This book originated as a set of lectures prepared for courses given by me at
the University of Linköping in Sweden and at the University of South
Australia in Australia. At Linköping University the material (apart from
Section 3.E) was delivered in a second year, single semester course (14 weeks,
2 two-hour lectures per week) to engineering students, with the first half
focused on the differential calculus of real-valued multivariable functions,
while the second half was divided between integral calculus and vector calculus. At the University of South Australia the subject was delivered in two separate semester courses (12 weeks, 2 two-hour lectures per week), the first of
which was offered to second year engineering, science and mathematics students and featured differential and integral calculus, including an introduction to partial differential equations. The second course, taken mostly by third year mathematics and science students, dealt with vector calculus, although only
the first five weeks of that course was covered by the material in this book.
The lectures generally were so well-received by students that it was thought
the material might appeal to a wider audience. Having taken the decision to
convert my notes into a book, I aimed for a document of manageable size
rather than generate yet another bulky tome on calculus. The result is a book
that students can carry easily to and from class, can take out and leaf through
on the library lawn, or in a booth of a pub, or while lying on the banks of a
river waiting for the fish to bite.