From 19b2186cff66471d8489c48120a5a6c073ed5103 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Tue, 30 Sep 2025 09:43:36 +0200 Subject: [PATCH] [Analysis] Setup and start --- .../analysis-ii/analysis-ii-cheat-sheet.pdf | Bin 107208 -> 172427 bytes .../analysis-ii/analysis-ii-cheat-sheet.tex | 14 +++++++++++--- semester3/analysis-ii/parts/diff-eq.tex | 2 -- .../analysis-ii/parts/diffeq/00_intro.tex | 7 +++++++ .../parts/diffeq/linear-ode/00_intro.tex | 2 ++ .../parts/diffeq/linear-ode/01_order-one.tex | 2 ++ .../linear-ode/02_constant-coefficient.tex | 0 .../linear-ode/03_harmonic-oscilator.tex | 0 .../diffeq/linear-ode/04_other-methods.tex | 0 .../parts/vectors/differentiation/intro.tex | 0 .../parts/vectors/integration/intro.tex | 0 11 files changed, 22 insertions(+), 5 deletions(-) delete mode 100644 semester3/analysis-ii/parts/diff-eq.tex create mode 100644 semester3/analysis-ii/parts/diffeq/00_intro.tex create mode 100644 semester3/analysis-ii/parts/diffeq/linear-ode/00_intro.tex 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+\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