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. 1921 Excerpt: ...at a finite number of points in any interval, however large. For example, let there be infinite discontinuities only at xx, x2, ... xn in x = a, f(x) being bounded in any interval (c, b), where ca; . Let atkxx....? &. Then we have, as above ( 59), "f(x)dx= Xif(x)dx+ f(x)dx+...+ fx)dx+ "f(x)dx, where xnC.cib, provided ...
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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. 1921 Excerpt: ...at a finite number of points in any interval, however large. For example, let there be infinite discontinuities only at xx, x2, ... xn in x = a, f(x) being bounded in any interval (c, b), where ca; . Let atkxx....? &. Then we have, as above ( 59), "f(x)dx= Xif(x)dx+ f(x)dx+...+ fx)dx+ "f(x)dx, where xnC.cib, provided that the integrals on the right-hand side exist. It will be noticed that the last integral I f(x) dx is an ordinary integral, f(x) being bounded and integrable in (c, b). If the integral f(x) dx also converges, we define the infinite poo J C integral I f(x)dx by Hie equation: J a f(x)dx=: if(x)dx+y(x)dx+...+ ' fx)dx+ f(x)dx. It is clear that this definition is independent of the position of c, since we have ' fx)dx+ fx)dx=C f(x)dx+ f(x)dx, J Xn J C J Xn J r' where Also we may write the above in the form f f(x)dx=' f(z)dx+2 f(x)dx+... + f(x)dx. J a J a J xx J xH The verbal alterations required in the definition of J f(x) dx 00 J-tO are obvious, and we define I f(x)dx, as before, as the sum of J-00 the integrals I f(x) dx and I f(x). J-x J a It is easy to show that this definition is independent of the position of the point a. 61. Tests for Convergence of f f(x) dx. It is clear that we J a need only discuss the case when there is a point of infinite discontinuity at an end of the interval of integration. If x = a is the only point of infinite discontinuity, we have "f(x) dx= Lt f fx)dx, Ja f-XJi+f when this limit exists. It follows at once, from the definition, that: I. The integral f f(x) dx is convergent and has the value I Ja when, any 'positive number e having been chosen, as small as we please, there is a positive number tj such that It follows from I. that, if I f(x) dx converges, to the arbitrary J a posi...
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Add this copy of Introduction to the Theory of Fourier's Series and to cart. $3.07, very good condition, Sold by ThriftBooks-Atlanta rated 5.0 out of 5 stars, ships from Austell, GA, UNITED STATES, published 1952 by Dover Publications.
Add this copy of Introduction to the Theory of Fourier's Series and to cart. $3.07, good condition, Sold by ThriftBooks-Reno rated 5.0 out of 5 stars, ships from Reno, NV, UNITED STATES, published 1952 by Dover Publications.
Add this copy of Introduction to the Theory of Fourier's Series and to cart. $3.24, very good condition, Sold by HPB-Ruby rated 4.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1950 by Dover Publications.
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Add this copy of Introduction to the Theory of Fourier's Series and to cart. $4.56, very good condition, Sold by Dinah Moe's Bookshop rated 4.0 out of 5 stars, ships from Clayton, MO, UNITED STATES, published 1952 by Dover Publications.
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Add this copy of Introduction to the Theory of Fourier's Series and to cart. $7.95, very good condition, Sold by Basement Seller 101 rated 5.0 out of 5 stars, ships from Cincinnati, OH, UNITED STATES, published 1930 by Dover Publications.
Add this copy of Introduction to the Theory of Fourier's Series and to cart. $10.75, very good condition, Sold by Sequitur Books rated 5.0 out of 5 stars, ships from Boonsboro, MD, UNITED STATES, published 1950 by Dover Publications.
Add this copy of An Introduction to the Theory of Fourier's Series and to cart. $11.75, very good condition, Sold by Dorley House Books rated 4.0 out of 5 stars, ships from Hagerstown, MD, UNITED STATES, published 1950 by Dover.
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Near Fine. 8vo. Third revisited edition reprinted; 368 clean, unmarked pages. with 96 examples and 39 figures and indices. An explanation of the theories as well as a section dealing with the Riemann-Lebesque theorem and its consequences; owner's name.
Add this copy of Introduction to the Theory of Fourier's Series and to cart. $12.12, good condition, Sold by Wonder Book - Member ABAA/ILAB rated 5.0 out of 5 stars, ships from Frederick, MD, UNITED STATES.
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Good. Good condition. Third Edition, Revised and Enlarged (Mathematics, Fouriers Series, Integrals, Math Theory) A copy that has been read but remains intact. May contain markings such as bookplates, stamps, limited notes and highlighting, or a few light stains. Bundled media such as CDs, DVDs, floppy disks or access codes may not be included.
Add this copy of Introduction to the Theory of Fourier's Series and to cart. $14.49, very good condition, Sold by Alien Bindings rated 5.0 out of 5 stars, ships from BALTIMORE, MD, UNITED STATES, published 1930 by Dover Publications.
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Very good. 3rd edition, 1930 printing. The covers look great. The binding is tight. The former owner's name and organization stamp has been marked out on the title page. The interior pages are clean and unmarked. Small scuff on the front flyleaf. Electronic delivery tracking will be issued free of charge. 368 pages.
