author Kyle Spaans Fri, 8 May 2009 15:07:38 +0000 (11:07 -0400) committer Kyle Spaans Fri, 8 May 2009 15:07:38 +0000 (11:07 -0400)
 lec02-0506.tex [new file with mode: 0644] patch | blob lec03-0508.tex [new file with mode: 0644] patch | blob

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
+
+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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+\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}