Plotting contour diagrams? how do i do that?

[starsiege]

im learning about contour diagrams in my calculus text but I am totally confused as to how one should start drawing those plots?

for example f(x,y) = x+y
then its supposed to go like

x+y = c
y = -x +c

^^i can see that the slope is 1
but how do i plot this graph?..im told that i should give values to c and plot it...but I am totally confused as to how i should do that (the answer is there too but i donno how they drew the graph/which method they used to draw it)



also I am totally confused as to how one can draw a contour diagram from the data given in a table

table of values for f(x,y) = X^2 - Y^2

i have attached the table here too


thank you

 

[John Creighto]

Connect the dots.

 

[starsiege]

well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

 

[John Creighto]

well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

Well, your curves are easy. Your first example is a straight line so you can use slope and intercept. Your second example looks like a hyperbolic functions so you could find the asymptotes and the point where it crosses the axis.

In general though it is not much different then plotting any function. Pick some x values, find the corresponding y values and plot. If you can find roots, asymptotes and extreme values that can reduce the number of points you need to find. You could use a graphing calculator if you are having trouble.

 

[pkleinod]

well..my main issue is how to find each separate contour line?

if i were to draw one line which dots/values should i use

Here is one procedure to find approximate dots from values in a table: Look along
each row and each column in the table to find the "box" through which the contour
might pass. Then do a linear interpolation to find the coordinates. Then connect the dots.

For example, suppose you look for the contour -1 in your table. Looking along the first
row in your table, this contour would have approximate dots at the
coordinates (-2.8, 3.0) and (2.8,3.0). Now do this for every row and
every column, collect the dots and connect them.

Now, write a computer programme to do this automatically and you will see that it is not as easy as the above instructions seem!

 

[HallsofIvy]

im learning about contour diagrams in my calculus text but I am totally confused as to how one should start drawing those plots?

for example f(x,y) = x+y
then its supposed to go like

x+y = c
y = -x +c

^^i can see that the slope is 1

I would hope that you could see the slope was -1!

but how do i plot this graph?..im told that i should give values to c and plot it...but I am totally confused as to how i should do that (the answer is there too but i donno how they drew the graph/which method they used to draw it)

Surely, if you are looking at functions of more than 1 variable, you learned long ago that the graph of y= -x+ c is a straight line! You only need two points to determine a straight line. when x= 0, y= c and when y= 0, x= c. Draw the straight line through the intercepts (0, c) and (c, 0). Do that for several different values of c.

also I am totally confused as to how one can draw a contour diagram from the data given in a table

table of values for f(x,y) = X^2 - Y^2

i have attached the table here too


thank you

Why make a table? That's what you do with functions you've never seen before! That's what a calculator does! You are supposed to be smarter than a calculator.

For any c, f(x,y)= c is x²- y²= c. You should recognise immediately that that is a hyperbola. If c is positive, the vertices are at (\sqrt{c}, 0) and (-\sqrt{c},0) and the asymptotes are the lines y= x+ \sqrt{c} and y= -x+ \sqrt{c}. If c is negative, the vertices are at (0, \sqrt{c}) and (0, -\sqrt{c}) and the same asymptotes as above. If c= 0, the asymptotes are the graph. It should take you about 3 minutes to draw several of those contours.