Geometric Algebra for Electrical Engineers

“2nd” edition of “Geometric Algebra for Electrical Engineers”

May 4, 2019 Geometric Algebra for Electrical Engineers No comments

I’ve refreshed my Geometric Algebra for Electrical Engineers book, which could be considered a 2nd edition of sorts. The amazon color and black-and-white versions have been updated, as well as the pdf and the leanpub version (all of those are in available in the previous link.)

Changelog:

V0.1.15-6 (May 2, 2019)

  • Update figures (thicker lines, remove some ticks, …) and link them to the mathematica link anchors.
  • “in figure fig.” -> “in fig”.
  • Extend my hacks of the classic thesis template to use 6×9 with smaller than default margins. Now have the preface page numbers not in the bleed area of the page.
  • Split colorlablebox into separate .sty (for phy452 notes.)
  • Fix pdfbookmarks for contents and list of figures (so that they don’t show up under the preface)
  • Index quaternion (Bruce Gould)
  • GAelectrodynamics.tex: Want scrheadings starting before contents otherwise page numbers are out of bounds (and the page headings are MIA)
  • Bruce: “May I suggest that the proofs should have the end-of-proof symbol at the end?” Used the amsthm proof environment to do this.
  • Theorem 1.2: turn the converse into a footnote, to be seen later. (Bruce)
  • Added Bruce Gould to the thanks.

 

Why to study electromagnetism with geometric algebra.

February 3, 2019 Geometric Algebra for Electrical Engineers No comments

The current draft of my book really ought to have some motivation in the preface. This is what I was thinking of.

Why you want to read this book.

When you first learned vector algebra you learned how to add and subtract vectors, and probably asked your instructor if it was possible to multiply vectors. Had you done so, you would have been told either “No”, or a qualified “No, but we can do multiplication like operations, the dot and cross products.” This book is based on a different answer, “Yes.” A set of rules that define a coherent multiplication operation are provided.

Were you ever bothered by the fact that the cross product was only defined in three dimensions, or had a nagging intuition that the dot and cross products were related somehow? The dot product and cross product seem to be complimentary, with the dot product encoding a projection operation (how much of a vector lies in the direction of another), and the magnitude of the cross product providing a rejection operation (how much of a vector is perpendicular to the direction of another). These projection and rejection operations should be perfectly well defined in 2, 4, or N dimemsions, not just 3. In this book you will see how to generalize the cross product to N dimensions, and how this more general product (the wedge product) is useful even in the two and three dimensional problems that are of interest for physical problems (like electromagnetism.) You will also see how the dot, cross (and wedge) products are all related to the vector multiplication operation of geometric algebra.

When you studied vector calculus, did the collection of Stokes’s, Green’s and Divergence operations available seem too random, like there ought to be a higher level structure that described all these similar operations? It turns out that such structure is available in the both the language of differential forms, and that of tensor calculus. We’d like a toolbox that doesn’t require expressing vectors as differentials, or resorting to coordinates. Not only does geometric calculus provides such a toolbox, it also provides the tools required to operate on functions of vector products, which has profound applications to electromagnetism.

Were you offended by the crazy mix of signs, dots and cross products in Maxwell’s equations? The geometric algebra form of Maxwells’s equation resolves that crazy mix, expressing Maxwell’s equations as a single equation. The formalism of tensor algebra and differential forms also provide simpler ways of expressing Maxwell’s equations, but are arguably harder to relate to the vector algebra formalism so familiar to electric engineers and physics practitioners. In this book, you will see how to work with the geometric algebra form of Maxwell’s equation, and how to relate these new techniques to familiar methods.

My book (Geometric Algebra for Electrical Engineers) now available in paper.

January 29, 2019 Geometric Algebra for Electrical Engineers No comments

Edition 0.1.14 of my first book, Geometric Algebra for Electrical Engineers is now available, in a variety of pricing options:

Both paper versions are softcover, and have a 6×9″ format, whereas the PDF is formatted as letter size.  The leanpub version was made when I had the erroneous impression that it was a print on demand service like kindle-direct-publishing (aka createspace.) — it’s not, but the set your own price aspect of their service is kind of neat, so I’ve left it up.

If you download the free PDF or buy the black and white version, and feel undercharged, feel free to send some bitcoin my way.