update and fix typo

pages/Math416/Math416_L10.md

@@ -40,7 +40,7 @@ EOP
 
 ### Complex Integral
 
-#### Definition 4.1
+#### Definition 6.1
 
 If $\phi(t)$ is a complex function defined on $[a,b]$, then the integral of $\phi(t)$ over $[a,b]$ is defined as
 
@@ -48,7 +48,7 @@ $$
 \int_a^b \phi(t) dt = \int_a^b \text{Re}\{\phi(t)\} dt + i\int_a^b \text{Im}\{\phi(t)\} dt
 $$
 
-#### Theorem 4.3 (Triangle Inequality)
+#### Theorem 6.3 (Triangle Inequality)
 
 If $\phi(t)$ is a complex function defined on $[a,b]$, then
 
@@ -74,7 +74,7 @@ Assume $\phi$ is continuous on $[a,b]$, the equality means $\lambda(t)\phi(t)$ i
 
 EOP
 
-#### Definition 4.4 Arc Length
+#### Definition 6.4 Arc Length
 
 Let $\gamma$ be a curve in the complex plane defined by $\gamma(t)=x(t)+iy(t)$, $t\in[a,b]$. The arc length of $\gamma$ is given by
 
@@ -117,7 +117,7 @@ $$
 \int_{\Gamma} f(\zeta) d\zeta=\int_0^{2\pi} f(\gamma(t))\gamma'(t) dt=\int_0^{2\pi} \frac{1}{Re^{-it}}iRe^{it} dt=2\pi i
 $$
 
-#### Theorem 4.11 (Uniform Convergence)
+#### Theorem 6.11 (Uniform Convergence)
 
 If $f_n(z)$ converges uniformly to $f(z)$ on $\Gamma$, assume length of $\Gamma$ is finite, then
 
@@ -144,7 +144,7 @@ $$
 
 EOP
 
-#### Theorem 4.6 (Integral of derivative)
+#### Theorem 6.6 (Integral of derivative)
 
 Suppose $\Gamma$ is a closed curve, $\gamma:[a,b]\to\mathbb{C}$ and $\gamma(a)=\gamma(b)$.