week 10 announcement

_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)).