From: Kyle Spaans <kspaans@student.math.uwaterloo.ca>
Date: Fri, 8 May 2009 15:07:38 +0000 (-0400)
Subject: part of lec 2, beginings of lec 3
X-Git-Url: http://git.csclub.uwaterloo.ca/?p=kspaans%2FMATH237;a=commitdiff_plain;h=1ce54f44c264f58c48f4f7ce868a3232a3a89345

part of lec 2, beginings of lec 3
---

diff --git a/lec02-0506.tex b/lec02-0506.tex
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+\documentclass{article}
+\usepackage{fullpage}
+\usepackage{amsmath}
+\author{Kyle Spaans}
+\date{May 6, 2009}
+\title{Calculus 3 Lecture Notes}
+\begin{document}
+\maketitle
+
+\section*{Lecture 2 -- Various 3D Drawings}
+There are a bunch of quadractic surfaces we can get: ellipsoid, cylinder,
+hyperboloid (``one sheet''), cone, hyperboloid (``two sheets''), up/down
+elliptic paraboloid. To visualize these, look up ``Interactive Gallery of
+Quadractic Surfaces''.
+
+Consider a function \[\frac{x^2}{a^2} + \frac{y^2}{b^2} + l \frac{z^2}{c^2} = k\]
+Let
+\[z = k \Rightarrow \frac{x^2}{a^2} + \frac{y^2}{b^2} = l - \frac{k^2}{c^2}\]
+from which we expect to want positive values on the right-hand-side,
+$\|k\| \le c$.
+
+Blah blah, a bunch of drawing stuff...
+
+\subsection*{Useful Inequalities}
+\begin{itemize}
+\item $\|x + y\| \le \|x\| + \|y\|$
+\item $\|x - y\| \le \|x\| + \|y\|$
+\item $\|x\| - \|y\| \le \|x\| \pm \|y\|$
+\item $\|y\| - \|x\| \le \|x\| \pm \|y\|$
+\item $\|a\| < b \Rightarrow -b < a < b$
+\item $\|a\| < b \Rightarrow -b < a < b$
+\item $\|ab\| = \|a\| \cdot \|b\|$
+\item $\|\frac{a}{b}\| = \frac{\|a\|}{\|b\|}$
+\item $a < b$ does not imply $a^2 < b^2$
+\item Given $0 < x < 1$, if $x^p < x^q \Rightarrow p > q$
+\end{itemize}
+
+\end{document}
diff --git a/lec03-0508.tex b/lec03-0508.tex
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+++ b/lec03-0508.tex
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+\documentclass{article}
+\usepackage{fullpage}
+\usepackage{amsmath}
+\author{Kyle Spaans}
+\date{May 8, 2009}
+\title{Calculus 3 Lecture Notes}
+\begin{document}
+\maketitle
+
+\section*{Lecture 3 -- Limits}
+Limits in two variables.
+
+\end{document}