diff --git a/50_ode/40_comparing_with_num_int.md b/50_ode/40_comparing_with_num_int.md
index 0a580a4c..0c936c75 100644
--- a/50_ode/40_comparing_with_num_int.md
+++ b/50_ode/40_comparing_with_num_int.md
@@ -15,9 +15,9 @@ $$
| order | Numerical Integration | method | ODE Solver |
|:---------:|:--------------------------------:|:--------:|:------------------------------------------------:|
-| 0th order | $$ F_k = f(x_k)\cdot \Delta x $$ | Euler | $$ x_{k+1} = x_{k} + \Delta t \cdot f(x_k, t_k) $$ |
-| 1st order | $$ F_k = \frac{\Delta x}{2}\left[f(x_k) + f(x_{k+1})\right] $$ | Heun | $$ x_{k+1} = x_{k} + \frac{\Delta t}{2} \left[f(x_k, t_k) + f(\hat{x}_{k+1}, t_{k+1})\right] $$ |
-| 2nd order | $$ F_k = \frac{\Delta x}{6}\left[f(x_k) + 4 \cdot f(x_{k+1}) + f(x_{k+2})\right] $$ | Runge-Kutta | $$ x_{k+1} = x_{k} + \frac{\Delta t}{6} \left[f(x_k, t_k) + 2 f(\hat{x}_{k+\frac{1}{2}}, t_{k+\frac{1}{2}})_1+ 2 f(\hat{x}_{k+\frac{1}{2}}, t_{k+\frac{1}{2}})_2 + f(\hat{x}_{k+1}, t_{k+1})\right] $$ |
+| 0th order | $$F_k = f(x_k)\cdot \Delta x$$ | Euler | $$x_{k+1} = x_{k} + \Delta t \cdot f(x_k, t_k)$$ |
+| 1st order | $$F_k = \frac{\Delta x}{2}\left[f(x_k) + f(x_{k+1})\right]$$ | Heun | $$x_{k+1} = x_{k} + \frac{\Delta t}{2} \left[f(x_k, t_k) + f(\hat{x}_{k+1}, t_{k+1})\right]$$ |
+| 2nd order | $$F_k = \frac{\Delta x}{6}\left[f(x_k) + 4 \cdot f(x_{k+1}) + f(x_{k+2})\right]$$ | Runge-Kutta | $$x_{k+1} = x_{k} + \frac{\Delta t}{6} \left[f(x_k, t_k) + 2 f(\hat{x}_{k+\frac{1}{2}}, t_{k+\frac{1}{2}})_1+ 2 f(\hat{x}_{k+\frac{1}{2}}, t_{k+\frac{1}{2}})_2 + f(\hat{x}_{k+1}, t_{k+1})\right]$$ |
* Numerical integration and ODE solvers share a fundamental principle: approximating solutions using weighted averages. In numerical integration, these averages are of function values, while in ODE solvers, they are of slopes.
수치 적분과 상미분방정식 해법은 모두 기본적으로 가중 평균을 사용하여 해를 근사한다. 수치 적분에서는 함수 값의 평균을 사용하고, 상미분 방정식 해법에서는 기울기의 평균을 사용한다.
* The accuracy of both numerical integration and ODE solvers is characterized by their order. Higher-order methods generally provide more accurate results but may be more computationally expensive.
수치적분과 상미분방정식 해법 모두 그 차수가 정확도를 결정한다. 차수가 높은 방법이 일반적으로 더 정확한 결과를 제공하지만, 계산 비용은 더 많이 들 수 있다.