Cleaned up subheadings.

Author: adowling2

fall2023/syllabus.md

@@ -142,7 +142,7 @@ If there is an extenuating circumstance, please email the instructor with CBE 60
 We will use Python 3 in this class. You have three options for using Python:
 1. (Recommended for Most People.) Use Google Colab, which allows you to complete all assignments from any internet-accessible computer.
 2. (Recommended for Advanced Users.) Install [anaconda3](https://www.anaconda.com/download/) on your computer. Anaconda is a free distribution of Python that includes standard packages for data analysis and scientific computing. You must install popular packages such as `numpy`, `scipy`, `pandas`, and `matplotlib`.
-3. Use anaconda3 installed on any ESC-maintained computer, e.g., B19 in Fitzpatrick Hall.
+3. Use anaconda3 installed on any ESC-maintained computer.
 
 ## Inclusiveness, Mental Health, and Disabilities
 

notebooks/04-dev/Linear-Algebra-in-Numpy.ipynb

@@ -86,7 +86,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #1\n",
+    "### Matrix Multiplication\n",
     "\n",
     "Multiplying two matrices $A$ $\\in$ $\\mathbb{R}^{n \\times m}$ and $B$ $\\in$ $\\mathbb{R}^{m \\times p}$ leads to the product $C \\in$ $\\mathbb{R}^{n \\times p}$ with elements $ \\mathbf{\\{C\\}_{ij}}$ = $\\sum_{k=1}^m  \\mathbf{\\{A\\}_{ik}}  \\mathbf{\\{B\\}_{kj}}$. This operation is defined only if the number of columns in $A$ and rows of $B$ is the same."
    ]
@@ -178,7 +178,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #2\n",
+    "### Matrix Transpose\n",
     "\n",
     "The *transpose* of $A$ $\\in$ $\\mathbb{R}^{n \\times m}$ is $A^T$ $\\in$ $\\mathbb{R}^{m \\times n}$ with the rows and columns of A interchanged, i.e.$ \\mathbf{\\{A^T\\}_{ij}} =  \\mathbf{\\{A\\}_{ji}}$."
    ]
@@ -224,11 +224,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #3\n",
+    "### Symmetric Matrix\n",
     "\n",
     "A *symmetric* matrix $A$ $\\in$ $\\mathbb{R}^{n \\times n}$ satisfies $A = A^T$.\n",
     "\n",
-    "## Property #4\n",
+    "### Diagonal Matrix\n",
     "\n",
     "A *diagonal* matrix $A$ $\\in$ $\\mathbb{R}^{n \\times n}$ has nonzero elements only on the diagonal, i.e., $ \\mathbf{\\{A\\}_{ij}} = 0, i \\neq j$."
    ]
@@ -279,7 +279,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #5\n",
+    "### Identity Matrix\n",
     "\n",
     "The *identity* matrix $I \\in \\mathbb{R}^{n \\times n}$ is defined as \n",
     "\n",
@@ -381,7 +381,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #1\n",
+    "### Determinant of Matrix Product\n",
     "\n",
     "det($AB$) = det($A$)det($B$)"
    ]
@@ -424,7 +424,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #2\n",
+    "### Determinant of Transpose\n",
     "\n",
     "det($A$) = det($A^T$)"
    ]
@@ -467,9 +467,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #3\n",
+    "### Determinant with Scalar Product\n",
     "\n",
-    "For an $n \\times n$ matrix with scalar $\\alpha$, det($\\alpha A$) = $\\alpha^n$det($A$)"
+    "For an $n \\times n$ matrix with scalar $\\alpha$, det($\\alpha A$) = $\\alpha^n$ det($A$)"
    ]
   },
   {
@@ -511,7 +511,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Property #4\n",
+    "### Determinant of Identify Matrix\n",
     "\n",
     "For an identity matrix $I$, det($I$) = 1."
    ]
@@ -622,7 +622,7 @@
     "tags": []
    },
    "source": [
-    "## Matrix Rank Definition\n"
+    "### Matrix Rank Definition\n"
    ]
   },
   {
@@ -642,7 +642,7 @@
     "tags": []
    },
    "source": [
-    "## Practice Activities\n"
+    "### Practice Activities\n"
    ]
   },
   {
@@ -777,7 +777,7 @@
     "tags": []
    },
    "source": [
-    "## Inverse of a Matrix Defnition\n",
+    "### Inverse of a Matrix Defnition\n",
     "\n",
     "**Rerference:** Section 2.2 of *Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes*, L. Biegler (2010)"
    ]
@@ -796,7 +796,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Practice Activities"
+    "### Practice Activities"
    ]
   },
   {
@@ -984,7 +984,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Explicit Inverse\n",
+    "### Explicit Inverse\n",
     "\n",
     "Calculate $x$ by explicitly using $A_l^{-1}$. Hint: Use linalg.inv( )."
    ]
@@ -1030,7 +1030,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## LU Decomposition\n"
+    "### LU Decomposition\n"
    ]
   },
   {
@@ -1129,7 +1129,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Is P orthogonal?"
+    "### Is P orthogonal?"
    ]
   },
   {
@@ -1181,7 +1181,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## MATLAB\n",
+    "### MATLAB\n",
     "\n",
     "Defines LU decomposition as follows:\n",
     "\n",
@@ -1260,7 +1260,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## SciPy\n",
+    "### SciPy\n",
     "\n",
     "Defines LU decomposition as:\n",
     "\n",
@@ -1344,7 +1344,7 @@
     "tags": []
    },
    "source": [
-    "## Verify our answer with `linalg.solve`\n",
+    "### Verify our answer with `linalg.solve`\n",
     "\n",
     "Solve the linear system using linalg.solve"
    ]
@@ -1464,7 +1464,7 @@
     "tags": []
    },
    "source": [
-    "## Eigenvalues/Eigenvectors Definition"
+    "### Eigenvalues/Eigenvectors Definition"
    ]
   },
   {
@@ -1489,7 +1489,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Practice Activities"
+    "### Practice Activities"
    ]
   },
   {
@@ -1760,7 +1760,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Vector Norm Properties"
+    "### Vector Norm Properties"
    ]
   },
   {
@@ -1780,7 +1780,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## *P*-norm Properties"
+    "### *P*-norm Properties"
    ]
   },
   {
@@ -1888,7 +1888,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Additional Matrix Norms"
+    "### Additional Matrix Norms"
    ]
   },
   {
@@ -2015,7 +2015,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Frobenius Norm"
+    "### Frobenius Norm"
    ]
   },
   {