The first edition of this book, published in German, came into being as
the result of lectures which the authors held over a period of
several Years since 1953 at the Universities of Helsinki and Zurich.
The Introduction, which follows, provides information on what motivated
our presentation of an absolute, coordinate- and dimension-free
infinitesimal calculus.
Little previous knowledge is presumed of the reader. It can be recommended
to students familiar with the usual structure, based on coordinates,
of the elements of analytic geometry, differential and integral
calculus and of the theory of differential equations. We are indebted to H. Keller, T. Klemola, T. Nieminen, Ph. Tondeur
and K. I. Virtanen, who read our presentation in our first manuscript,
for important critical remarks.