Update lecture_4.md - first formulation of learning goals

src/lecture_4.md

@@ -15,6 +15,14 @@ pi = np.pi
 _(based on chapters 9–11 of the book)_  
 Exercises 9.2, 9.4, 10.1, 10.2, 11.2, 11.5
 
+!!! summary "Learning goals"
+
+    After this lecture you will be able to:
+
+    - formulate equations of motion describing electrons and phonons in 1D.
+    - solve these equations to arrive at the corresponding dispersion relations.
+    - derive the group velocity, effective mass, and density of states from a dispersion relation.
+
 Last lecture:
 
 * Movement of a few atoms (Newton's equations)
@@ -245,6 +253,12 @@ Also a sanity check: when the energy is close to the bottom of the band, $E = E_
 
 ## More complex systems
 
+!!! summary "Learning goals"
+
+    After this lecture you will be able to:
+
+    - formulate equations of motion describing electrons and phonons in 1D when there is more than one degree of freedom per unit cell 
+    
 ### More hoppings in LCAO
 
 Consider electrons in a 1D atomic chain again