readme

README.md

@@ -0,0 +1,40 @@
+
+[alistairmichael.com/notes/applied.pdf](https://alistairmichael.com/notes/applied.pdf)
+
+## Compiling
+
+Use pdflatex with `pdflatex --interaction nonstopmode %O --shell-escape %S`
+
+Or latexmk with shell escape set in your `.latexmkrc`
+
+```
+$pdf_mode = 1;        # tex -> pdf
+$pdflatex = 'pdflatex --interaction nonstopmode %O --shell-escape %S'
+```
+
+```
+\usepackage{attachfile}
+\usepackage{caption}
+\usepackage{tocloft}
+\usepackage{enumitem}
+\usepackage{marginnote}
+\usepackage{graphicx}
+\usepackage{multicol}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{amsthm}
+\usepackage{bookmark}
+\usepackage{pgfplots}
+\usepackage{import}
+\usepackage{xcolor}
+\usepackage{soul}
+\usepackage[pdf]{graphviz}
+\usepackage{mathtools}
+\usepackage{amssymb}
+\usepackage[english]{babel}
+\usepackage{geometry}
+```
+
+
+

notes.tex

@@ -8,8 +8,9 @@
 \renewcommand{\captionfont}{\small}
 
 
+\usepackage[english]{babel}
 \usepackage{tocloft}
-
+\usepackage{titlesec}
 \usepackage{enumitem}
 \usepackage{marginnote}
 \usepackage{graphicx}
@@ -39,7 +40,7 @@
 \usepackage{amssymb}
 % for mathbb 
 
-\usepackage[english]{babel}
+
 
 \usepackage[top=2cm, bottom=3cm, outer=7cm, inner=1cm, heightrounded,
 marginparwidth=5cm, marginparsep=0.3cm]{geometry}
@@ -47,6 +48,8 @@ marginparwidth=5cm, marginparsep=0.3cm]{geometry}
 \title{MATH3102 Lecture Notes}
 \author{Alistair Michael}
 
+\titleformat{\chapter}{\normalfont\huge\bf}{\thechapter.}{20pt}{\huge\bf}
+
 \graphicspath{{images/}}
 
 \newcommand{\sforall}{\enspace\forall}
@@ -148,8 +151,10 @@ marginparwidth=5cm, marginparsep=0.3cm]{geometry}
 
 \maketitle
 
-This document has its \LaTeX{} source attached. \attachfile[description=Document
-text source,icon=Paperclip]{notes.tex}
+This document can be found at
+\href{https://alistairmichael.com/notes/applied.pdf}{alistairmichael.com/notes/applied.pdf} with source available at
+\href{https://git.topost.net/alistair/applied-notes}{git.topost.net/alistair/applied-notes}.
+It contains many typos and errors.
 
 \tableofcontents
 \listoflecture
@@ -1749,7 +1754,7 @@ $$R_0 U_{tt} = R_0 F + T'(U_A) U_{AA}$$
 $$\lambda = \frac {\ell }{\ell_0} = \frac {\ell - \ell_0 + \ell_0} {\ell_0} \sim
 \epsilon + 1 $$
 
-$\eimplies$ the reference state has $\lambda = 1 \Leftrightarrow \epsilon = 0$
+$\implies$ the reference state has $\lambda = 1 \Leftrightarrow \epsilon = 0$
 
 For a small enough $\epsilon$ any material will exhibit a linear stress--strain
 relation. 
@@ -1908,7 +1913,7 @@ For example for rubber the stress strain raltion looks something like
 \begin{figure}[htpb]
     \centering
     \begin{tikzpicture}{testppop}
-        \begin{axis}[ytick=none,xtick=none,xlabel=$\epsilon$, ylabel=$T$,]
+        \begin{axis}[ytick={},xtick={},xlabel=$\epsilon$, ylabel=$T$,]
             \addplot[domain=-1:2, samples=90,color=blue,]{ (x -0)^3 + 0};
     \end{axis}
 \end{tikzpicture}
@@ -2075,8 +2080,8 @@ $\implies$ the solution is given by D'Alembert's formula where $\rho=0$ and $f$
      mode of the forcing term.
 
         \begin{center}
-            \begin{tikzpicture}{hy}
-                \begin{axis}[xtick={3.141},xticklabels={$\ell$}, ytick=none,]
+            \begin{tikzpicture}{notes-figure9}
+                \begin{axis}[xtick={3.141},xticklabels={$\ell$}, ytick={},]
                     \addplot[domain=0:3.141 , samples=90, color=green]{ cos(deg(x))};
             \addlegendentry{$n = 1$}
                     \addplot[domain=0:3.141 , samples=90, color=black]{ cos(2 * deg(x))};
@@ -2432,7 +2437,7 @@ viscoelastic models explicitly very easiliy}
     Use laplace transform on $(*)$, $\hat U = L(U)$
     
     $$\begin{cases}
-    R_0 s^2 \hat U = L(G) s \hat U_{A A} $ where $L(G) = \fraC {\hat E}{s +
+    R_0 s^2 \hat U = L(G) s \hat U_{A A} $ where $L(G) = \frac {\hat E}{s +
     \frac 1 {\tau_0}}  \\
     \hat U_A (A = 0, s) = \hat F(s) \\
     \lim_{A \to \infty} \hat U(A, s) = 0
@@ -2482,7 +2487,7 @@ viscoelastic models explicitly very easiliy}
                   &=\int_{\sqrt{\frac {R_0}{\hat E}}A}^t Q(A, \hat t) F(t - \hat t) \: d\hat t \times H\left(t - \sqrt
                   {\frac{R_0}{\hat E}}A\right)  \\
                 \implies & U \text{ is zero wherever } t < \sqrt{\frac {R_0}A} , \\ 
-                \implies & A > t\sqrt {\frac {\haat E} {R_0}} = t \sqrt{\frac {E \tau_1}{\tau_0}
+                \implies & A > t\sqrt {\frac {\hat E} {R_0}} = t \sqrt{\frac {E \tau_1}{\tau_0}
                 \frac 1 {R_0}} \\
                     \text{For } F(t) &= \sin(t) \\
     \end{align*}
@@ -2664,7 +2669,7 @@ $$J = \det F = \det \underbrace{\nabla_A X}_{\text{Jacobi matrix}} \ne 0$$
 This is essentially the impenetrability assumption from 1D continuum mechanics in 
 three dimensions.
 
-At $t = 0$, $X(A, t= 0) = A \implies \F = \mathbb I \implies J = 1$
+At $t = 0$, $X(A, t= 0) = A \implies F = \mathbb I \implies J = 1$
 
 Since $J(t = 0) = 1$, $J \ne 0$ always implies $J(t) > 0$