Commit 7ac475c2 by Jim Hefferon

### new cover

parent 2f5b2f80
 ... ... @@ -124,4 +124,7 @@ General: Jad Nohra, Tom Lahore, Lopatin Vladimir Many corrections, large and small. 2014-Jan-08 Mana Borwornpadungkitti Correction to exercise answer. \ No newline at end of file Mana Borwornpadungkitti Correction to exercise answer. 2014-Feb-21 Mana Borwornpadungkitti Number of corrections to homogeom. \ No newline at end of file
asy/axes.asy 0 → 100644
 ... ... @@ -20513,12 +20513,12 @@ sage: p.save('bridges.pdf') \includegraphics{ch3.96} \end{center} For instance, the effect of $H$ on the unit vector whose angle with the $x$-axis is $\pi/3$ is this. the $x$-axis is $\pi/6$ is this. \begin{center} \includegraphics{ch3.97} \end{center} Verifying that the resulting vector has unit length and forms an angle of $-\pi/6$ with the $x$-axis is routine. angle of $-\pi/12$ with the $x$-axis is routine. \end{exparts} \end{ans}
 ... ... @@ -3561,19 +3561,23 @@ solution set's description. \begin{lemma} \label{th:GenEqPartHomo} %<*th:GenEqPartHomo> For a linear system, where $\vec{p}\/$ is any particular solution, the solution set equals this set. \begin{equation*} For a linear system and for any particular solution $\vec{p}\/$, the solution set equals % \begin{equation*} $\set{\vec{p}+\vec{h} \suchthat \text{ $$\vec{h}$$ satisfies the associated homogeneous system} } \end{equation*} associated homogeneous system} }$. %\end{equation*} % \end{lemma} % So fixing any particular solution gives the above % description of the solution set. \begin{proof} We will show mutual set inclusion, that any solution to the system is in the above set and that anything in the set is a solution of the system.\appendrefs{equality of sets} system.\appendrefs{set equality} %<*pf:GenEqPartHomo0> For set inclusion the first way, that if a vector solves the system ... ...
 ... ... @@ -35,8 +35,8 @@ than is a domain interval near $x=0$. The linear maps are nicer, more regular, in that for each map all of the domain spreads by the same factor. The map~$f_1$ on the left spreads all intervals apart to be twice as wide while on the right~$f_2$ keeps intervals the same length but reverses The map~$h_1$ on the left spreads all intervals apart to be twice as wide while on the right~$h_2$ keeps intervals the same length but reverses their orientation, as with the rising interval from $1$ to $2$ being transformed to the falling interval from $-1$ to~$-2$. ... ... @@ -169,7 +169,7 @@ The resulting shape has the same base and height as the square \end{center} For contrast, the next picture shows the effect of the map represented by $C_{2,1}(1)$. $C_{2,1}(2)$. Here vectors are affected according to their second component: $\binom{x}{y}$ slides horizontally by twice $y$. ... ... @@ -431,12 +431,12 @@ The Chain Rule multiplies the matrices. \includegraphics{ch3.96} \end{center} For instance, the effect of $H$ on the unit vector whose angle with the $x$-axis is $\pi/3$ is this. the $x$-axis is $\pi/6$ is this. \begin{center} \includegraphics{ch3.97} \end{center} Verifying that the resulting vector has unit length and forms an angle of $-\pi/6$ with the $x$-axis is routine. angle of $-\pi/12$ with the $x$-axis is routine. \end{exparts} \end{answer} \item ... ...