Single Variable and Multivariable Calculus

As many of you know, I am learning calculus on my own. I am using a single variable calculus textbook. However, the book is not too clear in terms of why it is called SINGLE VARIABLE. In not so many words, what is the most basic difference between single variable and multivariable calculus?

Re: Single Variable and Multivariable Calculus

You are dealing with functions that accept one variable. Multivariable calculus deals with functions that accept multiple variables. For example, $f(x,y) = x^2+y^2$. Try that out in wolframalpha. It produces a graph in three-dimensional space. Tangents in three-dimensional space can be multi-dimensional. Instead of a tangent line, you start talking about tangent planes (if you are looking at a two-dimensional object in three-dimensional space) or even tangent spaces (if you look at r-dimensional objects in n-dimensional space where $n>r$).

Re: Single Variable and Multivariable Calculus

Quote:

Originally Posted by

**nycmath** As many of you know, I am learning calculus on my own. I am using a single variable calculus textbook. However, the book is not too clear in terms of why it is called SINGLE VARIABLE. In not so many words, what is the most basic difference between single variable and multivariable calculus?

In u = f(x), there is one independent variable, namely x. In w = g(y, z), there are two independent variables, namely y and z. So the difference between univariate and multivariate calculus lies in the number of independent variables.

Re: Single Variable and Multivariable Calculus