daviddoji/CalculusWithJuliaNotes.jl
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

typos

Browse Source
This commit is contained in:
jverzani
2024-05-22 07:55:20 -04:00
parent f710cded15
commit 771bb06aa3
50 changed files with 120 additions and 426 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
quarto/ODEs/euler.qmd
View File

@@ -133,7 +133,7 @@ $$
\langle x_0, y_0 \rangle + h \cdot \langle 1, F(y_0, x_0) \rangle.
$$
The above uses vector notation to add the piece scaled by $h$ to the starting point. Rather than continue with that notation, we will use subscripts. Let $x_1$, $y_1$ be the postion of the tip of the vector. Then we have:
The above uses vector notation to add the piece scaled by $h$ to the starting point. Rather than continue with that notation, we will use subscripts. Let $x_1$, $y_1$ be the position of the tip of the vector. Then we have:
$$

4
quarto/ODEs/odes.qmd
View File

@@ -148,7 +148,7 @@ $$
U'(t) = -r U(t), \quad U(0) = U_0.
$$
This shows that the rate of change of $U$ depends on $U$. Large postive values indicate a negative rate of change - a push back towards the origin, and large negative values of $U$ indicate a positive rate of change - again, a push back towards the origin. We shouldn't be surprised to either see a steady decay towards the origin, or oscillations about the origin.
This shows that the rate of change of $U$ depends on $U$. Large positive values indicate a negative rate of change - a push back towards the origin, and large negative values of $U$ indicate a positive rate of change - again, a push back towards the origin. We shouldn't be surprised to either see a steady decay towards the origin, or oscillations about the origin.
What will we find? This equation is different from the previous two equations, as the function $U$ appears on both sides. However, we can rearrange to get:
@@ -678,7 +678,7 @@ We now attempt to solve these.
```{julia}
@syms alpha::real, γ::postive, v()
@syms alpha::real, γ::positive, v()
@syms x_0::real y_0::real v_0::real
eq₁ = Dₜ(Dₜ(u))(t) ~ - γ * Dₜ(u)(t)