kruby/notes-archive
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Spellchecker

Browse Source
This commit is contained in:
Indigo5684
2025-09-30 13:19:29 -05:00
parent 4a046047c3
commit 9e3784cfd6
24 changed files with 139 additions and 113 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
docs/math/diffeq/1-intro.md
View File

@@ -16,15 +16,15 @@ This section is from [Paul's Online Math Notes](https://tutorial.math.lamar.edu/
\[ a_n(t)y^{(n)}(t) + a_{n-1}(t)+y^{n-1}(t) + \ldots + a_1(t)y'(t) + a_0(t)y(t) = g(t) \]
Note that $a_n(t)$ does not depeond on any derivative of $y$, so the presence of terms such as $e^y$ or $\sqrt{y'}$ signal that the equation is *nonlinear*.
Note that $a_n(t)$ does not depend on any derivative of $y$, so the presence of terms such as $e^y$ or $\sqrt{y'}$ signal that the equation is *nonlinear*.
**Definition**. The *solution(s)* to a differential equation over an inverval $\alpha < t < \beta$ are any funcion(s) $y(t)$ that satisfy the differential equation.
**Definition**. The *solution(s)* to a differential equation over an interval $\alpha < t < \beta$ are any function(s) $y(t)$ that satisfy the differential equation.
**Definition**. The *initial conditions* are a condition or set of conditions that constrain the possible solution sets.
**Definition**. An *Initial Value Problem* is a differential equation along with the appropriate boundary or initial conditions.
**Definition**. The *integral of validity* for a solution to a differential equation is the largest possible interval containing the initial coniditions for which the solution is valid.
**Definition**. The *integral of validity* for a solution to a differential equation is the largest possible interval containing the initial conditions for which the solution is valid.
**Definition**. The *general solution* to a differential equation is the most general form a solution to a differential equation can take without requiring the initial conditions.