Theorem I
The change in slope between the tangents drawn to the elastic curve at any two points A and B is equal to the product of 1/EI multiplied by the area of the moment diagram between these two points.

Theorem II
The deviation of any point B relative to the tangent drawn to the elastic curve at any other point A, in a direction perpendicular to the original position of the beam, is equal to the product of 1/EI multiplied by the moment of an area about B of that part of the moment diagram between points A and B.

Area Moment Method:
Part 1: This Video
Part 2:    • Area Moment Method Part 2  Location ...  

Related Links:
http://mathalino.com/node/749
http://mathalino.com/node/786

Background Music:
Brooklin by Quincas Moreira (   / quinquilhariaaudio  . A royalty free music offered for download at YouTube Audio Library.