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authorChristian Kolset <christian.kolset@gmail.com>2025-05-09 12:35:08 -0600
committerChristian Kolset <christian.kolset@gmail.com>2025-05-09 12:35:08 -0600
commit8c2a961a3a82c5b7f54137d8e8867e0c20e3fbae (patch)
tree61288b1b880bc1a801a4a1fb767b323f85c22102 /tutorials
parent9f3a2c2e9109aadfb4f81257f8e5cfe3da42553b (diff)
Starting tutortial with 1. Theory 2. Engineering and 3. Code
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diff --git a/tutorials/module_3/numerical_differentiation.ipynb b/tutorials/module_3/numerical_differentiation.ipynb
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+++ b/tutorials/module_3/numerical_differentiation.ipynb
@@ -6,6 +6,15 @@
"metadata": {},
"source": [
"# Numerical Differentiation\n",
+ "WHAT IS IT?\n",
+ "Numerical Differentiation is a way we can use \n",
+ "\n",
+ "WHAT IS A DERIVATIVE?\n",
+ "\n",
+ "\n",
+ "HOW CAN WE CALCULATE IT?\n",
+ "\n",
+ "\n",
"We can find the derivate of both tabulated data and a continuous function using a finite difference method, which calculates rise over run of a function. To do this, we must first initalize our independant variable. Let's call this domain $x$ to be a vector such that $\\vec{x}$ =\n",
"$\\pmatrix{x_0, x_1, x_2, ...}$. This domain is also known as the **numerical grid**, is either determined by our data (often time) or can be set by us if it's a continuous function. The **step size** is defined as the spacing between adjacent points on the grid ($h = x_{i+1} - x_i$). Next, let's introduce the dependent variable $y$, this can be any function of $x$.\n",
"\n",
@@ -41,6 +50,7 @@
"id": "9b79e5ba-4b71-4aeb-b3fb-878c2d728f7e",
"metadata": {},
"source": [
+ "---\n",
"## Forward Difference\n",
"The forward difference method takes the point at which we want to find the derivative and the point *forwards* on the grid.\n",
"\n",