I need to know the names of two songs.?

In the movie Groundhog Day, towards the end, Phil (Bill Murray)plays 2 songs on the piano and impreses Rita. The first is a jazzy no,. the second a classical piece. I think maybe the second is Rhapsody in Blue, but I am not sure. Do you know what they are?
I need to know the names of BOTH songs.

Sergei Rachmaninov – Eighteenth Variation From Rapsodie On A Theme Of Paganini.. the classical peice.

Murray Perahia – Beethoven piano concerto 3

	Beethoven: The Complete Piano Concertos €18.61 …

	Bartok, Sonate Pour 2 Pianos Et Percussions €12.89 …

	Beethoven – Symphony No. 7, Piano Concerto No. 1, Overture to Coriolan / Solti, Perahia, London Symphony Orchestra [Import USA Zone 1] …

	Mozart : The Piano Concertos (les Concertos pour piano) €19.95 …

	Mozart : Intégrale des concertos pour piano (Coffret 12 CD) €29.98 …

	Concertos pour piano Nos 1 à 4 €17.49 …

	Satie: 3 Gymnopedies & 3 Gnossiennes for the Piano €2.12 These two fascinating works are combined into one volume that includes an interesting biography, background information on the writing of the music, indispensable performance suggestions and a listing of recommended readings and recordings….

	Marvin Kahn’s Breaks, Fillers, Endings, and Introductions for Popular Piano Playing €5.38 …

	Impromptu, Op. 90, No. 2 €0.61 …

	Mon frère Chilpéric, chronique des rois aux cheveux longs …