Multivariable calculus

Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.
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Partial derivatives, gradient, divergence, curl

Thinking about forms of derivatives in multi-dimensions and for vector-valued functions: partial derivatives, gradient, divergence and curl.
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All content in “Partial derivatives, gradient, divergence, curl”

Partial derivatives

Let's jump out of that boring (okay, it wasn't THAT boring) 2-D world into the exciting 3-D world that we all live and breathe in. Instead of functions of x that can be visualized as lines, we can have functions of x and y that can be visualized as surfaces. But does the idea of a derivative still make sense? Of course it does! As long as you specify what direction you're going in. Welcome to the world of partial derivatives!


Ever walk on hill (or any wacky surface) and wonder which way would be the fastest way up (or down). Now you can figure this out exactly with the gradient.


Is a vector field "coming together" or "drawing apart" at a given point in space. The divergence is a vector operator that gives us a scalar value at any point in a vector field. If it is positive, then we are diverging. Otherwise, we are converging!


Curl measures how much a vector field is "spinning". A bit of a pain to calculate, but could come in handy when we work with Stokes' and Greens' theorems later on.