By Steven G. Krantz

Complex variables is an actual, dependent, and desirable topic. offered from the viewpoint of contemporary paintings within the box, this new e-book addresses complicated themes in complicated research that verge on present parts of study, together with invariant geometry, the Bergman metric, the automorphism teams of domain names, harmonic degree, boundary regularity of conformal maps, the Poisson kernel, the Hilbert rework, the boundary habit of harmonic and holomorphic features, the inhomogeneous Cauchy–Riemann equations, and the corona problem.

The writer adroitly weaves those diversified subject matters to bare a few pleasant interactions. probably extra importantly, the themes are awarded with an knowing and clarification in their interrelations with different vital components of arithmetic: harmonic research, differential geometry, partial differential equations, strength conception, summary algebra, and invariant concept. even though the e-book examines complicated research from many various issues of view, it makes use of geometric research as its unifying theme.

This methodically designed booklet includes a wealthy choice of routines, examples, and illustrations inside every one person bankruptcy, concluding with an in depth bibliography of monographs, learn papers, and a radical index. looking to trap the mind's eye of complex undergraduate and graduate scholars with a uncomplicated historical past in complicated analysis—and additionally to spark the curiosity of professional staff within the field—the ebook imparts an effective schooling either in complicated research and in how sleek arithmetic works.