Calculus

We found 8 articles

Demystifying the cross product
The cross product is ubiquitous throughout linear algebra and vector calculus. It plays a major role in transformations of coordinate systems and is intimately related to the determinant. In fact, its definition in linear algebra courses is often given in terms of the determinant, which can seem mysterious and arbitrary. In this post, I want to ...
The Intermediate Value Theorem explained by everyday life
Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.
Where do Taylor series come from and why do we learn about them?
Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by
What is implicit differentiation and how does it work?
One topic that seemed a bit mysterious and magic to me when I first learned calculus was implicit differentiation. In this post, we’ll start by reviewing some examples of implicit differentiation and then discuss why implicit differentiation works.
But what is “dx” really? Calculus terms explained
The symbol “dx” comes up everywhere in calculus. For example:
An application of calculus: finding optimal road networks
Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.
Revolving curves to make solids
Have you ever wondered where the formulas for volumes that you studied way back in geometry come from?
Converting Polar to Cartesian Equations in Five Easy Steps
If polar equations have you second-guessing your future as a nuclear physicist, fret not! Almost every pre-calculus student I have tutored has struggled here, and it isn’t surprising at all. Remember the first time you saw an equation and were introduced to these strange x and y variables? It may seem like second nature now, but you were learning ...
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