Cornerstones

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge …

This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the …

This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the …

The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm

​​Hermitian Analysis: From Fourier Series to Cauchy-Riemann Geometry provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transf

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides f

Classical mechanics is a chief example of the scientific method organizing a "complex" collection of information into theoretically rigorous, unifying principles; in this sense, mechanics represents one of the highest forms of mathematical modeling.

This is a revised and extended version of my 1995 elementary introduction to partial di?erential equations. The material is essentially the same except for three new chapters. The ?rst (Chapter 8) is about non-linear equations of ?rst order and in pa

I am sure that something must be found. There must exist a notion of generalized functions which are to functions what the real numbers are to the rationals (G. Peano, 1912) Not that much effort is needed, for it is such a smooth and simple theory (F

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat vario

Geometric measure theory has roots going back to ancient Greek mathematics, for considerations of the isoperimetric problem (to ?nd the planar domain of given perimeter having greatest area) led naturally to questions about spatial regions and bounda

Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research. The author adroitl

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global vie

Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (

Advanced Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Basic Real Analysis</