From c1113b0a0c1ca2e7b414d5c89e464e85291958c5 Mon Sep 17 00:00:00 2001 From: Luc Date: Fri, 19 Jan 2024 13:34:20 +0100 Subject: [PATCH] Updated and moved mathematical physics to physics section. --- config/en/mkdocs.yaml | 6 +++--- docs/en/physics/index.md | 7 ++++--- .../mathematical-physics/signal-analysis/signals.md | 5 +++-- 3 files changed, 10 insertions(+), 8 deletions(-) rename docs/en/{mathematics => physics}/mathematical-physics/signal-analysis/signals.md (97%) diff --git a/config/en/mkdocs.yaml b/config/en/mkdocs.yaml index 84148e8..20faedb 100755 --- a/config/en/mkdocs.yaml +++ b/config/en/mkdocs.yaml @@ -112,12 +112,12 @@ nav: - 'Second order differential equations': mathematics/ordinary-differential-equations/second-order-ode.md - 'Systems of linear differential equations': mathematics/ordinary-differential-equations/systems-of-linear-ode.md - 'The Laplace transform': mathematics/ordinary-differential-equations/laplace-transform.md + + - 'Physics': + - physics/index.md - 'Mathematical physics': - 'Signal analysis': - 'Signals': mathematics/mathematical-physics/signal-analysis/signals.md - - - 'Physics': - - physics/index.md - 'Chemistry': - chemistry/index.md diff --git a/docs/en/physics/index.md b/docs/en/physics/index.md index b00ae27..f6a882e 100644 --- a/docs/en/physics/index.md +++ b/docs/en/physics/index.md @@ -5,10 +5,11 @@ Welcome to the physics page. Some special physical environments that will be use * *Principles*: a fundamental rule or concept in physics serving as a basis for reasoning. * *Assumptions*: a less fundamental rule or concept in physics that is taken to be true such that certain phenoma can be simplified. * *Definitions*: a precise and unambiguous description of the meaning of a physical term. It characterizes the meaning of a word by giving all the properties an only those properties that must be true. +* *Theorems*: a mathematical statement that is proved to be true using rigorous mathematical reasoning. In a mathematical text, the term theorem is often reserved for the most important results. * *Laws*: a physical statement that is proved to be true, under the made assumptions and posed principles. In a physical text, the term law is often reserved for the most important results. -* *Propositions*: an often interesting result, but generally less important than a law. -* *Lemmas*: a minor result whose purpose is to help in proving a law. It is a stepping stone on the path to proving a law. -* *Corollaries*: a result in which the proof relies heavily on a given law. +* *Propositions*: an often interesting result, but generally less important than a theorem or law. +* *Lemmas*: a minor result whose purpose is to help in proving a theorem or law. It is a stepping stone on the path to proving a theorem or law. +* *Corollaries*: a result in which the proof relies heavily on a given theorem or law. * *Proofs*: a convincing argument that a certain physical statement is necessarily true. A proof generally uses deductive reasoning and logic but also contains some amount of ordinary language. The physics sections of this wiki are based on various books and lectures. A comprehensive list of references can be found below. \ No newline at end of file diff --git a/docs/en/mathematics/mathematical-physics/signal-analysis/signals.md b/docs/en/physics/mathematical-physics/signal-analysis/signals.md similarity index 97% rename from docs/en/mathematics/mathematical-physics/signal-analysis/signals.md rename to docs/en/physics/mathematical-physics/signal-analysis/signals.md index 27b641e..b692113 100644 --- a/docs/en/mathematics/mathematical-physics/signal-analysis/signals.md +++ b/docs/en/physics/mathematical-physics/signal-analysis/signals.md @@ -3,6 +3,7 @@ ## Definitions > *Definition*: a signal is a function of space and time. +> > * Output can be analog or quantised. > * Input can be continuous or discrete. @@ -103,7 +104,7 @@ $$ \lim_{\varepsilon \;\downarrow\; 0} \int_{-\infty}^{\infty} f(t) D(t, \varepsilon)dt = \lim_{\varepsilon \;\downarrow\; 0} \frac{1}{\varepsilon} \int_{-\frac{\varepsilon}{2}}^{\frac{\varepsilon}{2}} f(t) dt = f(0), $$ -using the mean [value theorem for integrals](../calculus/integration.md#the-mean-value-theorem-for-integrals). +using the mean [value theorem for integrals](../../../mathematics/calculus/integration.md#the-mean-value-theorem-for-integrals). > *Definition*: the Dirac signal $\delta$ is a generalized signal defined by the properties > @@ -170,7 +171,7 @@ by definition. > f(t) * \delta(t - t_0) = f(t - t_0) > $$ > -> for all $t \in \mathbb{R}$ +> for all $t \in \mathbb{R}$. ??? note "*Proof*:"