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George Weigt 2007-04-26 16:04:54 -07:00
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commit ef7d77a450
1 changed files with 18 additions and 15 deletions

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man.tex
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@ -1,7 +1,7 @@
\documentclass[12pt,openany]{report}
\title{Eigenmath Manual}
\author{George Weigt}
\date{April 22, 2007}
\date{April 26, 2007}
\pagestyle{headings}
\usepackage{graphicx}
@ -405,7 +405,7 @@ The adjunct of a matrix is related to the cofactors as follows.
\medskip
\verb$C$
$$\left(\matrix{d&-c\cr -b&a}\right)$$
$$C=\left(\matrix{d&-c\cr -b&a}\right)$$
\medskip
\verb$adj(A)-transpose(C)$
@ -527,34 +527,37 @@ $$0$$
\label{integral}
\noindent
The function integral($f,x$) returns the integral of $f$ with respect to $x$.
$integral(f,x)$ returns the integral of $f$ with respect to $x$.
The $x$ can be omitted for expressions in $x$.
A multi-integral can be obtained by extending the argument list.
\medskip
{\tt integral(x{\char94}2)}
\verb$integral(x^2)$
$${1\over3}x^3$$
{\tt integral(x{\char94}2,x,x)}
\verb$integral(x*y,x,y)$
$${1\over4}x^2y^2$$
$${1\over12}x^4$$
\newpage
\noindent
\includegraphics[scale=0.5]{semicircle.png}
\medskip
\noindent
The eval function can be used to compute definite integrals.
The following example computes the integral of $x^2$
over a half circle.
A definite integral can be obtained with the help of $eval$.
The following example computes the integral of $f=x^2$
over the domain of a semicircle.
For each $x$ along the abscissa, $y$ ranges from 0 to $\sqrt{1-x^2}$.
\medskip
{\tt I=integral(x{\char94}2,y)}
\verb$I=integral(x^2,y)$
{\tt I=eval(I,y,sqrt(1-x{\char94}2))-eval(I,y,0)}
\verb$I=eval(I,y,sqrt(1-x^2))-eval(I,y,0)$
{\tt I=integral(I,x)}
{\tt eval(I,x,1)-eval(I,x,-1)}
\verb$I=integral(I,x)$
\verb$eval(I,x,1)-eval(I,x,-1)$
$${1\over8}\pi$$
\newpage