Notebook giving examples of use of partial derivatives, maximization and contour plotting---useful for material in Chapter 4 of Boas Partial derivatives---using "D" Partial deriv w.r.t. x D@Sin@x + y^2D,xD CosAx + y 2 E and w.r.t. y D@Sin@x + y^2D,yD 2yCosAx + y 2 E or both together D@Sin@x + y^2D, 88x, y<,1<D 9CosAx + y 2 E,2yCosAx + y 2 E= Second derivatives (partial w.r.t x first, then mixed partial, then mixed partial again, then second wr.t. y) D@Sin@x + y^2D, 88x, y<,2<D MatrixForm - Sin@x + y 2 D - 2ySin@x + y 2 D - 2ySin@x + y 2 D 2 Cos@x + y 2 D - 4y 2 Sin@x + y 2 D Taylor series with more than one variable Expanding about the origin: The O[y]^7 etc. terms tell us the size of the next terms in the expansion
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Notebook giving examples of
use of partial derivatives,
maximization and contour
plotting---useful for material
in Chapter 4 of Boas
Partial derivatives---using "D"
Partial deriv w.r.t. x
D@Sin@x + y^2D, xD
CosAx + y2E
and w.r.t. y
D@Sin@x + y^2D, yD
2 y CosAx + y2E
or both together
D@Sin@x + y^2D, 88x, y<, 1<D
9CosAx + y2E, 2 y CosAx + y
2E=
Second derivatives (partial w.r.t x first, then mixed partial, then mixed partial again, then second wr.t. y)