'In a class populated by students who already have some exposure to
the concept of a manifold, the presence of chapter 3 in this text
may make for an unusual and interesting course. The primary
function of this book will be as a text for a more conventional
course in the classical theory of curves and surfaces.'MAA
ReviewsThis engrossing volume on curve and surface theories is the
result of many years of experience the authors have had with
teaching the most essential aspects of this subject. The first half
of the text is suitable for a university-level course, without the
need for referencing other texts, as it is completely
self-contained. More advanced material in the second half of the
book, including appendices, also serves more experienced students
well.Furthermore, this text is also suitable for a seminar for
graduate students, and for self-study. It is written in a robust
style that gives the student the opportunity to continue his study
at a higher level beyond what a course would usually offer. Further
material is included, for example, closed curves, enveloping
curves, curves of constant width, the fundamental theorem of
surface theory, constant mean curvature surfaces, and existence of
curvature line coordinates.Surface theory from the viewpoint of
manifolds theory is explained, and encompasses higher level
material that is useful for the more advanced student. This
includes, but is not limited to, indices of umbilics, properties of
cycloids, existence of conformal coordinates, and characterizing
conditions for singularities.In summary, this textbook succeeds in
elucidating detailed explanations of fundamental material, where
the most essential basic notions stand out clearly, but does not
shy away from the more advanced topics needed for research in this
field. It provides a large collection of mathematically rich
supporting topics. Thus, it is an ideal first textbook in this
field.
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