update index

Author: GregVernon

contents/index.qmd

@@ -5,7 +5,7 @@ The finite element method pulls together many different mathematical concepts an
 Many of these fine details are rooted in an effort to demonstrate an efficient implementation of the finite element method and, not insignificantly, due to a historical necessity to work with floating-point arithmetic.
 
 And so while there are numerous textbooks that dive immediately into the details of implementation, in this lecture set we will begin by neglecting the concerns of efficiency and pragmatism of floating-point arithmetic for as long as possible -- only turning towards them once we have demonstrated the "big picture" of the finite element method and then desire to improve computational performance.
-Specifically, we will utilize symbolic calculations via the Python Sympy package, which will allow us to initially avoid the topic (and complexity) of quadrature and instead use symbolic integration and effortlessly compute derivatives (e.g., of basis functions) using symbolic operations.
+Specifically, we will utilize symbolic calculations via the [MATLAB Symbolic Toolbox](https://www.mathworks.com/products/symbolic.html), which will allow us to initially avoid the topic (and complexity) of quadrature and instead use symbolic integration and effortlessly compute derivatives (e.g., of basis functions) using symbolic operations.
 Instead of immediately introducing piecewise polynomials, we will begin with a single element and use degree refinement to increase accuracy (at the expense of computational cost).
 Furthermore, rather than using mathematical manipulations common to the derivation of weak formulations used in the finite element method, we will instead present FEM from a change-of-basis point-of-view.
 Only after demonstrating Galerkin's method on a variety of partial differential equations will we gradually apply these "best practices" into our method to improve computational efficiency.