Dive into Calculus : Vectors and Matrices

This course covers matrices and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

Topics include vectors and matrices, parametric curves, partial derivatives, double and triple integrals, and vector calculus in 2- and 3-space.

As its name suggests, multivariable calculus is the extension of calculus to more than one variable. That is, in single variable calculus you study functions of a single independent variable.In multivariable calculus we study functions of two or more independent variables.

These functions are interesting in their own right, but they are also essential for describing the physical world.

Many things depend on more than one independent variable. Here are just a few:

1. In thermodynamics pressure depends on volume and temperature.

2. In electricity and magnetism, the magnetic and electric fields are functions of the three space variables (x,y,z) and one time variable t.

3. In economics, functions can depend on a large number of independent variables, e.g., a manufacturer's cost might depend on the prices of 27 different commodities.

4. In modeling fluid or heat flow the velocity field depends on position and time.

Single variable calculus is a highly geometric subject and multivariable calculus is the same, maybe even more so. In your calculus class you studied the graphs of functions y=f(x) and learned to relate derivatives and integrals to these graphs. In this course we will also study graphs and relate them to derivatives and integrals. One key difference is that more variables means more geometric dimensions. This makes visualization of graphs both harder and more rewarding and useful.

By the end of the course you will know how to differentiate and integrate functions of several variables. In single variable calculus the Fundamental Theorem of Calculus relates derivatives to integrals. We will see something similar in multivariable calculus.