update notations and fix typos

This commit is contained in:
Zheyuan Wu
2025-02-25 20:41:35 -06:00
parent 419ea07352
commit 27bff83685
71 changed files with 920 additions and 430 deletions

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@@ -34,7 +34,7 @@ Set $F(x)=-f(x)$. and $q=-A+\epsilon>-A$. Apply main step, $\exists c_2\in (a,b)
We take $c=\min(c_1,c_2)$. Then $\forall x\in (a,c)$, $\frac{f(x)}{g(x)}<q$.
EOP
QED
### Higher Order Derivatives
@@ -114,6 +114,6 @@ By Mean Value Theorem, $\exists x_n\in (\alpha,x_{n-1})$ such that $g^{(n)}(x_n)
Since $g^{(n)}(\alpha)=0$ for $k=0,1,2,\cdots,n-1$, we can find $x_n\in (\alpha,x_{n-1})$ such that $g^{(n)}(x_n)=0$.
EOP
QED
## Chapter 6: Riemann-Stieltjes Integral