Skip to content
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension


Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
10 changes: 10 additions & 0 deletions .codespell-ignorelines
Original file line number Diff line number Diff line change
@@ -0,0 +1,10 @@
# SPDX-License-Identifier: FSFAP
# Copyright (C) 2025 Colin B. Macdonald
#
# Copying and distribution of this file, with or without modification,
# are permitted in any medium without royalty provided the copyright
# notice and this notice are preserved. This file is offered as-is,
# without any warranty.

# lines that codespell should ignore: whitespace matters!

13 changes: 13 additions & 0 deletions .codespell-ignorewords
Original file line number Diff line number Diff line change
@@ -0,0 +1,13 @@
# SPDX-License-Identifier: FSFAP
# Copyright (C) 2025 Colin B. Macdonald
#
# Copying and distribution of this file, with or without modification,
# are permitted in any medium without royalty provided the copyright
# notice and this notice are preserved. This file is offered as-is,
# without any warranty.

# words that codespell should not complain about

co-ordinates
co-ordinate
ans
30 changes: 30 additions & 0 deletions .github/workflows/main.yml
Original file line number Diff line number Diff line change
@@ -0,0 +1,30 @@
# SPDX-License-Identifier: FSFAP
# Copyright (C) 2025 Colin B. Macdonald
#
# Copying and distribution of this file, with or without modification,
# are permitted in any medium without royalty provided the copyright
# notice and this notice are preserved. This file is offered as-is,
# without any warranty.

name: CI

on:
push:
pull_request:
schedule:
- cron: '17 0 * * 0'
# Allows you to run this workflow manually from the Actions tab
workflow_dispatch:

jobs:
codespell:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v4
- uses: codespell-project/actions-codespell@v2
with:
ignore_words_file: .codespell-ignorewords
exclude_file: .codespell-ignorelines
check_filenames: true
check_hidden: true
skip: '*.pdf'
4 changes: 2 additions & 2 deletions Chapters/chapter2.tex
Original file line number Diff line number Diff line change
Expand Up @@ -1224,7 +1224,7 @@ \subsection{MATLAB: assigning matrices and {\tt det} and {\tt cross}

\subsection{MATLAB: generating scripts with the MATLAB editor}

Often times using the command window in MATLAB to solve a problem can be tedious, because if the need arises to redo the problem, or change a parameter, one has to rewrite it all. The editor comes in handy for such cases. The editor is a text window (accesed from the command window: {\tt File $\rightarrow$ New $\rightarrow$ Blank M-file}) where one can write commands in the same syntax as the editor, and when one runs it, the results appear in the command window exactly as if one had written them there one after the other.
Often times using the command window in MATLAB to solve a problem can be tedious, because if the need arises to redo the problem, or change a parameter, one has to rewrite it all. The editor comes in handy for such cases. The editor is a text window (accessed from the command window: {\tt File $\rightarrow$ New $\rightarrow$ Blank M-file}) where one can write commands in the same syntax as the editor, and when one runs it, the results appear in the command window exactly as if one had written them there one after the other.

For example, the code to generate three random orthogonal vectors would look something like this:
\begin{verbatim}
Expand Down Expand Up @@ -1853,7 +1853,7 @@ \subsection{Problems}
\begin{problem}
\label{op1_32}
Find the equation for the line through $[2,-1,-1]$ and parallel to each of the
two planes $x_1+x_2=0$ and $x_1-x_2+2x_3=0$. Express the equation fo the line
two planes $x_1+x_2=0$ and $x_1-x_2+2x_3=0$. Express the equation of the line
in both parametric and equation form.
\end{problem}

Expand Down
10 changes: 5 additions & 5 deletions Chapters/chapter3.tex
Original file line number Diff line number Diff line change
Expand Up @@ -1124,16 +1124,16 @@ \subsection{Connection of solutions to homogeneous and inhomogeneous systems.}
\]
To see the implications of this let us suppose that $\xx=\qq$ is any particular
solution to a (non-homogeneous) system of equations. Then if $\yy$ is any other
solution $\yy-\xx=\zz$ is a solution of the corresponding homogenous system.
solution $\yy-\xx=\zz$ is a solution of the corresponding homogeneous system.
So $\yy=\qq+\zz$. In other words any solution can be written as $\qq +$ some
solution of the corresponding homogenous system. Going the other way, if
$\zz$ is any solution of the corresponding homogenous system, then $\qq+\zz$
solution of the corresponding homogeneous system. Going the other way, if
$\zz$ is any solution of the corresponding homogeneous system, then $\qq+\zz$
solves the original system. This can be seen by plugging $\qq+\zz$ into the
equation. So the structure of the set of solutions is
\[
\xx = \qq + (\mbox{{\ \bf solution to homogeneous system}})
\]
As you run through all solutions to the homogenous system on the right,
As you run through all solutions to the homogeneous system on the right,
$\xx$ runs through all solutions of the original system. Notice that it doesn't
matter which $\qq$ you choose as the starting point. This is completely analogous
to the parametric form for a line, where the base point can be any
Expand Down Expand Up @@ -2720,7 +2720,7 @@ \section{Solutions to Chapter Problems}
\end{eqnarray*}
Hence, we have that $\qq = (-3, -6, 1, 7)$.

Now, to find $\aa$, the homogenous row echelon form is
Now, to find $\aa$, the homogeneous row echelon form is
$$
\left[\begin{array}{cccc|c}
1 & 2 & 2 & 2 & 0 \\
Expand Down
7 changes: 3 additions & 4 deletions Chapters/chapter4.tex
Original file line number Diff line number Diff line change
Expand Up @@ -3032,9 +3032,8 @@ \section{Solutions to Chapter Problems}
0&1 + t + {{t^2}\over{2}} + {{t^3}\over{3!}} + \cdots\cr
}\right] \\
&=&\left[\matrix{
e^t&
te^t\cr
0&e^t\cr
e^t & t e^t\cr
0 & e^t\cr
}\right]
\end{eqnarray*}
\item[d,e)] We are looking for all matrices that satisfy $B^2=A$. Let
Expand Down Expand Up @@ -4068,4 +4067,4 @@ \section{Solutions to Chapter Problems}
\end{eqnarray*}


\end{enumerate}
\end{enumerate}
6 changes: 3 additions & 3 deletions Chapters/chapter6.tex
Original file line number Diff line number Diff line change
Expand Up @@ -1779,7 +1779,7 @@ \subsection{The matrix exponential and differential equations}
cases. Consider the matrix $A=\left[\matrix{1&1\cr0&1}\right]$. This
matrix does not have a basis of eigenvectors. So it cannot be
diagonalized. However, in a homework problem, you showed that $e^{tA}
= \left[\matrix{e^t&te^t\cr 0&e^t}\right]$. Thus the solution to
= \left[\matrix{e^t & t e^t\cr 0 & e^t}\right]$. Thus the solution to
\[
\yy'(t) = \left[\matrix{1&1\cr 0&1}\right]\yy(t)
\]
Expand All @@ -1790,8 +1790,8 @@ \subsection{The matrix exponential and differential equations}
is
\[
\yy(t) = e^{tA}\left[\matrix{2\cr 1\cr}\right]
=\left[\matrix{e^t&te^t\cr 0&e^t}\right]\left[\matrix{2\cr 1\cr}\right]
=\left[\matrix{2e^t+te^t\cr e^t\cr}\right]
=\left[\matrix{e^t & t e^t\cr 0 & e^t}\right]\left[\matrix{2\cr 1\cr}\right]
=\left[\matrix{2e^t + t e^t\cr e^t\cr}\right]
\]
Notice that this solution involves a power of $t$ in addition to
exponentials.
Expand Down