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An award-winning science writer introduces us to mathematics using the extraordinary equation that unites five of mathematics' most important numbers

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(Hardback)

(Paperback)

(Paperback)

(Paperback)

A bestselling introductory course, this book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and intgration.

(Hardback)

Beginning with the basic facts of functional analysis, this title looks at Banach spaces, Lp spaces, and distribution theory, and highlights their roles in harmonic analysis. It uses the Baire category theorem to illustrate several points, including the existence of Besicovitch sets.

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A magisterial history of calculus (and the people behind it) from one of the world's foremost mathematicians.

(Hardback)

Reciprocity laws of various kinds play a central role in number theory. This book states several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. It also covers the zeta function of an abelian variety as a main theme.

(Paperback)

The aim of this work is to present a unified approach to the modern field of control theory and to provide a technique for making problems involving deterministic, stochastic, and adaptive processes of both linear and nonlinear type amenable to machine solution. Mr. Bellman has used the theory of dynamic programming to formulate, analyze, and prepa

(Hardback)

(Hardback)

Focuses on heat equations associated with non self-adjoint uniformly elliptic operators. This book provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. It then treats Lp properties of solutions to a wide class of heat equations.

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(Paperback)

The purpose of this book is to describe a certain number of results involving the study of non-linear analytic dependence of some functionals arising naturally in P.D.E. or operator theory.

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Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-know Yamabe type.

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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial different

(Hardback)

(Hardback)

Offers an introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. This book traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter.

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The description for this book, Calculus on Heisenberg Manifolds. (AM-119), will be forthcoming.

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In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. This book realizes this by creating a logarithmic Hodge theory. It uses the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure.

(Paperback)

(Paperback)

Formal verification increasingly has become recognized as an answer to the problem of how to create ever more complex control systems, which nonetheless are required to behave reliably. To be acceptable in an industrial setting, formal verification must be highly algorithmic; to cope with design complexity, it must support a top-down design methodo

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(Paperback)

The description for this book, Contributions to the Theory of Partial Differential Equations. (AM-33), will be forthcoming.