content: On the blackboard:
  * types for some examples, most importantly D
  * derivative of a function f : Func = REAL -> REAL
  * reminder of lim example from Thu 2018-01-25
  * using lim to define |D|
  
  Lecture 3.1 Live "coding" (typing)
  
  Exam question 2 from 2016-03:
  
  From exam 2016-03-16:
  
      Consider the following text from Mac Lane's "Mathematics, Form and
      Function" (page 182):
  
     \begin{quote}
       In these cases one tries to find not the values of |x| which
       make a given function |y = f(x)| a minimum, but the values of a given
       function |f(x)| which make a given quantity a minimum.  Typically,
       that quantity is usually measured by an integral whose integrand is
       some expression |F| involving both |x|, values of the function |y =
       f(x)| at interest and the values of its derivatives - say an
       integral
     \end{quote}
  
      $$∫_a^b F(y, y', x)dx,      where y = f(x).$$
  
      Give the types of the variables involved (|x|, |y|, |y'|, |f|, |F|,
      |a|, |b|) and the type of the four-argument integration operator:
  
      $$∫_.^. \cdot d\cdot$$
  
  \begin{code}
  type REAL = Double
  \end{code}
  
  Here is another variant:
  \begin{code}
  \end{code}
  