AN ELEMENTARY TREATISE ON FOURIER'S SERIES AND SPHERICAL, by William Elwood Byerly

By William Elwood Byerly

First released in 1893, Byerly's vintage treatise on Fourier's sequence and round, cylindrical, and ellipsoidal harmonics has been utilized in study rooms for good over a century. This useful exposition acts as a primer for fields comparable to wave mechanics, complex engineering, and mathematical physics. subject matters coated contain: . improvement in trigonometric sequence . convergence on Fourier's sequence . resolution of difficulties in physics by way of assistance from Fourier's integrals and Fourier's sequence . zonal harmonics . round harmonics . cylindrical harmonics (Bessel's services) . and extra. Containing a hundred ninety workouts and a necessary appendix, this reissue of Fourier's sequence might be welcomed via scholars of upper arithmetic all over. American mathematician WILLIAM ELWOOD BYERLY (1849-1935) additionally wrote components of Differential Calculus (1879) and components of necessary Calculus (1881).

Show description

Read or Download AN ELEMENTARY TREATISE ON FOURIER'S SERIES AND SPHERICAL, CYLINDRIC, AND ELLIPSOIDAL HARMONICS: With Applications to Problems in Mathematical Physics PDF

Similar mathematical physics books

Differential Equations: Their Solution Using Symmetries

In lots of branches of physics, arithmetic, and engineering, fixing an issue potential fixing a collection of standard or partial differential equations. approximately all equipment of creating closed shape strategies depend on symmetries. The emphasis during this textual content is on how to define and use the symmetries; this is often supported by means of many examples and greater than a hundred routines.

Advanced mathematical methods for scientists and engineers

OCRed pdf switched over model of the djvu dossier

Fluid-Structure Interaction and Biomedical Applications

This publication offers, in a methodical means, up-to-date and entire descriptions and analyses of a few of the main proper difficulties within the context of fluid-structure interplay (FSI). usually talking, FSI is likely one of the preferred and interesting difficulties in technologies and contains business in addition to organic functions.

Additional info for AN ELEMENTARY TREATISE ON FOURIER'S SERIES AND SPHERICAL, CYLINDRIC, AND ELLIPSOIDAL HARMONICS: With Applications to Problems in Mathematical Physics

Example text

14) – we obtain τ uτ = τ eτ or u τ = eτ . Direct integration leads to the solution of this equation in the form u(ξ, τ ) = eτ + g(ξ). 15) with g being an arbitrary differentiable function. The reader is asked to verify � the correctness of the solution. 2) we have dealt with an equation accompanied by a boundary condition given on one of the coordinate axes. 15), and let us add, one by one, the following conditions: u(0, y) = sin y, (i) u(x, 0) = sin x, u(x, 0) = 10. In the first case, we obtain sin y = u(0, y) = ey + g(y), thus g(y) = sin y − ey .

As we will see later, the wave equation with non-smooth initial conditions is, in the sense of the classical solution defined above, an ill-posed problem, since its classical solution does not exist. However, if we consider the solution in a more general sense, the problem becomes well-posed, the generalized solution exists, it is unique and stable with respect to “small” changes of given data. 5 Classification of Linear Equations of the Second Order In this section we state the classification of the basic types of PDEs of the second order that can be found most often in practical models.

On an unbounded domain, for example, on the interval Ω = (0, +∞), where it is not possible to speak about a value of the given function at the point “infinity”, the homogeneous Dirichlet boundary condition has the form u(0) = 0, lim u(x) = 0. x→+∞ As the differential equations themselves, the boundary conditions have also their physical interpretation. Vibrating string. Vibrations of a string of length l, which is fixed in a zero position in both ends, are described by a one-dimensional wave equation with homogeneous Dirichlet boundary conditions u(0, t) = u(l, t) = 0.

Download PDF sample

Rated 4.36 of 5 – based on 42 votes