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diff --git a/_weave/lecture02/jl_r4SbWN/optimizing_16_1.png b/_weave/lecture02/jl_r4SbWN/optimizing_16_1.png
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diff --git a/_weave/lecture02/jl_u4mnMm/optimizing_16_1.png b/_weave/lecture02/jl_u4mnMm/optimizing_16_1.png
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diff --git a/_weave/lecture02/optimizing/index.html b/_weave/lecture02/optimizing/index.html
diff --git a/_weave/lecture03/jl_V4oHyq/sciml_35_1.png b/_weave/lecture03/jl_V4oHyq/sciml_35_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_36_1.png → _weave/lecture03/jl_V4oHyq/sciml_36_1.png b/_weave/lecture03/jl_gD21qX/sciml_36_1.png → _weave/lecture03/jl_V4oHyq/sciml_36_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_37_1.png → _weave/lecture03/jl_V4oHyq/sciml_37_1.png b/_weave/lecture03/jl_gD21qX/sciml_37_1.png → _weave/lecture03/jl_V4oHyq/sciml_37_1.png
diff --git a/_weave/lecture03/jl_V4oHyq/sciml_41_1.png b/_weave/lecture03/jl_V4oHyq/sciml_41_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_42_1.png → _weave/lecture03/jl_V4oHyq/sciml_42_1.png b/_weave/lecture03/jl_gD21qX/sciml_42_1.png → _weave/lecture03/jl_V4oHyq/sciml_42_1.png
diff --git a/_weave/lecture03/jl_V4oHyq/sciml_45_1.png b/_weave/lecture03/jl_V4oHyq/sciml_45_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_35_1.png b/_weave/lecture03/jl_gD21qX/sciml_35_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_41_1.png b/_weave/lecture03/jl_gD21qX/sciml_41_1.png
diff --git a/_weave/lecture03/jl_gD21qX/sciml_45_1.png b/_weave/lecture03/jl_gD21qX/sciml_45_1.png
diff --git a/_weave/lecture03/sciml/index.html b/_weave/lecture03/sciml/index.html
diff --git a/_weave/lecture04/dynamical_systems/index.html b/_weave/lecture04/dynamical_systems/index.html
@@ -113,7 +113,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </span><span class='hljl-k'>end</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@time</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-0.000050 seconds &#40;1.00 k allocations: 86.062 KiB&#41;
+0.000054 seconds &#40;1.00 k allocations: 86.062 KiB&#41;
 1000-element Vector&#123;Vector&#123;Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -138,7 +138,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <pre class='hljl'>
 <span class='hljl-nd'>@time</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_push</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-0.012133 seconds &#40;4.50 k allocations: 336.016 KiB, 99.40&#37; compilation tim
+0.011324 seconds &#40;4.50 k allocations: 336.016 KiB, 99.43&#37; compilation tim
 e&#41;
 1000-element Vector&#123;Vector&#123;Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
@@ -164,7 +164,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <p>The first time Julia compiles the function, and the second is a straight call.</p> <pre class='hljl'>
 <span class='hljl-nd'>@time</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_push</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-0.000057 seconds &#40;1.01 k allocations: 99.984 KiB&#41;
+0.000056 seconds &#40;1.01 k allocations: 99.984 KiB&#41;
 1000-element Vector&#123;Vector&#123;Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -190,7 +190,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 <span class='hljl-k'>using</span><span class='hljl-t'> </span><span class='hljl-n'>BenchmarkTools</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-38.372 μs &#40;1001 allocations: 86.06 KiB&#41;
+27.531 μs &#40;1001 allocations: 86.06 KiB&#41;
 1000-element Vector&#123;Vector&#123;Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -215,7 +215,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_push</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-44.223 μs &#40;1006 allocations: 99.98 KiB&#41;
+33.333 μs &#40;1006 allocations: 99.98 KiB&#41;
 1000-element Vector&#123;Vector&#123;Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -248,7 +248,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </span><span class='hljl-k'>end</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_matrix</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-69.190 μs &#40;2001 allocations: 179.66 KiB&#41;
+66.845 μs &#40;2001 allocations: 179.66 KiB&#41;
 3×1000 Matrix&#123;Float64&#125;:
  1.0  0.8   0.752    0.80096   0.920338   …   1.98201    1.67886    1.4744
  0.0  0.56  0.9968   1.39785   1.81805        0.466287   0.656559   0.85300
@@ -265,7 +265,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </span><span class='hljl-k'>end</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_matrix_view</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-34.535 μs &#40;1002 allocations: 101.61 KiB&#41;
+34.956 μs &#40;1002 allocations: 101.61 KiB&#41;
 3×1000 Matrix&#123;Float64&#125;:
  1.0  0.8   0.752    0.80096   0.920338   …   1.98201    1.67886    1.4744
  0.0  0.56  0.9968   1.39785   1.81805        0.466287   0.656559   0.85300
@@ -282,7 +282,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </span><span class='hljl-k'>end</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save_matrix_resize</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-1.198 ms &#40;2318 allocations: 11.65 MiB&#41;
+1.043 ms &#40;2318 allocations: 11.65 MiB&#41;
 3×1000 Matrix&#123;Float64&#125;:
  1.0  0.8   0.752    0.80096   0.920338   …   1.98201    1.67886    1.4744
  0.0  0.56  0.9968   1.39785   1.81805        0.466287   0.656559   0.85300
@@ -388,15 +388,15 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <p>which would compute <code>f</code> and then take the values of <code>du</code> and update <code>u</code> with them, but that&#39;s 3 extra operations than required, whereas <code>u,du &#61; du,u</code> will change <code>u</code> to be a pointer to the updated memory and now <code>du</code> is an &quot;empty&quot; cache array that we can refill &#40;this decreases the computational cost by ~33&#37;&#41;. Let&#39;s see what the cost is with this newest version:</p> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-37.210 μs &#40;1000 allocations: 78.12 KiB&#41;
+25.919 μs &#40;1000 allocations: 78.12 KiB&#41;
 3-element Vector&#123;Float64&#125;:
   1.4744010677851374
   0.8530017039412324
  20.62004063423844
 </pre> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_mutate</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-7.301 μs &#40;3 allocations: 240 bytes&#41;
+7.291 μs &#40;3 allocations: 240 bytes&#41;
 3-element Vector&#123;Float64&#125;:
   1.4744010677851374
   0.8530017039412324
@@ -445,7 +445,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,</span><span class='hljl-nd'>@SVector</span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-8.766 μs &#40;2 allocations: 23.48 KiB&#41;
+8.850 μs &#40;2 allocations: 23.48 KiB&#41;
 1000-element Vector&#123;SVector&#123;3, Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -511,7 +511,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,</span><span class='hljl-nd'>@SVector</span><span class='hljl-p'>[</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>],</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-6.723 μs &#40;2 allocations: 23.48 KiB&#41;
+6.721 μs &#40;2 allocations: 23.48 KiB&#41;
 1000-element Vector&#123;SVector&#123;3, Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;
@@ -536,7 +536,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </pre> <p>And we can get down to non-allocating for the loop:</p> <pre class='hljl'>
 <span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system</span><span class='hljl-p'>(</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,</span><span class='hljl-nd'>@SVector</span><span class='hljl-p'>([</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>]),</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-6.502 μs &#40;1 allocation: 32 bytes&#41;
+6.496 μs &#40;1 allocation: 32 bytes&#41;
 3-element SVector&#123;3, Float64&#125; with indices SOneTo&#40;3&#41;:
   1.4744010677851374
   0.8530017039412324
@@ -552,7 +552,7 @@ <h1 class=title >How Iteration Works, An Introduction to Discrete Dynamics</h1>
 </span><span class='hljl-n'>u</span><span class='hljl-t'> </span><span class='hljl-oB'>=</span><span class='hljl-t'> </span><span class='hljl-nf'>Vector</span><span class='hljl-p'>{</span><span class='hljl-nf'>typeof</span><span class='hljl-p'>(</span><span class='hljl-nd'>@SVector</span><span class='hljl-p'>([</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>]))}(</span><span class='hljl-n'>undef</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span><span class='hljl-t'>
 </span><span class='hljl-nd'>@btime</span><span class='hljl-t'> </span><span class='hljl-nf'>solve_system_save!</span><span class='hljl-p'>(</span><span class='hljl-n'>u</span><span class='hljl-p'>,</span><span class='hljl-n'>lorenz</span><span class='hljl-p'>,</span><span class='hljl-nd'>@SVector</span><span class='hljl-p'>([</span><span class='hljl-nfB'>1.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>,</span><span class='hljl-nfB'>0.0</span><span class='hljl-p'>]),</span><span class='hljl-n'>p</span><span class='hljl-p'>,</span><span class='hljl-ni'>1000</span><span class='hljl-p'>)</span>
 </pre> <pre class=output >
-6.498 μs &#40;0 allocations: 0 bytes&#41;
+6.500 μs &#40;0 allocations: 0 bytes&#41;
 1000-element Vector&#123;SVector&#123;3, Float64&#125;&#125;:
  &#91;1.0, 0.0, 0.0&#93;
  &#91;0.8, 0.56, 0.0&#93;

diff --git a/...re04/jl_lshY2p/dynamical_systems_11_1.png → ...re04/jl_fP27tE/dynamical_systems_11_1.png b/...re04/jl_lshY2p/dynamical_systems_11_1.png → ...re04/jl_fP27tE/dynamical_systems_11_1.png