auto-update(nvim): 2025-01-09 16:15:17

documents/by-course/math-6a/course-notes/main.typ

@@ -1,4 +1,5 @@
 #import "./dvd.typ": *
+#import "@preview/cetz:0.3.1"
 
 #show: dvdtyp.with(
   title: "Math 6A Course Notes",
@@ -11,6 +12,50 @@
 
 = Lecture #datetime(day: 7, month: 1, year: 2025).display()
 
-== Parametric curves
+== Review of fundamental concepts
 
+You can parameterize curves.
 
+#example[Unit circle][
+  $
+    x = cos(t) \
+    y = sin(t)
+  $
+]
+
+For an implicit equation
+$ y = f(t) $
+Parameterize it by setting
+$ x = t \ y = f(t) $
+
+Parameterize a line passing through two points $arrow(p)_1$ and $arrow(p)_2$ by
+$ arrow(c)(t) = arrow(p)_1 + t (arrow(p)_2 - arrow(p)_1) $
+
+Take the derivative of each component to find the velocity vector. The
+magnitude of velocity is speed.
+
+#example[
+  $
+    arrow(c)(t) = <5t, sin(t)> \
+    arrow(v)(t) = <5, cos(t)>
+  $
+]
+
+== Polar coordinates
+
+Write a set of Cartesian coordinates in $RR^2$ as polar coordinates instead, by
+a distance from origin $r$ and angle about the origin $theta$.
+
+$ (x,y) -> (r, theta) $
+
+= Lecture #datetime(day: 9, month: 1, year: 2025).display()
+
+== Vectors
+
+A dot product of two vectors is a generalization of the sense of size for a
+point or vector.
+
+#example[
+  How far is the point $x_1, x_2, x_3$ from the origin? \
+  Answer: $x_1^2 + x_2^2 + x_3^2$
+]