Geometric Algebra for Electrical Engineers
Minimum price
Suggested price

Geometric Algebra for Electrical Engineers

About the Book

The multivector of geometric algebra extends vector algebra, providing a representation of points, directed line, plane, and volume segments.

Maxwell's equation in its multivector form is a compact and simple theoretical starting point for electromagnetic analysis.

This book details how geometric algebra may be applied to electromagnetic analysis and provides all of the prerequisite concepts and theory required to do so.

This book is suitable for students with an advanced undergraduate electrical engineering or physics background and aims to make the subject more accessible than the available research material.

About the Author

Peeter Joot
Peeter Joot

Peeter Joot is a math and physics enthusiast with a love of geometric algebra.

Peeter's education includes a B.A.Sc from UofT (1997 Engineering Science - computer engineering), 2019 UofT M.Eng (ECE electromagnetics), a lot of self-study, and non-degree study of most of the interesting 4th year UofT undergrad physics courses.

Peeter's day job is software development. He has over 20 years of experience with low level systems programing, operating system and hardware abstraction and exploitation, concurrency, and large scale refactoring. Peeter works for LzLabs and now has fun with PL/I, COBOL, JCL, VSAM, CICS and other legacy subsystems sure to scare away most developers of his generation.

Table of Contents


Document Version




List of Figures

1 Geometric Algebra.

1.1 Prerequisites.

1.1.1 Vector.

1.1.2 Vector space.

1.1.3 Basis, span and dimension.

1.1.4 Standard basis, length and normality.

1.2 Multivectors.

1.3 Colinear vectors.

1.4 Othogonal vectors.

1.5 Some nomenclature.

1.6 Two dimensions.

1.7 Plane rotations.

1.8 Duality.

1.9 Vector product, dot product and wedge product.

1.10 Reverse.

1.11 Complex representations.

1.12 Multivector dot product.

1.12.1 Dot product of a vector and bivector

1.12.2 Bivector dot product.

1.12.3 Problems.

1.13 Permutation within scalar selection.

1.14 Multivector wedge product.

1.14.1 Problems.

1.15 Projection and rejection.

1.16 Normal factorization of the wedge product.

1.17 The wedge product as an oriented area.

1.18 General rotation.

1.19 Symmetric and antisymmetric vector sums.

1.20 Reflection.

1.21 Linear systems.

1.22 A summary comparision.

1.23 Problem solutions.

2 Multivector calculus.

2.1 Reciprocal frames.

2.1.1 Motivation and definition.

2.1.2 R2 reciprocal frame.

2.1.3 R3 reciprocal frame.

2.1.4 Problems.

2.2 Curvilinear coordinates.

2.2.1 Two parameters.

2.2.2 Three (or more) parameters.

2.2.3 Gradient.

2.2.4 Vector derivative.

2.2.5 Examples.

2.2.6 Problems.

2.3 Integration theory.

2.3.1 Line integral.

2.3.2 Surface integral.

2.3.3 Volume integral.

2.3.4 Bidirectional derivative operators.

2.3.5 Fundamental theorem.

2.3.6 Stokes' theorem.

2.3.7 Fundamental theorem for Line integral.

2.3.8 Fundamental theorem for Surface integral.

2.3.9 Fundamental theorem for Volume integral.

2.4 Multivector Fourier transform and phasors.

2.5 Green's functions.

2.5.1 Motivation.

2.5.2 Green's function solutions.

2.5.3 Helmholtz equation.

2.5.4 First order Helmholtz equation.

2.5.5 Spacetime gradient.

2.6 Helmholtz theorem.

2.7 Problem solutions.

3 Electromagnetism.

3.1 Conventional formulation.

3.1.1 Problems.

3.2 Maxwell's equation.

3.3 Wave equation and continuity.

3.4 Plane waves.

3.5 Statics.

3.5.1 Inverting the Maxwell statics equation.

3.5.2 Enclosed charge.

3.5.3 Enclosed current.

3.5.4 Example field calculations.

3.6 Dynamics.

3.6.1 Inverting Maxwell's equation.

3.7 Energy and momentum.

3.7.1 Field energy and momentum density and the energy momentum tensor.

3.7.2 Poynting's theorem (prerequisites.)

3.7.3 Poynting theorem.

3.7.4 Examples: Some static fields.

3.7.5 Complex energy and power.

3.8 Lorentz force.

3.8.1 Statement.

3.8.2 Constant magnetic field.

3.9 Polarization.

3.9.1 Phasor representation.

3.9.2 Transverse plane pseudoscalar.

3.9.3 Pseudoscalar imaginary.

3.10 Transverse fields in a waveguide.

3.11 Multivector potential.

3.11.1 Definition.

3.11.2 Gauge transformations.

3.11.3 Far field.

3.12 Dielectric and magnetic media.

3.12.1 Statement.

3.12.2 Alternative form.

3.12.3 Gauge like transformations.

3.12.4 Boundary value conditions.

A Distribution theorems.

B Proof sketch for the fundamental theorem of geometric calculus.

C Green's functions.

C.1 Helmholtz operator.

C.2 Delta function derivatives.

D Energy momentum tensor for vector parameters.



The Leanpub 60 Day 100% Happiness Guarantee

Within 60 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.

Now, this is technically risky for us, since you'll have the book or course files either way. But we're so confident in our products and services, and in our authors and readers, that we're happy to offer a full money back guarantee for everything we sell.

You can only find out how good something is by trying it, and because of our 100% money back guarantee there's literally no risk to do so!

So, there's no reason not to click the Add to Cart button, is there?

See full terms...

80% Royalties. Earn $16 on a $20 book.

We pay 80% royalties. That's not a typo: you earn $16 on a $20 sale. If we sell 5000 non-refunded copies of your book or course for $20, you'll earn $80,000.

(Yes, some authors have already earned much more than that on Leanpub.)

In fact, authors have earnedover $13 millionwriting, publishing and selling on Leanpub.

Learn more about writing on Leanpub

Free Updates. DRM Free.

If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).

Most Leanpub books are available in PDF (for computers) and EPUB (for phones, tablets and Kindle). The formats that a book includes are shown at the top right corner of this page.

Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.

Learn more about Leanpub's ebook formats and where to read them

Write and Publish on Leanpub

You can use Leanpub to easily write, publish and sell in-progress and completed ebooks and online courses!

Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks.

Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. (Or, if you are producing your ebook your own way, you can even upload your own PDF and/or EPUB files and then publish with one click!) It really is that easy.

Learn more about writing on Leanpub