The second part of the twentyfourth class in Dr Joel Feinstein's G12MAN Mathematical Analysis module is about Rigorous Differential Calculus. Further module materials are available for download from The University of Nottingham open courseware site: http://unow.nottingham.ac.uk/resources/resource.aspx?hid=c6c045f6-286d-6b9f-b96c-36a998632fc3 and on iTunes U: http://itunesu.nottingham.ac.uk/albums/71.rss Dr Feinstein's blog may be viewed at: http://explainingmaths.wordpress.com Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham.