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Reverberations of a Stroke
In the early morning hours of Feb. 1, 2016, Karl Gustafson became instinctively aware that something catastrophic was happening inside him. A severe headache that had persisted for days had taken a sudden turn for the worse, and a clear inner voice ordered him to obtain immediate help. With determined effort, he tapped out the digits “9-1-1” on his phone—bringing an ambulance to his door quickly and saving his life. Emergency Room doctors would soon learn that Professor Gustafson, a renowned American mathematician, had suffered a deep brain hemorrhage, and that the situation was dire. By the time his condition was diagnosed, blood had pooled into all four ventricles of Gustafson’s brain and he was comatose. Against all odds and surprising everyone, the author emerged from a near-death state to go on to what he calls his “Second Life”. This is the story of his miraculous journey of recovery, an inspirational tale of grit and determination, in his own words.
Numerical Range
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more ...
Introduction to Partial Differential Equations and Hilbert Space Methods
This volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.
Innovations in Multivariate Statistical Analysis
The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of the American Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of th...
Applied Analysis by the Hilbert Space Method
Numerous worked examples and exercises highlight this unified treatment. Simple explanations of difficult subjects make it accessible to undergraduates as well as an ideal self-study guide. 1990 edition.
Hilbert Space Methods in Partial Differential Equations
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Physics and the Ultimate Significance of Time
Challenges the conventional view of the nature of time.
Antieigenvalue Analysis
Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.
David Hume's Critique of Infinity
This new study of David Hume s philosophy of mathematics critically examines his objections to the concept of infinity, and his alternative phenomenalist theory of space and time as constituted by minima sensibilia or sensible extensionless indivisibles.
