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Partial Differential Equations and the Finite Element Method
Partial Differential Equations and the Finite Element Method
A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution

Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and...

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design
Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design
Discover applications of Fourier analysis on finite non-Abelian groups

The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods.

Fourier Analysis on Finite Groups with Applications in...

Fourier Analysis (Graduate Studies in Mathematics)
Fourier Analysis (Graduate Studies in Mathematics)

Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calderón and Zygmund. The text was born from a graduate course taught at the Universidad Autónoma de Madrid and incorporates lecture notes from a course taught by José...

Probability and Schrodinger's Mechanics
Probability and Schrodinger's Mechanics

The presentation and interpretation of (non-relativistic) quantum mechanics is a very well-worked area of study; there have to be very good reasons for adding to the literature on this subject.

My reasons are (obviously) that I am far from satisfied with much of the published work and find difficulties with some points, in
...

The History of Approximation Theory: From Euler to Bernstein
The History of Approximation Theory: From Euler to Bernstein

The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing...

Fourier Transform Methods in Finance
Fourier Transform Methods in Finance

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market...

Fourier Analysis: An Introduction (Princeton Lectures in Analysis)
Fourier Analysis: An Introduction (Princeton Lectures in Analysis)

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical...

Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever
Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

Mathematical disputes offer indisputable proof that great mathematical minds are calculating in more ways than one. Fueled by greed, jealousy, ambition, and ego, they have plots worthy of a soap opera, pitting brother against brother, father against son, and student against mentor.

In the sixteenth century, Cardano and Tartaglia battled...

Logic and Philosophy of Mathematics in the Early Husserl (Synthese Library)
Logic and Philosophy of Mathematics in the Early Husserl (Synthese Library)

Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics....

Euclidean & Non-Euclidean Geometries: Development and History
Euclidean & Non-Euclidean Geometries: Development and History

This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high...

Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3)
Real Analysis: Measure Theory, Integration, and Hilbert Spaces (Princeton Lectures in Analysis) (Bk. 3)

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This...

Complex Analysis (Princeton Lectures in Analysis, No. 2)
Complex Analysis (Princeton Lectures in Analysis, No. 2)

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to...

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