From 18a89cefb61310641021ca0ea303529365dee23e Mon Sep 17 00:00:00 2001 From: Oliver Beckstein Date: Mon, 25 Mar 2024 09:20:12 -0700 Subject: [PATCH] week 10 announcement --- _announcements/week-10.md | 25 +++++++++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100644 _announcements/week-10.md diff --git a/_announcements/week-10.md b/_announcements/week-10.md new file mode 100644 index 0000000..1b14004 --- /dev/null +++ b/_announcements/week-10.md @@ -0,0 +1,25 @@ +--- +title: Week 10 Announcement +week: 10 +date: 2024-03-25 +--- + +A lot of physics can be formulated in the language of **linear +algebra** with vectors and matrices. Examples are problems in solid +body mechanics and quantum mechanics. Three commonly encountered +requirements are to find solutions to a matrix equation $$\mathsf{A} +\mathbf{x} = \mathbf{b}$$, finding the inverse of a matrix +$$\mathsf{A}^{-1}$$, and solving the eigenproblem $$\mathsf{A} +\mathbf{v}_i = \lambda_i \mathbf{v}_i$$. Instead of writing our own +solvers, we will learn how to use the routines in +[numpy.linalg](https://numpy.org/doc/stable/reference/routines.linalg.html), +NumPy's linear algebra module, which provides efficient and +well-tested algorithm. + +A matrix solver is also needed for generalizing the *Newton-Raphson* +[root finding algorithm from the last module]({{ site.baseurl }}{% +link modules/root_finding/Root_finding.md %}) to arbitrary +dimensions. We will develop a general Newton-Raphson solver (and also +learn how to calculate the Jacobian using partial derivatives, based +on the central difference algorithm from the [lesson on +differentiation](modules/ODEs/differentiation.md)).