up expressed in terms of elliptic E() and F() functions. Was associated with the evaluation of the charge of a circular segment of line charge.
Integrals for Line charge problem, including some of the special angle cases that seem to require separate evaluation. Also has a plot linechargeFig1.eps, and some plots (not in the book) of the integrands.
Figure for circular arc of line charge. One arc of charge on the x-y plane at a fixed radius. Field point, azimuthal angles for the range of the line charge.
Figure for (magnetic) vector potential: vectorPotentialFig1.eps.
Cool toroidal segment figure for the book. toroidFig1.eps
This is the figure for pillbox integration volume that was used in the boundary value analysis of Maxwell's equations.
Verify hand calculation from polarization.tex (also set as a problem). Got my hand calculation wrong. Try this with Mathematica instead. Has some additional checking of the solution.
A plot of a rotated ellipse showing the major and minor axes, and the angle of rotation. This was related to an elliptically polarized plane wave.
Figure (linearPolarizationFig1.eps) showing the electric and magnetic field directions for a linearly polarized field propagating at a fixed angle to the horizontal in the transverse plane.
Jones vector related calculations for GA representation of plane wave.
Vector addition and vector (and scalar) sign figures: VectorsWithOppositeOrientationFig1.eps, vectorAdditionFig1.eps, scalarOrientationFig1.eps.
Hyperbolic cosine and arctan double angle reductions. Probably for cosh parameterization of an ellipse.
Figure for amperesLawBetweenTwoCurrents.eps. Circles surrounding two currents, with respective phicap vectors around those sources.
Uses my GA30.m package to compute the values of the energy momentum tensor multivectors, and relate those to the conventional tensor description of the same. Calculates the expansion of the adjoint of the energy momentum tensor, and also the expansion of some of the adjoint energy momentum tensor terms for the Poynting vector.
Simple integrals for plane current distributions.
Elliptic integrals for charge and current distribution on a ring.
Some integrals related to circular current/charge distributions. A Manipulate that plots the magnitude of one of the integrands. A plot (chargeAndCurrentOnRingFig1.eps) that shows the geometric of the current ring and coordinate system used to solve or express the problem.
Symbolic evaluation of integrals for a cylindrical field distribution of finite and infinite length.
This notebook has transformation techniques to translate a couple of circular charge distribution integrals into their elliptic integral form. It also has plots of some of the electric and magnetic fields obtained from solving one such problem.
A CliffordBasic calculation of the strain portion of the stress tensor, and an explicit demonstration that it is symmetric.
A somewhat random seeming complex exponential evaluation using CliffordBasic, and an R3 bivector argument.
Some R2 complex exponential calculations using CliffordBasic.
This is a figure that has an equilateral triangle in the corner of the first quadrant. This was used to illustrate that the product of two complex exponentials is another complex exponential (in R3), but the bivector argument for that resulting exponential describes (in general) a different plane.
Figure: radialVectorCylindricalFig1.eps. Notebook uses a dynamic (Manipulate) to generate the figure at a desirable angle and radius.
Figure (dualityInR3Fig1.eps) showing the R3 dual plane to a vector graphically. The scaling of the dual plane was only for illustration purposes and did not match the length of the vector.
Verify answers for normal factorization problem. 2.16
Figures that illustrate two rectangular factorizations of a bivector in R3.
A nice little figure illustrating an infinitesimal neighbourhood around a given point. This was used as a figure in the somewhat tedious verification of a Green's function, done in one of the appendixes.
The purpose of this notebook is to show (i.e. decode) the meaning visually of the various Mathematica FourierTransform FourierParameters options available. Shows all the conventions (modern physics, pure math, signal processing, classical physics).
Hyperbolic parameterization of an ellipse, and contours for the associated curvilinear coordinates. ellipticalContoursFig1.eps, and ellipticalContoursFig1.eps figures.
Figure: 2dmanifoldFig1.eps. CliffordBasic calculation of the basis elements above and the area element. Same calculation using my GA30.m package. Generation of mmacell text for the book showing the input and output cells for the CliffordBasic calculation.
Reciprocal basis computation with conventional vector algebra. Same calculation using bivectors. Display the cells for the book latex.
A CliffordBasic solution to an R4 linear system a x + b y = c, using wedge products to solve. Also includes mmacell output to embed the solution in the book as Mathematica input and output.
CliffordBasic calculations for Figure 1.20 reflection (reflectionFig1.eps), but not the figure itself. Also has mmacell output for the input and output cells for this calculation.
Plot (curvilinearPolarFig1.eps) that shows a 2d vector in polar coordinates, the radial vector, and the angle relative to the horizon.
Spherical polar basis and volume element. Calcuation of the curvilinear basis elements done with conventional vector algebra, and CliffordBasic. Also includes mmacell output for the book.
Bivector square and parallelogram figures, Figures for 90 degree rotations. Figure for line intersection. Figure for vector addition, showing scaled multiples of orthonormal bases elements.
Unit bivectors figures in R3. unitBivectorsFig1.eps, unitBivectorsFig2.eps.
Pictoral addition of different size and shape bivectors.
A figure that shows different shape representations of unit bivectors in R2. Includes parallelogram, square, circle and ellipse representations. Also includes inscribed arc to show the orientation of the bivectors. That was done using Arrow in combination with BSplineCurve, where the points on the curve come from evaluating CirclePoints.
This is the notebook for a few bivector related illustrations. The first is two circular representations of a bivector viewed from a 3D vantage point. Another is a bivector addition figure, with two bivectors summed in 3D. That figure was confusing (but cool), and has been left out of the book. The last figure separates the space between those bivectors summed in the second figure showing the summands and the sum all distinct. The current draft of the book includes this figure, but it is still a bit confusing.
A hand calculation seemed to show that I had the wrong expressions for alphaL, alphaR in my polarization notes. Here's a check of the correction of those expressions
Uses geometric algebra to calculate the spherical polar position vector, and then take derivatives to find the trivector volume element (Jacobian).
figure in reciprocal.tex
This is a graphical illustration of bivector addition, connecting the normals of the bivectors head to tail like vector addition. The magnitudes of the bivectors are represented by the unit normals scaled by the area of the bivector representations. The notebook includes a Manipulate expression that can be used to interactively examine the effect of changing the size of each of the summed bivectors.