In the previous post we reviewed the function of two variables. In this post we will review certain notions regarding the functions of more than 2 variables:
Functions of more than two variables
Level surface of a function of three variables
Limit of a function of three or more variables
Partial derivatives of a function of three variables
Maxima and Minima Problems
In this post we review the following notions:
Critical points in a function of three variables
Local extremum and the saddle point in a function of two variables
Directional derivatives and the gradient
Review the following posts:
Directional derivatives of a function of two variables
Directional derivatives of a function of two variables (continued)
Maximum directional derivative
The next post will be about Critical points, local extremum, absolute maxima and minima
In this post, we are going to review the chain rule for the partial derivatives of z = f(x,y) where x and y are functions of two independent variables u and v. Then we will review the higher order partial derivatives.
Chain rule of a function of two variables x and y where x and y are function of two independent variablesThe Chain rule
Partial derivatives
Objectives:
1) Review level curves and contour maps
2) Limit and continuity
Level curves and contour map
Given a function f(x,y) and a number c of its range, a level curve of the function with two variables f(x, y) for the value c is the set of points that satisfy the equation f(x, y) = c. A graph of the various level curves of a function with two variables is called a contour map.
