Lectures On the Theory of Maxima And Minima of Functions of Several Variables
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In our eReader you can find the full English version of the book. Read Lectures On the Theory of Maxima And Minima of Functions of Several Variables 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 Lectures On the Theory of Maxima And Minima of Functions of Several Variables
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, . . . . «n)» and consequently f {^x^, Xi, .... X^ has on the position (ai, a^. , . . . . A„) neither a maximum nor a minimum value.
We therefore have as a second condition for the existence of a maximum or a minimum of the function XC^n -^21 • • • -^n) on the position («!, i?2>- • • -^n) that, in case the second derivatives of the function /"(j^i, ;i:2, . . . . ;i^„) do not all vanish at this position, the homogeneous quadratic form f^\\ dx^dx Iai, a2, an ' must be always negative or always p...ositive for arbitrary values of ^1, /^2, /?„.
THEORY OF THE HOMOGENEOUS QUADRATIC FORMS.
8. There are two kinds of integral homogeneous functions of the second degree, or, as they are usually called, quadratic forms, viz. : I. , formce indefinita;'* which with real values of the vari- ables can become both positive and negative, and that, too, for values of the variables, whose absolute values do not exceed an arbitrarily small quantity; II. , formce definitce, which with real values of the variables have always the same sign.
What to read after Lectures On the Theory of Maxima And Minima of Functions of Several Variables?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, . . . . «n)» and consequently f {^x^, Xi, .... X^ has on the position (ai, a^. , . . . . A„) neither a maximum nor a minimum value.
We therefore have as a second condition for the existence of a maximum or a minimum of the function XC^n -^21 • • • -^n) on the position («!, i?2>- • • -^n) that, in case the second derivatives of the function /"(j^i, ;i:2, . . . . ;i^„) do not all vanish at this position, the homogeneous quadratic form f^\\ dx^dx Iai, a2, an ' must be always negative or always p...ositive for arbitrary values of ^1, /^2, /?„.
THEORY OF THE HOMOGENEOUS QUADRATIC FORMS.
8. There are two kinds of integral homogeneous functions of the second degree, or, as they are usually called, quadratic forms, viz. : I. , formce indefinita;'* which with real values of the vari- ables can become both positive and negative, and that, too, for values of the variables, whose absolute values do not exceed an arbitrarily small quantity; II. , formce definitce, which with real values of the variables have always the same sign.
What to read after Lectures On the Theory of Maxima And Minima of Functions of Several Variables?
You can find similar books in the "Read Also" column, or choose other free books by Harris Hancock to read onlineMoreLess
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