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Graphs and Tables of the Mathieu Functions and Their First Derivatives (Paperback)
Loot Price: R585
Discovery Miles 5 850
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Graphs and Tables of the Mathieu Functions and Their First Derivatives (Paperback)
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Loot Price R585
Discovery Miles 5 850
Expected to ship within 10 - 15 working days
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Mathieu functions are employed in solving a variety of problems in
mathematic (al?) physics. In many cases the configuration involves
elliptical coordinates. Of course, the circular geometry is the
degenerate case of the elliptical cross section. This volume
contains values for, and curves of the angular and radial Mathieu
functions and their first derivatives. The latter are often needed
in the solution of problems, in particular in solving
electromagnetic wave propagation problems. Also included are data
on zero crossings of the radial Mathieu functions. These are often
needed for determining the cut-off frequencies for propagating
modes. Other tables are available for the Mathieu functions, but
there is very little data available for derivatives or zero
crossings. It is felt that the principal value of this volume is in
the multitude of curves included. The analyst dealing with
elliptical cases can, by inspection of the curves, find values of
the functions and derivatives at the origin, maxima and minima,
zero crossings, and qualitative behavior of the plots as a function
of several parameters. To the author's knowledge, this is the most
extensive presentation of plotted information. It is hoped that the
information will be helpful in the solution of practical problems.
This book is divided into two sections. Section I deals only with
the functions themselves, defining the equations and terminology
used and presenting the tabular data and curves. Section II treats
the derivatives and the zeros. Again the terminology and equations
for the first derivatives are given. The Mathieu functions are
named after Emile L. Mathieu (1835-1890), a French mathematician,
who in 1868 published an article dealing with vibratory movement of
the elliptic membrane. The asteroid 27947 Emilemathieu is named in
his honor.
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