Update documentation

_sources/book/projects/project2.md

@@ -57,7 +57,7 @@ $$ (bb_eq_2)
 where $\hat{x} \equiv x/L$ is a dimensionless (unitless) varible, $\hat{x} \in [0,1]$, and $\lambda = \frac{F L^2}{\gamma}$. (See problem 1.)
 
 ```{note}
-Here we have been a bit sloppy with our notation. Technically, the functions $u(x)$ and $u(\hat{x})$ are two *different* functions, so we should have used e.g. notation like $u_x(x)$ and $u_{\hat{x}}(\hat{x})$. The key thing is that the functions are related as $u_x(x) = u_{\hat{x}}(\hat{x})$.
+Here we have been a bit sloppy with our notation. Technically, due to our change of variable, the functions $u(x)$ and $u(\hat{x})$ are two *different* functions, so we should have used e.g. notation like $u_x(x)$ for the original function and $u_{\hat{x}}(\hat{x})$ for the function after the variable change. The key thing is that the functions are related as $u_{\hat{x}}(\hat{x}(x)) = u_x(x)$.
 ``` 
 
 ----

_sources/lecture_notes/2024/README.md

@@ -64,7 +64,20 @@
   - Code example: `error_analysis`
 - LU decomposition
   - What it is
-  - What it's good for
+  - What it's good for:
+    - Solving matrix equations  
+
+
+### Lecture 7, September 12:
+
+- Continue discussion LU decomposition
+  - What it's good for:
+    - Finding the determinant
+    - Finding the inverse
+  - How: algorithm for determining the L and U matrices
+  - PLU decomposition
+- Overview of topics for Project 2
+- Scaling equations
 
 
 

book/projects/project2.html

@@ -754,7 +754,7 @@ <h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to t
 <p>where <span class="math notranslate nohighlight">\(\hat{x} \equiv x/L\)</span> is a dimensionless (unitless) varible, <span class="math notranslate nohighlight">\(\hat{x} \in [0,1]\)</span>, and <span class="math notranslate nohighlight">\(\lambda = \frac{F L^2}{\gamma}\)</span>. (See problem 1.)</p>
 <div class="admonition note">
 <p class="admonition-title">Note</p>
-<p>Here we have been a bit sloppy with our notation. Technically, the functions <span class="math notranslate nohighlight">\(u(x)\)</span> and <span class="math notranslate nohighlight">\(u(\hat{x})\)</span> are two <em>different</em> functions, so we should have used e.g. notation like <span class="math notranslate nohighlight">\(u_x(x)\)</span> and <span class="math notranslate nohighlight">\(u_{\hat{x}}(\hat{x})\)</span>. The key thing is that the functions are related as <span class="math notranslate nohighlight">\(u_x(x) = u_{\hat{x}}(\hat{x})\)</span>.</p>
+<p>Here we have been a bit sloppy with our notation. Technically, due to our change of variable, the functions <span class="math notranslate nohighlight">\(u(x)\)</span> and <span class="math notranslate nohighlight">\(u(\hat{x})\)</span> are two <em>different</em> functions, so we should have used e.g. notation like <span class="math notranslate nohighlight">\(u_x(x)\)</span> for the original function and <span class="math notranslate nohighlight">\(u_{\hat{x}}(\hat{x})\)</span> for the function after the variable change. The key thing is that the functions are related as <span class="math notranslate nohighlight">\(u_{\hat{x}}(\hat{x}(x)) = u_x(x)\)</span>.</p>
 </div>
 <hr class="docutils" />
 <p><strong>Discretization:</strong> We discretize this by dividing our <span class="math notranslate nohighlight">\(\hat{x}\)</span> range into <span class="math notranslate nohighlight">\(n\)</span> parts, i.e. we will have <span class="math notranslate nohighlight">\(n+1\)</span> points <span class="math notranslate nohighlight">\(\hat{x}_0\)</span>, <span class="math notranslate nohighlight">\(\hat{x}_1\)</span>, <span class="math notranslate nohighlight">\(\ldots\)</span>, <span class="math notranslate nohighlight">\(\hat{x}_{n-1}\)</span>, <span class="math notranslate nohighlight">\(\hat{x}_{n}\)</span>. Thus we have a stepsize</p>

lecture_notes/2024/README.html

@@ -595,6 +595,11 @@ <h1 class="site-logo" id="site-title">FYS3150/FYS4150 course material</h1>
    Lecture 6, September 6:
   </a>
  </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-7-september-12">
+   Lecture 7, September 12:
+  </a>
+ </li>
 </ul>
 
     </nav>
@@ -644,6 +649,11 @@ <h2> Contents </h2>
    Lecture 6, September 6:
   </a>
  </li>
+ <li class="toc-h2 nav-item toc-entry">
+  <a class="reference internal nav-link" href="#lecture-7-september-12">
+   Lecture 7, September 12:
+  </a>
+ </li>
 </ul>
 
                         </nav>
@@ -754,9 +764,32 @@ <h2>Lecture 6, September 6:<a class="headerlink" href="#lecture-6-september-6" t
 <li><p>LU decomposition</p>
 <ul>
 <li><p>What it is</p></li>
-<li><p>What it’s good for</p></li>
+<li><p>What it’s good for:</p>
+<ul>
+<li><p>Solving matrix equations</p></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+</section>
+<section id="lecture-7-september-12">
+<h2>Lecture 7, September 12:<a class="headerlink" href="#lecture-7-september-12" title="Permalink to this headline">#</a></h2>
+<ul class="simple">
+<li><p>Continue discussion LU decomposition</p>
+<ul>
+<li><p>What it’s good for:</p>
+<ul>
+<li><p>Finding the determinant</p></li>
+<li><p>Finding the inverse</p></li>
+</ul>
+</li>
+<li><p>How: algorithm for determining the L and U matrices</p></li>
+<li><p>PLU decomposition</p></li>
 </ul>
 </li>
+<li><p>Overview of topics for Project 2</p></li>
+<li><p>Scaling equations</p></li>
 </ul>
 </section>
 </section>