Here's a summary of what you should know going into multivariable calculus.
Welcome to multivariable calculus! There are a lot of exciting and fundamentally visual topics ahead. In order to best understand these ideas, there are two main prerequisites we recommend before starting:
- Single-variable calculus (such as AP Calculus AB/BC)
- Vectors and matrices
If you've already seen these, but you still want to quickly brush up on the essentials before beginning multivariable calculus, then this article is here to highlight a few of the more crucial skills that you should have going into the course.
The biggest prerequisite for multivariable calculus is good old single-variable calculus. (Now that we're in multivariable land, we need this new adjective "single-variable" to keep track of which version we're talking about.) Specifically, be sure that you are comfortable with the following broad concepts:
- Differentiation (including the power rule, product rule, quotient rule, and chain rule)
- What the derivative represents
- Critical points and optimization
- Integration and the Fundamental Theorem of Calculus
- Parametric equations and polar coordinates
Feel free to spend a little time reviewing any of these topics. The preparation will pay off as we get into multivariable calculus.
Vectors and matrices
The second big prerequisite for multivariable calculus is vectors and matrices. Both of these topics are super useful, because they let us talk about multi-dimensional coordinates and sometimes entire transformations with just one object, which we can then manipulate.
Here are the six concepts that we'll need:
These concepts aren't always taught prior to taking single-variable calculus, so it's completely fine if some of them feel new. Whether you need to learn it for the first time or just want to brush up, each concept links to a review article that introduces the idea and gives practice using it. If you still feel uncomfortable after reading a review article, it will have links to other content that will help you learn.
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