Norton's Complex Variables for Scientists and Engineers is a new
textbook, originally written for the Complex Analysis term of an
undergraduate Mathematical Methods of Physics sequence at UCLA. It
does not assume any prior knowledge of complex numbers or functions
and is therefore suitable for a first course in the subject for
undergraduate students who have had an introductory course in the
standard calculus of real variables.
The book provides a thorough grounding in the theory of complex
functions. The mathematics is careful, yet accessible to any
student who knows basic calculus. It covers the subjects essential
in any scientific or engineering discipline that uses mathematics
beyond the elementary level. The reader will find a clear
presentation of complex differentiation and integration, Cauchy's
theorem and integral formula, and infinite series and products.
There is a long and thorough section on applying the residue
theorem to the evaluation of real integrals, and a section on
special functions and their integral representations. The book
includes the conformal property of analytic functions and its
applications to boundary value problems in electrostatics; a
topological analysis that leads to the extension of the residue
theorem to multiply-connected regions and contours; a section on
the method of steepest descent; a section on the Riemann zeta
function; and a discussion of the convergence of integral
representations, which is rarely presented in detail in
introductory texts. Those who want to see the mathematics done
carefully, and who are looking for more than a 'cook-book'
treatment that presents the basic techniques without exploring all
the nooks and crannies of the subject, will find these sections
especially satisfying. The preface suggests how to extract a
bare-bones course for those in a hurry, without losing sight of the
beauty and depth of the subjects.
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