The final movement of the Eroica, at last, placed the symphony on an even keel as Beethoven abandoned the brisk rondo of Mozart and Haydn and presents us with a vast theme and variations, complementary in scope and import to the sonata allegro of movement one.
The Eroica represents a departure from Beethoven's normal method of composition in that it appears to have been conceived from back to front. Sketches for the Eroica show Beethovens planning for the first three movements but the finale absent. The reason is that he had, in a sense, already planned the finale. The thematic basis for the fourth movement is a simple tune that is found in his 12 German Contradances WoO 14, Die Geschöpfe des Promethus (The Creatures of Prometheus) Op 43 as well as the Variations, Op 35. The Op. 35 were completed just prior to starting work on the Eroica so that he already had his blueprint for the finale.
Michael Steinberg in The Symphony: A Listener's Guide says of the theme, "The bass of Beethoven's contradance/ Prometheus theme is simple, sturdy, easily grasped, remembered, and identified. The melody up above shares these characteristics. It is also readily subject to transformation and decoration, though it has a sufficiently clear profile to keep it recognizable no matter what happens to it. Beethoven's first and perhaps most remarkable discovery in his 1802 Piano Variations was that the bass all by itself, in spite of its neutrality, has attractive possibilities."
Just the sort of tune that appealed Beethoven.