An Elementary Treatise On Calculus
An Elementary Treatise On Calculus
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In our eReader you can find the full English version of the book. Read An Elementary Treatise On Calculus Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book An Elementary Treatise On Calculus
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To quickly assess the difficulty of the text, read a short excerpt:
'x=0 ■1 /»a;=Zn- = - I y sinnx • dx (3) -1 nr=2w = — I y cosnx ' dx (4) ^ Jx=0 A complete proof of Fourier's theorem would involve a proof that the right-hand member of equation (1) is a convergent series. * This, however, will here be taken for granted. The proof then reduces to a derivation of equations (2), (3) and (4).
* This matter is discussed in Chapter III of Byerly's Fourier^ s Series and Spherical Harmonics, Ginn and Co. , Boston, 1893.
200 CALCULUS.
In this proof a consideration of a...verage values is most important, and the student should therefore look over Art. 73 again.
Another matter of import- ance is to understand clearly 'V^A^Bin nx ^ ^^le meaning of the equation y = sin nx (and y = cos nx) when n is an integer. Now y = sin nx is the equation of a sine curve. If n = 1 this sine curve makes a posi- tive "arch" between x = and x = TT, and a negative "arch'* between x = tt and x = 27r.
In general the sine curve y = sin nx makes a positive arch between x = and x = -, and a negative arch between x = - n' n and X = — as shown in Fig.
What to read after An Elementary Treatise On Calculus?
You can find similar books in the "Read Also" column, or choose other free books by William S William Suddards Franklin to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
'x=0 ■1 /»a;=Zn- = - I y sinnx • dx (3) -1 nr=2w = — I y cosnx ' dx (4) ^ Jx=0 A complete proof of Fourier's theorem would involve a proof that the right-hand member of equation (1) is a convergent series. * This, however, will here be taken for granted. The proof then reduces to a derivation of equations (2), (3) and (4).
* This matter is discussed in Chapter III of Byerly's Fourier^ s Series and Spherical Harmonics, Ginn and Co. , Boston, 1893.
200 CALCULUS.
In this proof a consideration of a...verage values is most important, and the student should therefore look over Art. 73 again.
Another matter of import- ance is to understand clearly 'V^A^Bin nx ^ ^^le meaning of the equation y = sin nx (and y = cos nx) when n is an integer. Now y = sin nx is the equation of a sine curve. If n = 1 this sine curve makes a posi- tive "arch" between x = and x = TT, and a negative "arch'* between x = tt and x = 27r.
In general the sine curve y = sin nx makes a positive arch between x = and x = -, and a negative arch between x = - n' n and X = — as shown in Fig.
What to read after An Elementary Treatise On Calculus?
You can find similar books in the "Read Also" column, or choose other free books by William S William Suddards Franklin to read onlineMoreLess
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