Mathematical Analysis

# An Elementary Treatise on Fourier's Series and Spherical, by William Elwood Byerly PDF

By William Elwood Byerly

ISBN-10: 1116151464

ISBN-13: 9781116151466

It is a pre-1923 historic copy that used to be curated for caliber. caliber insurance was once carried out on each one of those books in an try to eliminate books with imperfections brought by means of the digitization method. although we have now made top efforts - the books can have occasional mistakes that don't abate the studying adventure. We think this paintings is culturally very important and feature elected to carry the ebook again into print as a part of our carrying on with dedication to the renovation of revealed works world wide. this article refers back to the Bibliobazaar variation.

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Extra resources for An Elementary Treatise on Fourier's Series and Spherical, Cylindrical, and Ellipsoidal Harmonics, With Applications to Problems in Mathematical Physics

Example text

45 DEVELOPMENT IN TRIGONOMETRIC SERIES. 46 29. Although any function can be expressed both as a sine series and as a cosine series, and the function and either series will be equal for all values of x between zero and π, there is a decided difference in the two series for other values of x. Both series are periodic functions of x having the period 2π. If then we let y equal the series in question and construct the portion of the corresponding curve which lies between the values x = −π and x = π the whole curve will consist of repetitions of this portion.

83, p. 78), the coefficients in y = a1 sin x + a2 sin 2x + a3 sin 3x + · · · + an sin nx (2) can be determined so that the curve represented by (2) will pass through any n arbitrarily chosen points of the curve y = f (x) (3) whose abscissas lie between 0 and π and are all different, and these coefficients will have but one set of values. For the sake of simplicity suppose that the n points are so chosen that their projections on the axis of X are equidistant. π = ∆x; then the co¨ordinates of the n points will be [∆x, f (∆x)], Call n+1 [2∆x, f (2∆x)], [3∆x, f (3∆x)], · · · [n∆x, f (n∆x)].

Int. Cal. Art. 83, p. 78), the coefficients in y = a1 sin x + a2 sin 2x + a3 sin 3x + · · · + an sin nx (2) can be determined so that the curve represented by (2) will pass through any n arbitrarily chosen points of the curve y = f (x) (3) whose abscissas lie between 0 and π and are all different, and these coefficients will have but one set of values. For the sake of simplicity suppose that the n points are so chosen that their projections on the axis of X are equidistant. π = ∆x; then the co¨ordinates of the n points will be [∆x, f (∆x)], Call n+1 [2∆x, f (2∆x)], [3∆x, f (3∆x)], · · · [n∆x, f (n∆x)].