The Elementary Properties of the Elliptic Functions with Examples Alfred Cardew Dixon 9781147564303 Books
Download As PDF : The Elementary Properties of the Elliptic Functions with Examples Alfred Cardew Dixon 9781147564303 Books
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The Elementary Properties of the Elliptic Functions with Examples Alfred Cardew Dixon 9781147564303 Books
I have been always fascinated by Elliptic Fuctions, in fact I own no less than 5 books on this subject, this classics reprint is excellent.But you must have adequate mathematical background on the complex function theory and calculus. But there is one complaint, not only in this books, but in all books by Merchant Books publisher, I don't understand why they do not provide the date of the original pubication date of all these classic books!! Due to copyright? But if this is the reaon, they do not have the right to publish that!!! Just printing the date of publication I do not think this would violate that. Compared with Cornell University's publication, which they are doing the same things, at least they publish the date of the original book. Other readers known the reason? Please tell me if so!!!
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The Elementary Properties of the Elliptic Functions with Examples Alfred Cardew Dixon 9781147564303 Books Reviews
This book initially foregoes the elliptic integrals to introduce Jacobi's elliptic functions sn, cn, and dn directly. The author begins by examining the exponential function which is introduced via the initial value problems d exp(x) / dx = exp(x) and exp(0) = 1. From this, the author shows, one is able to deduce the addition formula for the exponential function, exp(x+y) = exp(x)*exp(y). The author then moves on to show how the same approach can be applied to the circular functions sin and cos and demonstrates that not only can one deduce the correct addition formula but also that these functions are periodic.
Finally the author applies this approach to introducing Jacobi's elliptic functions.
That's all in chapter one which the author ends by introducing Glaisher's convenient notation. In chapter two, the author first demonstrates the periodicity of the elliptic functions and Jacobi's imaginary transformation. He also expends quite a bit of effort showing that there cannot exist a function on the complex numbers having three independent periods.
Chapter three tackles various addition theorems. This is noteworthy as addition theorems are generally considered rather advanced results, and this book makes them appear pretty simple to arrive at.
Chapter four covers theorems for multiplication and division of the argument analogous to half angle formulas in trigonometry.
Chapter five covers integration. There are a number of useful results here.
Chapter six covers addition formulas for the ancillary functions E and Pi which arise in connection with Jacobi's elliptic functions, and chapter seven covers Weierstrass' notation for elliptic functions.
Chapter eight is a very short chapter on differentiation with respect to the argument while chapter nine covers differentiation with respect to the modulus.
Chapter ten is by far the longest chapter in the book. It covers two applications. The first to algebraic curves which I found mostly incomprehensible and the second to the circular pendulum which I found rather hard to follow in spite of being fairly familiar with the topic.
Appendix A provides some graphical representations of the elliptic functions which could have been much better, and appendix B ends the book with a short history of the notation.
Overall, I felt this was book that started out excellent and went into a bit of decline towards the end. Nonetheless, this is the most approachable introduction to this sometimes all too arcane topic I have yet to see, and manages to cover quite a bit of the material necessary for anyone wishing to come up to speed on elliptic functions.
I have been always fascinated by Elliptic Fuctions, in fact I own no less than 5 books on this subject, this classics reprint is excellent.
But you must have adequate mathematical background on the complex function theory and calculus. But there is one complaint, not only in this books, but in all books by Merchant Books publisher, I don't understand why they do not provide the date of the original pubication date of all these classic books!! Due to copyright? But if this is the reaon, they do not have the right to publish that!!! Just printing the date of publication I do not think this would violate that. Compared with Cornell University's publication, which they are doing the same things, at least they publish the date of the original book. Other readers known the reason? Please tell me if so!!!
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