docs: fix reported textbook typos

content/cauchy_goursat_theorem.html

@@ -371,7 +371,7 @@ <h2>Simply and multiply connected domains</h2>
               </p>
 
               <div class="theorem">
-                If a function $f$ is analytic throughout a simply simple connected domain $D,$ 
+                If a function $f$ is analytic throughout a simply connected domain $D,$ 
                 then
                 \[
                 \int_C f(z) \, dz = 0.
@@ -429,7 +429,7 @@ <h2>Simply and multiply connected domains</h2>
 
 
               <div class="corollary">
-                A function $f$ that is analytic throughout a simply simple connected domain $D$ 
+                A function $f$ that is analytic throughout a simply connected domain $D$ 
                 must have an antiderivative everywhere in $D.$
               </div>
 

content/cauchy_integral_formula.html

@@ -315,7 +315,7 @@ <h2>An extension of the Cauchy Integral Formula</h2>
       </div>
 
       <p>
-        In general, we can use induction to obtain the second remarkabl formula:
+        In general, we can use induction to obtain the second remarkable formula:
       </p>
       <div class="scroll-wrapper">
         \begin{eqnarray}\label{general-derivative}
@@ -368,12 +368,12 @@ <h2>An extension of the Cauchy Integral Formula</h2>
           \[
           \frac{z+1}{z^4+2iz^3} = \frac{\dfrac{z+1}{z+2i}}{z^3}
           \]
-          we can identiry, $z_0=0,$ $n=2$ and $f(z) = \dfrac{z+1}{z+2i}.$
+          we can identify $z_0=0,$ $n=2$ and $f(z) = \dfrac{z+1}{z+2i}.$
           Then
           \[
           f^{(2)}(z) = \frac{2-4i}{(z+2i)^3},
           \]
-          and so $f(0) = \ds\frac{2i+1}{4i}.$ Hence, by (\ref{general-integral-der}) we find
+          and so $f^{(2)}(0) = \ds\frac{i+2}{4}.$ Hence, by (\ref{general-integral-der}) we find
         </p>
         <div class="scroll-wrapper">
           \begin{eqnarray*}

content/logarithmic_function.html

@@ -232,7 +232,7 @@ <h2>Branches of logarithms</h2>
                 </p>
 
                 <p>Now, let $\alpha$ be any real number. If we restrict the value of $\theta$ so that $\alpha &lt;
-                    \theta &lt; \alpha + 2n\pi$ , then the function
+                    \theta &lt; \alpha + 2\pi$ , then the function
                     </p><div class="scroll-wrapper">
                         \begin{eqnarray}\label{log3}
                     \log z=\ln r +i\theta \quad (r&gt; 0, \alpha &lt; \theta &lt; \alpha + 2\pi ),
@@ -576,4 +576,4 @@ <h2>Final remark</h2>
   <script async src="js/prism.js"></script>
 </body>
 
-</html>
+</html>