fix some small issues

src/fourier.md

@@ -98,7 +98,8 @@ representing complex conjugation is not required.
 
 We can normalize the basis functions - the normalized functions are
 $$\phi_n(x) = \sqrt{\frac{2}{L}} \sin(k_n x)$$ where of course
-$n=1, 2, \ldots$.\
+$n=1, 2, \ldots$.
+
 **Exercise** Check that this is the correct normalization. Also show
 that two such functions for different indices $n$ and $m$ are
 orthogonal.
@@ -123,7 +124,7 @@ as a result of the delta function. Writing out the inner product as an
 integral, we have
 $$\tilde{D}_n = \sqrt{\frac{2}{L}} \int_0^L \sin(n\pi x/L) f(x) dx.$$
 What we have seen is quite miraculous. If we pluck a string in the
-middle, its shape is given by $ f(x) = a (\textbar{}L/2-x\textbar{} +
+middle, its shape is given by $ f(x) = a (|L/2-x | +
 L/2).$ This can apparently also be written as an infinite sum over sine
 functions! This is demonstrated in the picture below, where the
 triangular shape of a plucked string just before it is released, is
@@ -185,7 +186,8 @@ position and speed of the string are obviously real. In fact, the
 complex form of the solution has just been used for convenience. Once we
 have found a complex solution, we have two real solutions available: the
 real and the imaginary part of the complex solution. The complex
-function is just a quick way of finding these two meaningful solutions.\
+function is just a quick way of finding these two meaningful solutions.
+
 **Exercise** Verify these statements, i.e. show that
 ${\left\langle{\phi_n}\right|} \phi_m \rangle = \delta_{nm}$.