## Contour Plots

### Introduction:

In the Multivariate Calculus and other Mathematical equations when we want to draw a graph of the given equation we used contour plots

There are various equations that we discussed and implemented using python. Contour plots also called Level Plots. This is a way to show a three-dimensional surface on a two-dimensional plane.

The contour of a two-variable function is a curve that connects points with the same values. A contour line or an isoline of a two-variable function is a curve along which the function has a constant value. The independent variables x and y are usually limited to a regular grid called meshgrid.

It is a cross-section of the 3D graph of the function f (x, y) parallel to the x, y plane.

It represents graphically two predictor variables X Y on the y-axis and a response variable Z as contours. Contours are often called the z-slices or iso-response values. A contour plot is appropriate if you want to see how the value of Z changes with the function of two inputs X and Y,

such that Z = f(X, Y).

For example, I
n geography and meteorology Contour lines are used. In cartography, a contour line connects points of equal height at a certain level, such as the mean sea level.

Matplotlib API contains contour() and contourf() functions.
It draws contour lines and filled contours, respectively.

The functions need three parameters x,y, and z. In this section, discuss both contour() and contourf() functions to draw the graph for the given equations.

contour() - to create contour plots
contourf() - to create filled contour plots

we will discuss both types here.

using contour():-

plt.contour() -This function is used to create contour plots. Three arguments: a grid of x values, a grid of y values, and a grid of z values used here. The x and y values represent positions on the plot, and the z values will be represented through the contour levels.

The most simple way to prepare such information is to use the np.meshgrid function, which builds two-dimensional grids from one-dimensional arrays.

## You can check Plotting using contour in Python. we discuss these equations in detail here.

The list of equations are given below:

1. To plot function f(x,y) = 10-x2-ywhen value of z = [1,6,9]

2. To plot function f(x,y) = x2 + y2  when value of z =  [1,6,9]

3. To plot function f(x,y) = x3-y when value of z = [1,6]

4. To plot function f(x,y) = (x2 + y2 ) /4 when value of z = [1,5,8]

5. To plot function f(x,y) = 4x2+y2  when value of z = [0,1,3,5]

6. To plot function f(x,y) = 2-x-y when value of z = [-6,-4,-2,0,2,4,6]

Using Contourf():-

plt.contourf() -This function is used to create filled contour plots. Three arguments: a grid of x values, a grid of y values, and a grid of z values used here. The x and y values represent positions on the plot, and the z values will be represented through the contour levels. the most simple way to prepare such information is to use the np.meshgrid function, which builds two-dimensional grids from one-dimensional arrays.

## You can check Plotting using contourf() in Python. we discuss these equations in detail here.

The list of equations are given below:

1. To plot function f(x,y) = 10-x2-ywhen value of z = [1,6,9]

2. To plot function f(x,y) = x2 + y2  when value of z =  [1,6,9]

3. To plot function f(x,y) = x3-y when value of z = [1,6]

4. To plot function f(x,y) = (x+ y2 ) /4 when value of z = [1,5,8]

5. To plot function f(x,y) = 4x2+y when value of z = [0,1,3,5]

6. To plot function f(x,y) = 2-x-y when value of z = [-6,-4,-2,0,2,4,6]