typos

doc/src/week35/week35.do.txt

@@ -551,11 +551,11 @@ Let now $\bm{y}=\bm{A}\bm{x}$, where $\bm{A}$ is an $m\times n$ matrix and the m
 y_i = \sum_{j=0}^{n-1}a_{ij}x_j,
 \]
 !et
-with $\all i=0,1,2,\dots,m-1$. The individual matrix elements of $\bm{A}$ are given by the symbol $a_{ij}$.
+with $\forall i=0,1,2,\dots,m-1$. The individual matrix elements of $\bm{A}$ are given by the symbol $a_{ij}$.
 It follows that the partial derivatives of $y_i$ with respect to $x_k$ 
 !bt
 \[
-\frac{\partial y_i }{\partial x_k}= a_{ik} \all i=0,1,2,\dots,m-1.
+\frac{\partial y_i }{\partial x_k}= a_{ik} \forall i=0,1,2,\dots,m-1.
 \]
 !et
 
@@ -576,7 +576,7 @@ multiplications
 
 !bt
 \[
-\alpha = \bm{y}^T\bm{A}\bm{x}$,
+\alpha = \bm{y}^T\bm{A}\bm{x},
 \]
 !et
 with $\bm{y}$ a vector of length $m$, $\bm{A}$ an $m\times n$ matrix and $\bm{x}$ a vector of length $n$. We assume also that $\bm{A}$ does not depend on any of the two vectors.
@@ -584,7 +584,7 @@ In order to find the derivative of $\alpha$ with respect to the two vectors, we
 $\bm{z}^T=\bm{y}^T\bm{A}$, a vector of length $n$. We have then
 !bt
 \[
-\alpha = \bm{z}^T\bm{x}$,
+\alpha = \bm{z}^T\bm{x},
 \]
 !et
 which means that (using our previous example) we have
@@ -612,7 +612,7 @@ matrix with dimension $n\times n$.
 
 !bt
 \[
-\alpha = \bm{x}^T\bm{A}\bm{x}$,
+\alpha = \bm{x}^T\bm{A}\bm{x},
 \]
 !et
 with $\bm{x}$ a vector of length $n$.
@@ -620,7 +620,7 @@ with $\bm{x}$ a vector of length $n$.
 We write out the specific sums involved in the calculation of $\alpha$
 !bt
 \[
-\alpha = \sum_{i=0}^{n-1}\sum_{j=0}^({n-1}x_i a_{ij}x_j, 
+\alpha = \sum_{i=0}^{n-1}\sum_{j=0}^{n-1}x_i a_{ij}x_j, 
 \]
 !et
 taking the derivative of $\alpha$ with respect to a given component $x_k$ we get the two sums
@@ -629,7 +629,7 @@ taking the derivative of $\alpha$ with respect to a given component $x_k$ we get
 \frac{\partial \alpha}{\partial x_k}  = \sum_{i=0}^{n-1}a_{ik}x_i+\sum_{j=0}^{n-1}a_{kj}x_j, 
 \]
 !et
-for $\all k =0,1,2,\dots,n-1$. We identify these sums as
+for $\forall k =0,1,2,\dots,n-1$. We identify these sums as
 !bt
 \[
 \frac{\partial \alpha}{\partial \bm{x}}  = \bm{x}^T\left(\bm{A}^T+\bm{A}\right).
@@ -670,7 +670,7 @@ and the partial derivative
 \frac{\partial \alpha}{\partial z_k}  = \sum_{i=0}^{n-1}\left(x_i\frac{\partial y_i}{\partial z_k}+y_i\frac{\partial x_i}{\partial z_k}\right),
 \]
 !et
-for $\all k =0,1,2,\dots,n-1$. We can rewrite the partial derivative in a more compact form as
+for $\forall k =0,1,2,\dots,n-1$. We can rewrite the partial derivative in a more compact form as
 !bt
 \[
 \frac{\partial \alpha}{\partial \bm{z}}  = \bm{x}^T\frac{\partial \bm{y}}{\partial \bm{z}}+\bm{y}^T\frac{\partial \bm{x}}{\partial \bm{z}},