From 8e16f97bfbbbcc7ab046a8e5e69b1f8588f3e193 Mon Sep 17 00:00:00 2001
From: eggy <danielchen04@hotmail.ca>
Date: Tue, 10 Jan 2023 11:38:11 -0500
Subject: [PATCH] chore: add starter content

---
 docs/1b/ece106.md  | 39 +++++++++++++++++++++++++++++++++++++++
 docs/1b/ece108.md  |  1 +
 docs/1b/ece140.md  |  3 +++
 docs/1b/math119.md |  4 ++++
 4 files changed, 47 insertions(+)
 create mode 100644 docs/1b/ece140.md

diff --git a/docs/1b/ece106.md b/docs/1b/ece106.md
index dc3064d..6d4dede 100644
--- a/docs/1b/ece106.md
+++ b/docs/1b/ece106.md
@@ -1,3 +1,42 @@
 # ECE 106: Electricity and Magnetism
 
+## MATH 117 review
 
+!!! definition
+    A definite integral is composed of:
+    
+    - the **upper limit**, $b$,
+    - the **lower limit**, $a$,
+    - the **integrand**, $f(x)$, and
+    - the **differential element**, $dx$.
+
+$$\int^b_a f(x)\ dx$$
+
+The original function **cannot be recovered** from the result of a definite integral unless it is known that $f(x)$ is a constant.
+
+## N-dimensional integrals
+
+Much like how $dx$ represents an infinitely small line, $dx\cdot dy$ represents an infinitely small rectangle. This means that the surface area of an object can be expressed as:
+
+$$dS=dx\cdot dy$$
+
+Therefore, the area of a function can be expressed as:
+
+$$S=\int^x_0\int^y_0 dy\ dx$$
+
+where $y$ is usually equal to $f(x)$, changing on each iteration.
+
+!!! example
+    The area of a circle can be expressed as $y=\pm\sqrt{r^2-x^2}$. This can be reduced to $y=2\sqrt{r^2-x^2}$ because of the symmetry of the equation.
+    
+    $$
+    \begin{align*}
+    A&=\int^r_0\int^{\sqrt{r^2-x^2}}_0 dy\ dx \\
+    &=\int^r_0\sqrt{r^2-x^2}\ dx
+    \end{align*}
+    $$
+
+!!! warning
+    Similar to parentheses, the correct integral squiggly must be paired with the correct differential element.
+
+## Cartesian coordinates
diff --git a/docs/1b/ece108.md b/docs/1b/ece108.md
index d628bb3..73d77e0 100644
--- a/docs/1b/ece108.md
+++ b/docs/1b/ece108.md
@@ -1,2 +1,3 @@
 # ECE 108: Discrete Math 1
 
+## Truth tables
diff --git a/docs/1b/ece140.md b/docs/1b/ece140.md
new file mode 100644
index 0000000..2242b97
--- /dev/null
+++ b/docs/1b/ece140.md
@@ -0,0 +1,3 @@
+# ECE 140: Linear Circuits
+
+## Voltage, current, and resistance
diff --git a/docs/1b/math119.md b/docs/1b/math119.md
index 70cb124..c113a40 100644
--- a/docs/1b/math119.md
+++ b/docs/1b/math119.md
@@ -1 +1,5 @@
 # MATH 119: Calculus 2
+
+## Multivariable functions
+
+### Sketching multivariable functions