Multivariable Calculus
What is Multivariable Calculus?
Multivariable calculus is the study of functions of multiple variables, with the understanding that these functions can be thought of as vectors. In particular, it encompasses the study of partial derivatives, multiple integrals, and vector calculus.
Partial derivatives allow for the determination of how a function changes when one of its variables is changed, while holding the other variables constant. This is especially useful in optimization problems, where the aim is to find the maximum or minimum value of a function.
Multiple integrals extend the concept of a single integral to functions of multiple variables. Essentially, this allows for the calculation of the area or volume under a curve. Vector calculus is the study of how vectors interact with one another, including the analysis of vector fields. This is particularly useful in physics, where the behavior of objects in a given field can be predicted.
Multivariable Calculus Resources
Math Flash Cards
Learn math facts with a wide variety of flash cards and box sets for any math learning needs
Applications of multivariable derivatives
The tools of partial derivatives, the gradient, etc. can be used to optimize and approximate multivariable functions. These are very useful in practice, and to a large extent this is why people study multivariable calculus....
Multivariable calculus
In multivariable calculus, we progress from working with numbers on a line to points in space. It gives us the tools to break free from the constraints of one-dimension, using functions to describe space, and space to describe functions....
Multivariable Calculus Course Assistant
Get help for your Multivariable Calculus class. Solutions for higher-dimensional problems with support for partial derivatives and multiple integrals. Evaluate any numeric expression, or substitute a value for a variable Plot 2D or 3D functions of...
Integrating multivariable functions
There are many ways to extend the idea of integration to multiple dimensions: Line integrals, double integrals, triple integrals, surface integrals, etc. Each one lets you add infinitely many infinitely small values, where those values might come fro...
Multivariable Calculus
Professor Raffi Hovasapian helps you develop your Multivariable Calculus intuition with clear explanations of concepts before reinforcing an understanding of the material through step-by-step examples. See why Dr. Hovasapian is one of the most loved...