fixed typos

diff --git a/examples/step-53/doc/intro.dox b/examples/step-53/doc/intro.dox
index 93519dc785e8a16d2c30e0e4b0ed85c985345c8b..f86e5b6d2d8057b1c6df648b820cf0cb2ab4790b 100644 (file)
--- a/examples/step-53/doc/intro.dox
+++ b/examples/step-53/doc/intro.dox
@@ -71,7 +71,7 @@ program the details of your geometry:
 - Integration: When using higher order finite element methods, it is often
   necessary to compute integrals using curved approximations of the boundary,
   i.e., describe each edge or face of cells as curves, instead of straight
-  line segments or bilinear patches). The same is, of course, true when
+  line segments or bilinear patches. The same is, of course, true when
   integrating boundary terms (e.g., inhomogenous Neumann boundary
   conditions). For the purpose of integration, the various Mapping classes
   then provide the transformation from the reference cell to the actual cell.

diff --git a/include/deal.II/fe/mapping.h b/include/deal.II/fe/mapping.h
index 32be5cc56935d3858cdb47d0e031c1df3ccc64df..6713a4b1d9f4833beab16643d9b41c2f18affb9c 100644 (file)
--- a/include/deal.II/fe/mapping.h
+++ b/include/deal.II/fe/mapping.h
@@ -891,7 +891,7 @@ public:
    * The mapping types currently implemented by derived classes are:
    * <ul>
    * <li> @p mapping_contravariant: maps a vector field on the reference cell
-   * is to the physical cell through the Jacobian:
+   * to the physical cell through the Jacobian:
    * @f[
    * \mathbf u(\mathbf x) = J(\hat{\mathbf  x})\hat{\mathbf  u}(\hat{\mathbf  x}).
    * @f]

diff --git a/include/deal.II/grid/manifold.h b/include/deal.II/grid/manifold.h
index df0284b85f7777b620111f29048bed05b3931abb..80b3067a0a763f7c042554a5700a8b4335a28b21 100644 (file)
--- a/include/deal.II/grid/manifold.h
+++ b/include/deal.II/grid/manifold.h
@@ -66,7 +66,7 @@ namespace Manifolds
  *
  * In the most essential use of manifolds, manifold descriptions are used
  * to create a "point between other points". For example, when a triangulation
- * creates a new vertex on a cell, face, or edge , it determines the new
+ * creates a new vertex on a cell, face, or edge, it determines the new
  * vertex' coordinates through the following function call:
  *   @code
  *     ...