Elements of the Differential And Integral Calculus
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In our eReader you can find the full English version of the book. Read Elements of the Differential And Integral 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 Elements of the Differential And Integral Calculus
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It has already been shown that, if the ordinate of a curve be regarded as a function of the abscissa, the first differential coefficient will be equal to the tangent of the angle which the tangent line forms with the axis of abscis- sas (Art. 15). We now propose to show the relation between a curve and the second differential coefficient^ the ordinate being regarded as a function of the abscissa.
Let AP be the abscissa and PM the ordinate of a curve. From P lay off on the axis of abscissas PP' ...= h, 3. Nd PP'' = 2 h. Draw the ordinates PM, FM^P^'^r^• also the lines MMN, MM"; and lastly, MQ, M'Q!, parallel to the M' / J> M' ^ N ^.^^ Q P".
DIFFERENTIAL CALCULUS.
129 axis of abscissas. Then will M'Q = NQ', and we shall have /M/_. A-^A V'M ^~^ dx\ "^ dx" 1. 2 + &c. , ^ dx \ dx" 1. 2 P^M' pffj^ff.
FM^=M'Q'=^h-\--%~+ &c. Dx dar 1. 2 M'^Q'-M'Q=+M^N=:-^h^^- &c.
Now, since the sign of the first member of the equation is essentially positive, the sign of the second member will also be positive (Alg.
What to read after Elements of the Differential And Integral Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Charles Davies to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It has already been shown that, if the ordinate of a curve be regarded as a function of the abscissa, the first differential coefficient will be equal to the tangent of the angle which the tangent line forms with the axis of abscis- sas (Art. 15). We now propose to show the relation between a curve and the second differential coefficient^ the ordinate being regarded as a function of the abscissa.
Let AP be the abscissa and PM the ordinate of a curve. From P lay off on the axis of abscissas PP' ...= h, 3. Nd PP'' = 2 h. Draw the ordinates PM, FM^P^'^r^• also the lines MMN, MM"; and lastly, MQ, M'Q!, parallel to the M' / J> M' ^ N ^.^^ Q P".
DIFFERENTIAL CALCULUS.
129 axis of abscissas. Then will M'Q = NQ', and we shall have /M/_. A-^A V'M ^~^ dx\ "^ dx" 1. 2 + &c. , ^ dx \ dx" 1. 2 P^M' pffj^ff.
FM^=M'Q'=^h-\--%~+ &c. Dx dar 1. 2 M'^Q'-M'Q=+M^N=:-^h^^- &c.
Now, since the sign of the first member of the equation is essentially positive, the sign of the second member will also be positive (Alg.
What to read after Elements of the Differential And Integral Calculus?
You can find similar books in the "Read Also" column, or choose other free books by Charles Davies to read onlineMoreLess
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