Readers wanted for quaternion handbook


Readers wanted for handbook with exercises in real quaternion calculus

My name is Svetlin Georgiev Georgiev. … I am professor – researcher of Ordinary and Partial Differential equations. From 3 years ago I began to study Clifford analysis and quaternion analysis. I decided to make a handbook with exercises in real quaternion calculus. … there are many papers but the papers do not include many examples. Also I think before trying to publish this handbook it would be good to inform about the project on some website. I will very much appreciate the opinion of interested readers for the handbook.

Please send me an email if you want obtain the draft of the handbook. I am waiting for your comments.

With best regards,

Svetlin Georgiev
Email: sgg2000bg_at_yahoo.com

Current Contents (revised: 9 September 2009)

1 Notations
2 Quaternion operations
3 Exponents and Logarithms
4 Trigonometry
5 Hyperbolic
6 Inverse hyperbolic and trigonometric functions
7 Equivalent quaternions and roots of quaternion
8 Applications to plane geometry
9 Quaternion matrices
10 Monomials and polynomials
11 Quaternion sequences
12 Limit of functions, continuous functions, left differentiable functions, right differentiable functions
13 Spherical linear interpolation, spherical cubic interpolation
14 Quaternion differential forms
15 Quaternion holomorphic functions
16 Integration
17 Quaternion Fourier transform
18 Fractional quaternion Fourier transform
19 Quaternion operator calculus
20 Quaternion linear differential equations of first order
21 Quaternion linear system of ordinary differential equations
22 Quaternion partial differential equations of first order
23 Quaternion linear partial differential equations of second order
24 Quaternion distribution: definition, limit of quaternion distributions
25 Differentiation of quaternion distributions, convolution of quaternion distribution, tensor multiplication of quaternion distributions

References

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24 Comments

Filed under publications

24 responses to “Readers wanted for quaternion handbook

  1. Dear Svetlin, please enter the contact mode! Best, Bernd Schmeikal

  2. Lester Welch

    Is the handbook available electronically? If so, have a link?

    • Dear Lester,
      I asked Svetlin about his handbook. He says it will soon be available online, he is preparing a new extended version. Please contact him directly, if you are interested in the previous version:

      Svetlin Georgiev: sgg2000bg_at_yahoo.com

      With kind regards, Eckhard

  3. There is a new chapter
    “23. Differentiation of quaternion distributions, convolution of quaternion distributions, tensor multiplication of quaternion distributions”

  4. There is a new chapter
    “22. Quaternion distribution : definition, limit of quaternion distributions”

  5. There is a newe chapter
    “21. Quaternion linear partial differential equations of second order”

  6. There is a new chapter
    “20. Quaternion partial differential equations of first order”

  7. There is a new chapter
    “19. Quaternion linear system of ordinary differential equations “.

  8. There is a new chapter
    18. Quaternion linear differential equations of first order

  9. There is a new chapter
    “17. Quaternion operator calculas”

  10. There is a new chapter
    “16. Quaternion Fourier Transform”

  11. There is a new chapter
    15. Integration

  12. There is new chapter
    14. Quaternion holomorphic functions

  13. There is a new chapter
    13. Real quaternion valued forms.

  14. In accordance with reader’s suggestion I add new chapter “12. Spherical linear interpolation, spherical cubic interpolation”.

  15. There is a new chapter
    11. Limit of functions, continuous functions, left differentiable functions, right differentiable functions

  16. Miguel Martinez

    I have not seen any books that offer many examples of Quatenion Calculus – your book seems like a good idea to me.

    Professor Svetlin Georgiev is excellent researcher
    and educator.
    I was his student at Oxford University.

  17. There is a new chapter
    “Quaternion series”

  18. Next chapters:
    10. Functions
    11. Differentiation
    12. Integration
    13. Transformations

  19. There is a new chapter. Chapter 9: monomials and polynomials.

  20. I find that the education is important.
    Therefore, before using computer programs every student and researcher ought to have education to make by oneself the basic operations, in this case basic quaternionic arithmetic operations.

  21. A few years ago I wrote a software tool that you might find useful. It is a quaternion data class for MatLab.

    It allows you to perform quaternion arithmetic with a computer. It was built by the recursive application of the Cayley-Dickson construction, so it also can do octonion arithmetic. It also does sedenion arithmetic to the extent sedenions make any sense.

    If you are a little familiar with Matlab, you might find it interesting.

    It also includes the traditional trigonometric and exponential functions and comes with a test program that shows how to use the whole package.

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