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Tuesday, April 21, 2020 | History

3 edition of A Hypercomplex Calculus with Applications to Special Relativity found in the catalog.

A Hypercomplex Calculus with Applications to Special Relativity

Clyde M. Davenport

A Hypercomplex Calculus with Applications to Special Relativity

  • 4 Want to read
  • 36 Currently reading

Published .
Written in English


The Physical Object
FormatPaperback
Number of Pages217
ID Numbers
Open LibraryOL11694625M
ISBN 100962383708

This original Dover textbook is based on an advanced undergraduate course taught by the author for more than 50 years. It introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. edition. The first field equation of the hypercomplex action contain Newton’s static law of gravity paired with a time-dependent term and thus is consistent with special relativity. There is also an Ampere-like equation so that a 4-potential theory can account for bending of both time and space caused by gravity. T. G. Vold: "An introduction to geometric algebra with an application to rigid body mechanics" and "An introduction to geometric calculus and its application to electrodynamics" Am. J. Phys. vol. 61, no. 6, pp. , A. Lewis, a ps-format intro can be down-loaded from his webpage.


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A Hypercomplex Calculus with Applications to Special Relativity by Clyde M. Davenport Download PDF EPUB FB2

Davenport:‘A Commutative Hypercomplex Calculus, with Applications to Special Relativity’, Privately Published, Knoxville; ISBN Google Scholar W.

Hamilton:‘On a New Species of Imaginary Quantities Connected with the Theory of Quaternions’, Proceedings of the Royal Irish Academy 2, pp.

–Cited by: Cover title: A hypercomplex calculus with applications to special relativity. "An expanded, revised, and more-expository version of a thesis presented by the author for an MS degree the University of Tennessee in June, "--Acknowledgements. Semi-Riemannian Geometry With Applications to Relativity and millions of other books are available for Amazon by: Einstein's Special Theory of Relativity is a superb place to begin a serious study of physics.

Judging from his book, Helliwell must be a fine teacher. He achieves a rare clarity. For instance, the derivation of the standard kinematic results starting from Einstein s postulates is outstandingly clear/5(14).

Special Relativity by Philip Harris. Objective of this book is to explain the principle of relativity; its importance and universal application. Topics covered includes: Background History, The Lorentz Transformations, Spacetime, Dynamics and Kinematics, Four-Vectors, Relativity and Electromagnetism.

Author(s): Philip Harris. This book is devoted to a rigorous mathematical treatment of the flat Minkowski spacetime of special relativity. It pays particular attention to the Lorentz group and the causal structure of the theory, but also treats the electromagnetic field tensor, spinors, and the topology of Minkowski spacetime.

There is an old book by Max Born, called Einstein's Theory of Relativity which explains the Special Relativity in great detail without any advanced mathematics and a little bit of General Relativity. It is suitable for those who has not yet started to physics degree or will not, but would like to understand the theory in a deeper and mathematical manner.

This book covers the following topics: Special Relativity, Lorentzian Geometry, Introduction to General Relativity, Null Structure Equations, Applications to Null Hypersurfaces, Christodoulou’s Memory Effect, Black Holes, Lagrangian Theories and the Variational Principle, Hyperbolic Equations and Wave Propagation on Black Holes.

The Mathematics of Special Relativity Jared Ruiz Advised by Dr. Steven Kent it is due. The road to the development, understanding, and actual application of the theory of relativity is a long and twisted one, and credit cannot be given to one man alone. galaxy, etc. In special relativity, we assume that all motion is uniform (there is File Size: KB.

Chapter 2 Frames of Reference 11 same event in some other reference frame. In Newtonian physics, this relation is provided by the Galilean transformation equations, and in special relativity by the Lorentz Size: KB. Basic Relativity.

This is A Hypercomplex Calculus with Applications to Special Relativity book comprehensive textbook for advanced undergraduates and beginning graduate students in physics or astrophysics, developing both the formalism and the physical ideas of special and general relativity in a logical and coherent way.

The book is in two parts.5/5(1). Clyde M. Davenport is the author of A Commutative Hypercomplex Calculus With Applications To Special Relativity ( avg rating, 0 ratings, 0 reviews).

Special Relativity (SR) (SCHRODINGER¨, OSKAR KLEIN, WALTER GORDON, A Hypercomplex Calculus with Applications to Special Relativity book, PAUL DIRAC ) leads to an equation which requires some coefficients which can neither be real nor complex but rather must be hypercomplex.

It is conventional to write down the DIRAC equation using pairwise anti-commuting matrices. However, a unitary ring of. Davenport, A Commutative Hypercomplex Calculus with Applications to Special Relativity (Privately published, Knoxville, Tennessee, ).

A History of Algebra Book. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions.

A system of hypercomplex numbers is defined for each dimension that is a power of 2. In each of these dimensions, the numbers are associative and commutative but their advantages lie in the ease of Cited by: 2.

Irene Sabadini, Michael Shapiro, Frank Sommen(), Hypercomplex Analysis, Springer. Clyde Davenport () A Hypercomplex Calculus with Applications to Special Relativity, ISBN 6. This book provides a thorough introduction to Einstein's special theory of relativity, suitable for anyone with a minimum of one year's university physics with calculus.

It is Cited by: It is the purpose of this book to provide an introduction to the Special Theory of Relativity which is accessible to any stu­ dent who has had an introduction to general physics and some slight acquaintance with the calculus.

Much of the material is at a level suitable for high school students who have had advanced placement in physics and. This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult.

Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general 3/5(1).

A commutative hypercomplex calculus with applications to special relativity by Clyde M. Davenport 2 editions - first published in Clyde Davenport () A Hypercomplex Calculus with Applications to Special Relativity ISBN Clyde Davenport () Commutative Hypercomplex Mathematics.

Soo-Chang Pei, Ja-Han Chang & Jian-Jiun Ding () "Commutative reduced biquaternions and their Fourier transform for signal and image processing", IEEE Transactions on Signal Processing – another book) to understand the twin paradox. General relativity, with its complicated-looking tensor calculus, appeared hopelessly out of reach.

Although those days are long gone, I have tried my best to write the book I would have liked to read back then. All of special relativity can be derived from two principles 1) Physics is the same in any inertial reference frame.

If you're riding in your car on the highway (with the windows up) and you drop a ball it falls in the same way as if you were stopped at a stop sign and dropped the same ball.

The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The second derivative of a function is simply the derivative of the first derivative of the function.

Similarly, the third derivative is the derivative of the second derivative. This idea can be extended to form any number of subsequent derivatives, where the n th derivative of y. Books shelved as general-relativity: A First Course in General Relativity by Bernard Schutz, General Relativity by Robert M.

Wald, Spacetime and Geometry. The general theory of relativity, together with the necessary parts of the theory of invariants, is dealt with in the author’s book Die Grundlagen der allgemeinen Relativitätstheorie (The Foundations of the General Theory of Relativity) — Joh.

Ambr. Barth, ; this book assumes some familiarity with the special theory of relativity. vFile Size: 1MB. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics.

Calculus/Vector Calculus and so on in special relativity book recommandation. Ask Question Asked 4 years, Book on gamma functions with applications in. Purchase Semi-Riemannian Geometry With Applications to Relativity, Volume - 1st Edition. Print Book & E-Book. ISBNIn mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.

It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus.

This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course.

Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers as a simple extension of the field of complex numbers is extensively studied in the book.

Get Stuff. For a fee: Books, Buttons, Turquoise Einstien T-shirts, and No Stinking Higgs t-shirts For free: Doing Physics with Quaternions (much of this site, pages), Lectures on Dynamic Graphs and Unified Field Theory (75 pages). A few good papers: Sudbery's first paper (memo,44 pages) on why quaternion analysis is no good.

a commutative hypercomplex calculus with applications to special relativity Download Book A Commutative Hypercomplex Calculus With Applications To Special Relativity in PDF format. You can Read Online A Commutative Hypercomplex Calculus With Applications To Special Relativity here in PDF, EPUB, Mobi or Docx formats.

Divided into 14 chapters, the book covers elementary concepts of Special relativity, as well as the advanced studies on General relativity. The recent theories like Kerr geometry, Sagnac effect, Vaidya geometry, Raychaudhuri equation and Gravitation physics vis-Ã-vis Quantum physics are presented in easy-to-understand language and simple style.

or biquaternionsare usedexplicitly: italsocoverspapers inwhicha hypercomplex coordinate-free whole-symbol system allied to quaternions is used (e.g., Clifford-1The only exceptions to this rule are papers or books of general interest, and papers included for completeness when. ↑ C. Davenport:‘An Extension of the Complex Calculus to Four Real Dimensions, with an Application to Special Relativity’, M.

Thesis, University of Tennessee, Knoxville. ↑ Clyde Davenport () A Hypercomplex Calculus with Applications to Special Relativity ISBN Get this from a library.

The mathematics of Minkowski space-time: with an introduction to commutative hypercomplex numbers. [Francesco Catoni;] -- "Hyperbolic numbers are proposed for a rigorous geometric formalization of the space-time symmetry of two-dimensional Special Relativity.

The system of hyperbolic numbers as a simple extension of the. In G. Baley Price published a book on bicomplex numbers, multicomplex numbers, and their function theory. Professor Price also gives some history of the subject in the preface to his book. Another book developing bicomplex numbers and their applications is by Catoni, Bocaletti, Cannata, Nichelatti & .Davenport.

Clyde M. An Extension of the Complex Calculus to Four Real Dimensions, with an Application to Special Relativity. M.S. thesis. University of Tennessee, Knoxville. Knoxville, Tennessee.

Book: Davenport, Clyde M. A Hypercomplex Calculus with Applications to Special Relativity. University of Tennessee, Knoxville.An Extension of the Complex Calculus to Four Real Dimensions, with an Application to Special Relativity (M.S. thesis). Knoxville, Tennessee: University of Tennessee, Knoxville.

^ Davenport, Clyde M. (). A Hypercomplex Calculus with Applications to Special Relativity. Knoxville, Tennessee: University of Tennessee, Knoxville. ISBN