A key ingredient in learning mathematics is problem solving. This is the strength, and no doubt
Advanced calculus is not a single theory. However, the various sub-theories, including
vector analysis, in?nite series, and special functions, have in common a dependency on the
fundamental notions of the calculus. An important objective of this second edition has been to
modernize terminology and concepts, so that the interrelationships become clearer. For exam-
ple, in keeping with present usage fuctions of a real variable are automatically single valued;
di?erentials are de?ned as linear functions, and the universal character of vector notation and
theory are given greater emphasis. Further explanations have been included and, on occasion,
the appropriate terminology to support them.
The order of lectures is modestly rearranged to provide what may be a more logical
structure.
A brief introduction is provided for most lectures. Occasionally, a historical note is
included; however, for the most part the purpose of the introductions is to orient the reader
to the content of the lectures