From: Kyle Spaans 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 new file mode 100644 index 0000000..7020919 --- /dev/null +++ b/lec02-0506.tex @@ -0,0 +1,38 @@ +\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 new file mode 100644 index 0000000..4e04e84 --- /dev/null +++ b/lec03-0508.tex @@ -0,0 +1,13 @@ +\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}