auto-update(nvim): 2025-01-07 15:29:58

documents/by-course/math-4b/course-notes/dvd.typ

@@ -0,0 +1,329 @@
+#import "@preview/ctheorems:1.1.3": *
+#import "@preview/showybox:2.0.3": showybox
+
+#let colors = (
+  rgb("#9E9E9E"),
+  rgb("#F44336"),
+  rgb("#E91E63"),
+  rgb("#9C27B0"),
+  rgb("#673AB7"),
+  rgb("#3F51B5"),
+  rgb("#2196F3"),
+  rgb("#03A9F4"),
+  rgb("#00BCD4"),
+  rgb("#009688"),
+  rgb("#4CAF50"),
+  rgb("#8BC34A"),
+  rgb("#CDDC39"),
+  rgb("#FFEB3B"),
+  rgb("#FFC107"),
+  rgb("#FF9800"),
+  rgb("#FF5722"),
+  rgb("#795548"),
+  rgb("#9E9E9E"),
+)
+
+#let dvdtyp(
+  title: "",
+  subtitle: "",
+  author: "",
+  abstract: none,
+  bibliography: none,
+  paper-size: "a4",
+  date: "today",
+  body,
+) = {
+  set document(title: title, author: author)
+
+  set std.bibliography(style: "springer-mathphys", title: [References])
+
+  show: thmrules
+
+  set page(
+    numbering: "1",
+    number-align: center,
+    header: locate(loc => {
+      if loc.page() == 1 {
+        return
+      }
+      box(stroke: (bottom: 0.7pt), inset: 0.4em)[#text(
+          font: "New Computer Modern",
+        )[
+          *#author* --- #datetime.today().display("[day] [month repr:long] [year]")
+          #h(1fr)
+          *#title*
+        ]]
+    }),
+    paper: paper-size,
+    // The margins depend on the paper size.
+    margin: (
+      left: (86pt / 216mm) * 100%,
+      right: (86pt / 216mm) * 100%,
+    ),
+  )
+
+
+  set heading(numbering: "1.")
+  show heading: it => {
+    set text(font: "Libertinus Serif")
+    set par(first-line-indent: 0em)
+
+    if it.numbering != none {
+      text(rgb("#2196F3"), weight: 500)[#sym.section]
+
+      text(rgb("#2196F3"))[#counter(heading).display() ]
+    }
+    it.body
+  }
+
+  set text(font: "New Computer Modern", lang: "en")
+
+  show math.equation: set text(weight: 400)
+
+
+  // Title row.
+  align(center)[
+    #set text(font: "Libertinus Serif")
+    #block(text(weight: 700, 26pt, title))
+
+
+    #if subtitle != none [#text(12pt, weight: 500)[#(
+          subtitle
+        )]]
+
+    #if author != none [#text(16pt)[#smallcaps(author)]]
+    #v(1.2em, weak: true)
+
+    #if date == "today" {
+      datetime.today().display("[day] [month repr:long] [year]")
+    } else {
+      date
+    }
+
+  ]
+
+  if abstract != none [
+    #v(2.2em)
+    #set text(font: "Libertinus Serif")
+    #pad(x: 14%, abstract)
+    #v(1em)
+  ]
+
+  set outline(fill: repeat[~.], indent: 1em)
+
+  show outline: set heading(numbering: none)
+  show outline: set par(first-line-indent: 0em)
+
+  show outline.entry.where(level: 1): it => {
+    text(font: "Libertinus Serif", rgb("#2196F3"))[#strong[#it]]
+  }
+  show outline.entry: it => {
+    h(1em)
+    text(font: "Libertinus Serif", rgb("#2196F3"))[#it]
+  }
+
+
+  // Main body.
+  set par(
+    justify: true,
+    first-line-indent: 1em,
+  )
+
+  body
+
+  // Display the bibliography, if any is given.
+  if bibliography != none {
+    show std.bibliography: set text(footnote-size)
+    show std.bibliography: set block(above: 11pt)
+    show std.bibliography: pad.with(x: 0.5pt)
+    bibliography
+  }
+}
+
+#let thmtitle(t, color: rgb("#000000")) = {
+  return text(
+    font: "Libertinus Serif",
+    weight: "semibold",
+    fill: color,
+  )[#t]
+}
+#let thmname(t, color: rgb("#000000")) = {
+  return text(font: "Libertinus Serif", fill: color)[(#t)]
+}
+
+#let thmtext(t, color: rgb("#000000")) = {
+  let a = t.children
+  if (a.at(0) == [ ]) {
+    a.remove(0)
+  }
+  t = a.join()
+
+  return text(font: "New Computer Modern", fill: color)[#t]
+}
+
+#let thmbase(
+  identifier,
+  head,
+  ..blockargs,
+  supplement: auto,
+  padding: (top: 0.5em, bottom: 0.5em),
+  namefmt: x => [(#x)],
+  titlefmt: strong,
+  bodyfmt: x => x,
+  separator: [#h(0.1em).#h(0.2em) \ ],
+  base: "heading",
+  base_level: none,
+) = {
+  if supplement == auto {
+    supplement = head
+  }
+  let boxfmt(name, number, body, title: auto, ..blockargs_individual) = {
+    if not name == none {
+      name = [ #namefmt(name)]
+    } else {
+      name = []
+    }
+    if title == auto {
+      title = head
+    }
+    if not number == none {
+      title += " " + number
+    }
+    title = titlefmt(title)
+    body = bodyfmt(body)
+    pad(
+      ..padding,
+      showybox(
+        width: 100%,
+        radius: 0.3em,
+        breakable: true,
+        padding: (top: 0em, bottom: 0em),
+        ..blockargs.named(),
+        ..blockargs_individual.named(),
+        [#title#name#titlefmt(separator)#body],
+      ),
+    )
+  }
+
+  let auxthmenv = thmenv(
+    identifier,
+    base,
+    base_level,
+    boxfmt,
+  ).with(supplement: supplement)
+
+  return auxthmenv.with(numbering: "1.1")
+}
+
+#let styled-thmbase = thmbase.with(
+  titlefmt: thmtitle,
+  namefmt: thmname,
+  bodyfmt: thmtext,
+)
+
+#let builder-thmbox(color: rgb("#000000"), ..builderargs) = styled-thmbase.with(
+  titlefmt: thmtitle.with(color: color.darken(30%)),
+  bodyfmt: thmtext.with(color: color.darken(70%)),
+  namefmt: thmname.with(color: color.darken(30%)),
+  frame: (
+    body-color: color.lighten(92%),
+    border-color: color.darken(10%),
+    thickness: 1.5pt,
+    inset: 1.2em,
+    radius: 0.3em,
+  ),
+  ..builderargs,
+)
+
+#let builder-thmline(
+  color: rgb("#000000"),
+  ..builderargs,
+) = styled-thmbase.with(
+  titlefmt: thmtitle.with(color: color.darken(30%)),
+  bodyfmt: thmtext.with(color: color.darken(70%)),
+  namefmt: thmname.with(color: color.darken(30%)),
+  frame: (
+    body-color: color.lighten(92%),
+    border-color: color.darken(10%),
+    thickness: (left: 2pt),
+    inset: 1.2em,
+    radius: 0em,
+  ),
+  ..builderargs,
+)
+
+#let problem-style = builder-thmbox(
+  color: colors.at(11),
+  shadow: (offset: (x: 2pt, y: 2pt), color: luma(70%)),
+)
+
+#let exercise = problem-style("item", "Exercise")
+#let problem = exercise
+
+#let theorem-style = builder-thmbox(
+  color: colors.at(6),
+  shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
+)
+
+#let example-style = builder-thmbox(
+  color: colors.at(16),
+  shadow: (offset: (x: 3pt, y: 3pt), color: luma(70%)),
+)
+
+#let theorem = theorem-style("item", "Theorem")
+#let lemma = theorem-style("item", "Lemma")
+#let corollary = theorem-style("item", "Corollary")
+
+#let definition-style = builder-thmline(color: colors.at(8))
+
+// #let definition = definition-style("definition", "Definition")
+#let proposition = definition-style("item", "Proposition")
+#let remark = definition-style("item", "Remark")
+#let observation = definition-style("item", "Observation")
+
+// #let example-style = builder-thmline(color: colors.at(16))
+
+#let example = example-style("item", "Example")
+
+#let proof(body, name: none) = {
+  [_Proof_]
+  if name != none {
+    [ #thmname[#name]]
+  }
+  [.]
+  body
+  h(1fr)
+
+  // Add a word-joiner so that the proof square and the last word before the
+  // 1fr spacing are kept together.
+  sym.wj
+
+  // Add a non-breaking space to ensure a minimum amount of space between the
+  // text and the proof square.
+  sym.space.nobreak
+
+  $square.stroked$
+}
+
+#let fact = thmplain(
+  "item",
+  "Fact",
+  titlefmt: strong,
+  separator: ".",
+
+  inset: 0pt,
+)
+#let abuse = thmplain(
+  "item",
+  "Abuse of Notation",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)
+#let definition = thmplain(
+  "item",
+  "Definition",
+  titlefmt: strong,
+  separator: ".",
+  inset: 0pt,
+)

documents/by-course/math-4b/course-notes/main.typ

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+#import "./dvd.typ": *
+
+#show: dvdtyp.with(
+  title: "Math 4B Course Notes",
+  author: "Youwen Wu",
+  date: "Winter 2025",
+  subtitle: [Taught by Guofang Wei],
+)
+
+#outline()
+
+= Course logistics
+
+The textbook is Elementary Differential Equations, 11th edition, 2017. Chapters
+1-4, 6, 7, and 9 will be covered.
+
+Attendance to discussion sections is mandatory.
+
+= Lecture #datetime(day: 7, month: 1, year: 2025).display()
+
+== Trivial preliminaries
+
+#definition[
+  An ODE involves an unknown function of a single variable and its derivatives
+  up to some fixed order. The order of an ODE is the order of the highest
+  derivative that appears.
+]
+
+#example[First order ODE][
+  $ (dif y) / (dif x) = y^2 $
+]
+
+#example[Second order ODE][
+  $
+    y'' &= x \
+    integral.double y'' dif x &= integral.double x dif x \
+    y &= 1 / 6 x^3 + C
+  $
+]
+
+#definition[
+  A function $y(x)$ defined on $(a,b)$ is a *solution* of the ODE
+  $ y' = F(x,y) $
+  if and only if
+  $ y'(x) = F(x, y(x)), forall x in (a,b) $
+]
+
+#problem[
+  Check that $y(x) = 20 + 10e^(-x / 2)$ is a solution to the ODE
+  $ y' = -1 / 2 y + 10 $
+]
+
+#definition[
+  A first order ODE
+  $ y' = F(x,y) $
+  is called *linear* if there are functions $A(x)$ and $B(x)$ such that
+  $ F(x,y) = A(x) y + B(x) $
+]
+
+#example("Linear ODEs")[
+  - $y' = x$
+  - $y' = y$
+  - $y' = x^2$
+]
+
+#example("Nonlinear ODEs")[
+  - $y' = y^2$
+]
+
+#definition[
+  *Equilibrium solutions* for the ODE
+  $ y' = F(x,y) $
+  are solutions $y(x)$ such that $y'(x) = 0$, that is, $y(x)$ is constant.
+]
+
+#example[
+  The equation
+  $ y' = y(y +2) $
+  has two equilibria
+  $
+    y(x) &= 0 \
+    y(x) &= -2
+  $
+]
+
+#problem[
+  What are the equilibria of the equation
+  $ y' = y(y - x) $
+]

documents/by-course/math-4b/course-notes/package.nix

@@ -0,0 +1,37 @@
+{
+  pkgs,
+  typstPackagesCache,
+  typixLib,
+  cleanTypstSource,
+  flakeSelf,
+  ...
+}:
+let
+  src = cleanTypstSource ./.;
+  commonArgs = {
+    typstSource = "main.typ";
+
+    fontPaths = [
+      # Add paths to fonts here
+      # "${pkgs.roboto}/share/fonts/truetype"
+    ];
+
+    virtualPaths = [
+      # Add paths that must be locally accessible to typst here
+      # {
+      #   dest = "icons";
+      #   src = "${inputs.font-awesome}/svgs/regular";
+      # }
+    ];
+
+    XDG_CACHE_HOME = typstPackagesCache;
+    SOURCE_DATE_EPOCH = builtins.toString flakeSelf.lastModified;
+  };
+
+in
+typixLib.buildTypstProject (
+  commonArgs
+  // {
+    inherit src;
+  }
+)