Bibliography

Historical

[1729] Bruce A Hedman.
An earlier date for 'Cramer's rule'.
Historica Mathematica, 26(4):365-368, November 1999.

[1819] W.G. Horner.
A new method of solving numerical equations of all orders, by continuous approximation.
Philosophical Transactions of the Royal Society of London, 109:308-335, July 1819.

[1841] Baron Augustin Cauchy.
Resume d'un memoire sur la mecanique celeste et sur un nouveau calcul appele calcul des limites.
In: Bachelier, editor,  Exercices d'Analyse et de Physique Mathematique, volume 2, pages 41-98. Bachelier, Paris, France, 1841.

[1844] Sir William R. Hamilton.
On quaternions; or on a new system of imaginaries in algebra.
Philosophical Magazine and Journal of Science, 25:10-13, July 1844.

[1844] Hermann Grassmann.
The extension theory of 1844.
In: A New Branch of Mathematics: The Ausdehnungslehre of 1844, and Other Works, pages 2-295. Open Court, Chicago, US-IL, 1995.
(Translated by Lloyd C. Kannenberg).

[1848] Sir William R. Hamilton.
Note by Professor Sir W.R. Hamilton, respecting the researches of John T. Graves, Esq.
Transaction of the Royal Irish Academy, 21:338-341, 1848.

[1855] Hermann Grassmann.
Sur les differents genres de multiplication.
Journal fur die reine und angewandte Mathematik, 49:123-141, 1855.

[1855] Hermann Grassmann.
On the various types of multiplication.
In: A New Branch of Mathematics: The Ausdehnungslehre of 1844, and Other Works, pages 451-468. Open Court, Chicago, US-IL, 1995.
(Translated by Lloyd C. Kannenberg).

[1862] Hermann Grassmann.
Extension Theory, volume 19 of  History of Mathematics.
American Mathematical Society, Providence, US-RI, 2000.
(Translated by Lloyd C. Kannenberg).

[1873] James C. Maxwell.
A Treatise on Electricity and Magnetism, volume 1.
Clarendon Press, Oxford, UK, 1873.

[1873] James C. Maxwell.
A Treatise on Electricity and Magnetism, volume 2.
Clarendon Press, Oxford, UK, 1873.

[1877] Hermann Grassmann.
Der ort der Hamilton'schen quaternionen in der Ausdehnungslehre.
Mathematische Annalen, 12:375-386, 1877.

[1877] Hermann Grassmann.
The position of the Hamiltonian quaternions in extension theory.
In:  A New Branch of Mathematics: The Ausdehnungslehre of 1844, and Other Works, pages 525-538. Open Court, Chicago, US-IL, 1995.
(Translated by Lloyd C. Kannenberg).

[1878] William K. Clifford.
Applications of Grassmann's extensive algebra.
American Journal of Mathematics, 1(4):350-358, 1878.

[1881] J.W. Gibbs.
Elements of Vector Analysis.
Tuttle, Morehouse and Taylor, New Haven, 1881-4.

[1884] J.H. Poynting.
On the transfer of energy in the electromagnetic field.
Philosophical Transactions of the Royal Society of London, 175:343-361, 1884.

[1893] Oliver Heaviside.
Electromagnetic Theory, volume 1.
The Electrician Printing and Publishing Company, London, UK, 1893.

[1894] Heinrich Hertz.
Untersuchungen uber die ausbreitung der elecktrischen kraft.
In: Gesammelte Werke on Heinrich Hertz, volume 2. J.A. Barth, Leipzig, Germany, 1894.

[1925] F. Gill.
Oliver Heaviside.
The Bell System Technical Journal, pages 349-354, July 1925.

[1927] W. Pauli.
Zur quantenmechanik des magnetischen elektrons.
Zeitschrift fur Physik, 43(9-10):601-623, 1927.

[1928] P.A.M. Dirac.
The quantum theory of the electron.
Proceedings of the Royal Society. Series A, Containing Papers of a Mathematical and Physical Character, 117(778):610-624, February 1928.

[1930] P.A.M. Dirac.
A theory of electrons and protons.
Proceedings of the Royal Society. Series A, Containing Papers of a Mathematical and Physical Character, 126(801):360-365, January 1930.

[1996] Kane Yee.
Numerical solution of initial boundary value problems involving Maxell's equations in isotropic media.
IEEE Transactions on Antennas and Propagation, 14(3):302-307, May 1966.

[1997] Frank Smithies.
Cauchy and the Creation of Complex Function Theory.
Cambridge University Press, Cambridge, UK, 1997.

[2002] M. Chisholm.
Such Silver Currents: the Story of William and Lucy Clifford 1845-1929.
Lutterworth Press, Cambridge, UK, March 2002

Contemporary

[1989] Alan McIntosh.
Clifford algebras and the higher-dimensional Cauchy integral.
In: Z. Ciesielski, editor,  Approximation and Function Spaces, number 22 in BCP series, pages 253-267. Banach Center Publications, Warsaw, Poland, 1989.

[1996] M. Mitrea.
Hypercomplex variable techniques in harmonic analysis.
In: John Ryan, editor,  Clifford Algebras in Analysis and Related Topics, volume 21 of  Studies in Advanced Mathematics, pages 103-128.
CRC Press, Boca Raton, US-NY, 1996.

[1999] Alan McIntosh and Marius Mitrea.
Clifford algebras and Maxwell's equations in Lipschitz domains.
Mathematical Methods in the Applied Sciences, 22(18):1599-1620, December 1999.

[2001] A. Axelsson, R. Grognard, J. Hogan, and A. McIntosh.
Harmonic analysis of Dirac operators on Lipschitz domains.
In F. Brackx, editor, Clifford Analysis and its Applications,  volume 25 of  NATO Science Series II, Mathematics Physics and Chemistry, pages 231-246, Dordrecht, Netherlands, 2001. Kluwer.

[2002] Andreas Axelsson.
Transmission Problems for Dirac's and Maxwell's Equations with Lipschitz Interfaces.
PhD thesis, Australian National University, Canberra, Australia, November 2002.

[2007] Ajalawit Chantaveerod, Andrew D. Seagar, and Tuptim Angkaew.
Calculation of electromagnetic field with integral equation based on Clifford algebra.
In: Progress in Electromagnetic Research Symposium (PIERS'07), pages 62-71, Prague, Czech Republic, August 27-30 2007.

[2009] Ajalawit Chantaveerod and Andrew Seagar.
Iterative solutions for electromagnetic fields at perfectly reflective and transmissive interfaces using Clifford algebra and the multi-dimensional Cauchy integral.
IEEE Transactions on Antennas and Propagation, 57(11):3489-3499, November 2009.

[2012] Andrew Seagar.
Calculation of electromagnetic fields in three dimensions using the Cauchy integral.
IEEE Transactions on Magnetics, 48(2):175-178, February 2012.

[2015] Andrew Seagar and Ajalawit Chantaveerod.
An EM scattering algorithm for all materials.
In: International Conference on Electromagnetics in Advanced Applications (ICEAA'15), pages 256-259, Turin, Italy, September 7-11 2015.

[2016] Andrew Seagar.
Application of Geometric Algebra to Electromagnetic Scattering - the Clifford-Cauchy-Dirac Technique.
Springer, Singapore, 2016.

[2016] Andrew Seagar and Hugo Espinosa.
A numerical comparison between EFIE/MoM and CCD methods for EM scattering in two dimensions.
In: International Conference on Electromagnetics in Advanced Applications (ICEAA'16), pages 328-330, Cairns, Australia, September 19-23 2016.

[2017] Andrew Seagar.
Accuracy of CCD technique for EM scattering from lossless and lossy dielectrics with different basis functions.
In: International Conference on Electromagnetics in Advanced Applications (ICEAA'17), pages 425-428, Verona, Italy, September 11-15 2017.

[2018] Andrew Seagar.
First order wavelike phenomena with electromagnetic and acoustic applications.
IEEE Transactions on Antennas and Propagation, 57(7):3526-3531, July 2018.

[2020] Morteza Shahpari and Andrew Seagar.
Leveraging prior known vector Green's functions in solving perturbed Dirac equation in Clifford algebra.
Advances in Applied Clifford Algebras, 30(4):56/1-56/17, August 2020.

[2023] Andrew Seagar.
Numerical Calculations in Clifford Algebra - A Practical Guide for Engineers and Scientists.
John Wiley and Sons, United Kingdom, 2023.