Electronic Resource
Hermitian analysis : from fourier series to cauchy-riemann geometry
This book aims both to synthesize much of undergraduate mathematics and to introduce research topics in geometric aspects of complex analysis in several variables.
The topics all relate to orthogonality, real analysis, elementary complex variables,
and linear algebra. I call the blend Hermitian analysis. The book developed from
my teaching experiences over the years and specifically from Math 428, a capstone
honors course taught in Spring 2013 at the University of Illinois. Many of the
students in Math 428 had taken honors courses in analysis, linear algebra, and beginning abstract algebra. They knew differential forms and Stokes’ theorem. Other
students were strong in engineering, with less rigorous mathematical training, but
with a strong sense of how these ideas get used in applications.
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