diff --git a/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf b/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf index 7a87bf1..57526b1 100644 Binary files a/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf and b/semester3/analysis-ii/analysis-ii-cheat-sheet.pdf differ diff --git a/semester3/analysis-ii/analysis-ii-cheat-sheet.tex b/semester3/analysis-ii/analysis-ii-cheat-sheet.tex index 764d522..e14639e 100644 --- a/semester3/analysis-ii/analysis-ii-cheat-sheet.tex +++ b/semester3/analysis-ii/analysis-ii-cheat-sheet.tex @@ -4,11 +4,13 @@ \input{\dir/include.tex} \load{recommended} -\setup{Analysis II} +\setupCheatSheet{Analysis II} \begin{document} -\startDocument +\maketitle \usetcolorboxes +\setcounter{numberingConfig}{3} +\setcounter{numberSubsections}{1} % ╭────────────────────────────────────────────────╮ @@ -56,13 +58,19 @@ If you discover any errors, please open an issue or fix the issue yourself and t This Cheat-Sheet was designed with the HS2025 page limit of 10 A4 pages in mind. Thus, the whole Cheat-Sheet can be printed full-sized, if you exclude the title page, contents and this page. +You could also print it as two A5 pages per A4 page and also print the +\color{MidnightBlue}\fbox{\href{https://github.com/janishutz/eth-summaries/blob/master/semester2/analysis-i/cheat-sheet.pdf}{Analysis I summary}}\color{black} +\smallhspace in the same manner, allowing you to bring both to the exam % ╭────────────────────────────────────────────────╮ % │ Content │ % ╰────────────────────────────────────────────────╯ -\input{parts/diff-eq.tex} +\newsection +\section{Differential Equations} +\input{parts/diffeq/00_intro.tex} + \end{document} diff --git a/semester3/analysis-ii/parts/diff-eq.tex b/semester3/analysis-ii/parts/diff-eq.tex deleted file mode 100644 index b08b52c..0000000 --- a/semester3/analysis-ii/parts/diff-eq.tex +++ /dev/null @@ -1,2 +0,0 @@ -\newsection -\section{Differential Equations} diff --git a/semester3/analysis-ii/parts/diffeq/00_intro.tex b/semester3/analysis-ii/parts/diffeq/00_intro.tex new file mode 100644 index 0000000..fe40fc7 --- /dev/null +++ b/semester3/analysis-ii/parts/diffeq/00_intro.tex @@ -0,0 +1,7 @@ +\subsection{Introduction} +\shortex $f'(x) = f(x)$ has only solution $f(x) = ae^x$ for any $a \in \R$; +$f' - a = 0$ has only solution $f(x) = \int_{x_0}^{x} a(t) \smallhspace \dx t$ + +\setcounter{all}{6} +\shorttheorem Let $F: \R^2 \rightarrow \R$ be a differential function of two variables. Let $x_0 \in \R$ and $y_0 \in \R^2$. +The Ordinary Differential Equation (ODE) $y' = F(x, y)$ has a unique solution $f$ defined on a ``largest'' interval $I$ that contains $x_0$ such that $y_0 = f(x_0)$ diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex new file mode 100644 index 0000000..1b295b1 --- /dev/null +++ b/semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex @@ -0,0 +1,2 @@ +\newsection +\subsection{Linear Differential Equations} diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex new file mode 100644 index 0000000..7fd74fc --- /dev/null +++ b/semester3/analysis-ii/parts/diffeq/linear-ode/01_order-one.tex @@ -0,0 +1,2 @@ +\newsection +\subsection{Linear Differential Equations of first order} diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/02_constant-coefficient.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/02_constant-coefficient.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/03_harmonic-oscilator.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/03_harmonic-oscilator.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester3/analysis-ii/parts/diffeq/linear-ode/04_other-methods.tex b/semester3/analysis-ii/parts/diffeq/linear-ode/04_other-methods.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester3/analysis-ii/parts/vectors/differentiation/intro.tex b/semester3/analysis-ii/parts/vectors/differentiation/intro.tex new file mode 100644 index 0000000..e69de29 diff --git a/semester3/analysis-ii/parts/vectors/integration/intro.tex b/semester3/analysis-ii/parts/vectors/integration/intro.tex new file mode 100644 index 0000000..e69de29