Other typos

Author: coolbluealan

content/conformal_mapping.html

@@ -317,7 +317,7 @@ <h1>Conformal Mapping</h1>
 
       <div id="section2">
 
-        <h2>Analytics functions</h2>
+        <h2>Analytic functions</h2>
 
         <p>
           A remarkable geometrical property enjoyed by all complex
@@ -328,7 +328,7 @@ <h2>Analytics functions</h2>
 
         <div class="theorem">
           If $f$ is analytic in a domain $D$ containing $z_0,$ and if
-          $f'(z_0)\neq 0,$ then $w=f(z)$ is a conformal mapping at $z_0.$
+          $f'(z_0)\neq 0,$ then $w=f(z)$ is conformal at $z_0.$
         </div>
 
         <div class="proof">
@@ -383,7 +383,7 @@ <h2>Analytics functions</h2>
           <div class="scroll-wrapper">
             \begin{eqnarray*}
             \text{arg}\left(f'\left(z_0\right)\cdot z_2'\right)-\text{arg}\left(f'\left(z_0\right)\cdot z_1'\right) &amp;= &amp;
-            \text{arg}\left(f'\left(z_0\right) z_2'\right) +
+            \text{arg}\left(f'\left(z_0\right)\right) +
             \text{arg}\left(z_2'\right)-\left[\text{arg}\left(f'\left(z_0\right)\right)+ \text{arg}\left(z_1'\right)
             \right]\\
             &amp;=&amp; \text{arg}\left(z_2'\right) - \text{arg}\left(z_1'\right).
@@ -720,7 +720,7 @@ <h2>Local inverses</h2>
         <p>
           throughout $V.$
           Since the Cauchy-Riemann equations hold for $u$ and $v,$ they also
-          fold for $x$ and $y,$ that is
+          hold for $x$ and $y,$ that is
           \[
           x_u = y_v \quad \text{and}\quad x_v = - y_u.
           \]

content/fundamental_theorem_of_algebra.html

@@ -144,7 +144,7 @@ <h1>The Fundamental Theorem <br>of Algebra</h1>
               $p(z)$ has 6 roots. 
               <strong>Why does $p(z),$ a polynomial of degree eight, have only six
                 roots?</strong> The reason is that two of the roots are <em>double roots</em>
-              (we also say that its <em>multiplicy is two</em>),
+              (we also say that its <em>multiplicity is two</em>),
               and this fact is also evident in the picture. The <em>single roots</em>
               occur at
               \[