The most significant change in this third edition is the inclusion of a new (starred)
Chapter 17 on planetary motion, in which calculus is employed for a substantial
physics problem.
In preparation for this, the old Appendix to Chapter 4 has been replaced by
three Appendices: the first two cover vectors and conic sections, while polar
coordinates are now deferred until the third Appendix, which also discusses the polar
coordinate equations of the conic sections. Moreover, the Appendix to Chapter 12
has been extended to treat vector operations on vector-valued curves.
Another large change is merely a rearrangement of old material: "The
Cosmopolitan Integral," previously a second Appendix to Chapter 13, is now an
Appendix to the chapter on "Integration in Elementary Terms" (previously
Chapter 18, now Chapter 19); moreover, those problems from that chapter which used
the material from that Appendix now appear as problems in the newly placed
Appendix.
A few other changes and renumbering of Problems result from corrections, and
elimination of incorrect problems.