Excerise 12 Section 1 Exercise 17

Describe in words and sketch the level curves for the given c values.

\[f(x,y)=x−y^2 ;c=−2,0,2\]

Solution:

When c=0. \[f(x,y)=x−y^2=c=0, y=±x√x.\]

The horizontal plane at c=0 will intersect the surface following a parabola that is facing right.

With \[c=−2, y=±√X+2\] and with c=2, y=±√x−2, so the intersection will have the same shape (parabola) just shifted by 2.

Demonstarting through 3 level plot

library(ggplot2)

x <- seq(-5,20,0.05)
y <- seq(-5, 5,0.05)
xy <- data.frame(expand.grid(x=x, y=y))
z <- xy$x-xy$y^2
f <- data.frame(xy, z)
ggplot(f, aes(x, y, z=z))+
  geom_raster(aes(fill=z))+
  geom_contour(breaks=c(-2,0,2), colour="white")+
  xlab("x")+ylab("y")

What were the most valuable elements you took away from this course?

Course gave me good understanding of Linear alegebra , calculus and probility. I practiced solution by hand and through R programming. I always found these topics difficult but flexible schedulel and good study material helped me understand better.