\documentclass[11pt]{article}

\usepackage[psamsfonts]{amsfonts}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{fullpage}
\usepackage{array}
\usepackage{supertabular}

\renewcommand{\rmdefault}{\sfdefault}

\newcounter{lecturectr}
\newcommand{\lecture}
     {\addtocounter{lecturectr}{1} %
       Day \arabic{lecturectr}}

\newcommand{\ds}{\displaystyle}

\title{Mathematics 15.3 -- Term Syllabus}
\author{The Undergraduate Program Committee}
\date{\today}
\pagestyle{empty}

\begin{document}
\maketitle
\vskip -.2in

\thispagestyle{empty}
\newcommand{\PreserveBackslash}[1]{\let\temp=\\#1\let\\=\temp}
\let\PBS=\PreserveBackslash 
\renewcommand{\arraystretch}{2}
%\setlength{\extrarowheight}{2pt}
\setlength{\tabcolsep}{8pt}
\tabletail{\hline}

\hskip-.3in
\begin{supertabular}
{|l
|>{\PBS\raggedright\hspace{0pt}}p{.28\textwidth}
|>{\PBS\raggedright\hspace{0pt}\parskip=5pt}p{.55\textwidth}|}
\hline
\textbf{Lecture}
&\textbf{Topics/Sections}
&\textbf{Some Standard Examples/Concepts}
\\ \hline
\lecture
&
&Overview of expectations for course, 
revised syllabus and discussion.  Circuit problem. 
\\ \hline
\lecture
&
&Electric circuits.  Series solution to first order ODEs.
\\ \hline
\lecture
&
&Taylor Series, geometric series.
\\ \hline
\lecture
&
&Discussion of homework. Absolute vs conditional convergence. 
Integral tests.
\\ \hline
\lecture
&
&Ratio test, comparison test.
\\ \hline
\lecture
&
&The mathematician's view of simple closed circuits. 
Reality versus its model.  (General second order ODE with 
constant coefficients. Homogeneous and inhomogeneous. 
Main theorem of ODE's.)
\\ \hline
\lecture
&
&Matrix version of the circuit problem. 
Comparison with diagonal matrices.  Exponential of matrix.
\\ \hline
\lecture
&
&Matrix algebra, properties of a matrix not dependent on coordinates, 
computation of eigenvalues.  Solve Wednesday's circuit problem.
\\ \hline
\lecture
&
&Relax and review.
\\ \hline
\lecture
&
&The heat equation on a wire.  Setting it up.
\\ \hline
\lecture
&
&Turning the heat equation into an eigenvalue problem.  
Possible solutions.
\\ \hline
\lecture
&
&Student presentation of models.  Three ways to look at a chime.
\\ \hline

\lecture
&
&General discussion of Fourier series.  Idea of vector 
spaces of functions, linear independence, completeness, etc.
\\ \hline
\lecture
&
&Discussion of colloquium with Beth Bradley. 
[on an application of the wave equation.]
\\ \hline
\lecture
&
&Bring your solutions to the wave equation for your chime. 
Student presentations of solutions.  Oscilloscope will do 
Fourier analysis and tell you what frequencies are present.
\\ \hline
\lecture
&
&Guest demo:  Building guitars using the wave equation. 
The round drumhead. Mook's vibrating membrane.
\\ \hline
\lecture
&
&Guest presentation: analysis of oboe sounds and questions 
for speaker. In class modelling problem: human voice.
\\ \hline
\lecture
&
&Relax and review.
\\ \hline
\lecture
&
&Set up of Schrodinger's equation.  Probability distributions.  
Discussion of symmetry issues for that and the spring model.  
Idea of symmetry group.
\\ \hline
\lecture
&
&Separation of variables.  Eigenvalue problem associated to hydrogen.
\\ \hline
\lecture
&
&The group of rotations, invariant subspaces, representations.
\\ \hline
\lecture
&
&Student presentation of homework problems
\\ \hline
\lecture
&
&Schur's lemma, intro to spherical polynomials
\\ \hline
\lecture
&
&the spherical polynomials, intro to last assignment
\\ \hline


\lecture
&
&Homework: compute the allowable eigenvalues for hydrogen.  
Can you adjust parameters so that they match the real ones?
\\ \hline
\lecture
&
&Demo:  look at Balmer lines.  Discussion of final exam.
\\ \hline
\lecture
&
&Surveys,--pass out take-home;
collect homework from Schrodinger's equation (all).
\\ \hline
\lecture
&
&
\\ \hline

\end{supertabular}


\end{document}





























