Here’s our first set of slides, which gives an overview of the course, and dives into our first example: curvature of curves in the plane.

# Category: Slides

## Slides — The Simplicial Complex

## Slides—Exterior Algebra

Our next lecture will cover one of the basic tools we’ll use throughout the rest of the course: *exterior algebra*. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about *volumes* rather than just vectors. If you felt ok working with things like the cross product and the determinant in your linear algebra/vector calculus courses, this shouldn’t be too big of a leap. (If not, could be a good moment for a review!)

These slides should also be helpful for those who have started on the homework. 🙂

## Slides—Differential Forms in \(R^n\)

## Slides—Exterior Calculus in \(R^n\)

Later this week we’ll start talking about *exterior calculus*, which is a modern language used across differential geometry, mathematical physics, geometric computation… and the rest of our class! :-). Initially this language can look a bit daunting, but by making some connections with familiar ideas from vector calculus (like grad, div, and curl), we’ll see that it’s actually not so bad once you get down to concrete calculations. Slides here:

## Slides — Discrete Exterior Calculus

## Slides — Curves

After our long journey to understand exterior calculus (and its discrete counterpart), we will start putting these tools to work to manipulate real curves and surfaces. This lecture studies smooth and discrete curves, which illustrate many of the important features of geometry embedded in \(\mathbb{R}^n\).