Introductory Course in Differential Equations for Students in Classical and Engineering Colleges
by Murray
Format: Paperback
ISBN13: 9781151837141
Paperback|9781151837141
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Overview
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: ...series is lor m = 0, Ar = Ar-l. r r + 3 A0(l-hx + &x2). Then At = A0 =-J-4o, For TO = _ 3, Ar = Ll Note L contains a general discussion to be read after Exs. 1, 2. and the particular integral is that is, 2xr(l + JLa;-2 + 2jJx-4 +...Y V 61 8 ) Ex. 3. Show by the method of integration in series, that the general d'v solution of--+ y = 0 is A cos x + B sin x. Ex.4. (22 + l)g + x+2, = 0. Ex.5. 2g-x + (l-x = x Ex.6. (l-a;2)g_2a;+"(n + l)y = 0. 83. Equations of Legendre, Bessel, Riccati, and the hypergeometric series. A fuller discussion of integration in series than is here attempted is beyond the limits of an introductory course in differential equations. The purpose of Art. 82 has merely been to give the student a little idea of a method which is of wide application; and which is used in solving four very important equations that often occur in investigations in applied mathematics, --the equations of Riccati, Bessel, Legendre, and the hypergeometric series. Johnson's Differential Equations, Arts. 171-180, discusses the methods to be followed when two roots of (6) Art. 82, become equal, the corresponding series then being identical; and when two of the roots differ by a multiple of s, one series then being included in the other; and when a coefficient Ar is infinite. The equations referred to above, and references to be consulted concerning them, are as follows: t Legendre's equation is In connection with this article, the student is advised to read W. E. Byerly, Fourier's Series and Spherical Harmonics, Arts. 14-18. t Adrien Marie Legendre (1752-1833) was the author of Elements of Geometry, published in 1794, the modern rival of Euclid. He is noted for his researches in Elliptic Functions and Theory of Numbers. He was the creator, w...
| ISBN-13 | 9781151837141 |
|---|---|
| ISBN-10 | 1151837148 |
| Weight | 0.38 Pounds |
| Dimensions | 9.00 x 6.00 x 0.26 In |
| List Price | $14.14 |
| Format | Paperback |
|---|---|
| Pages | 110 pages |
| Publisher | |
| Published On | 2010-01-01 |
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