Hardcover | March 2015 | ISBN: 9780691161297
296 pp. | 7 x 10 | 49 line illus.
This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis.
Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green’s functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs.
Provides an accessible yet rigorous introduction to partial differential equations
Draws connections to advanced topics in analysis
Covers applications to continuum mechanics
The ideal textbook for beginning graduate and advanced undergraduate courses
Solutions manual (available only to professors) and supplementary materials are available online
An online illustration package is available to professors
Michael Shearer is professor of mathematics at North Carolina State University. He is a fellow of the American Mathematical Society. Rachel Levy is associate professor of mathematics at Harvey Mudd College. She is a recipient of the 2013 Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member and creator of the Grandma Got STEM project.
Hardcover | June 2015 | ISBN: 9780691119274
704 pp. | 6 x 9 | 55 halftones.
This is the first full-scale biography of Leonhard Euler (1707?83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler’s eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler’s massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler’s work in its multilayered context?personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler’s fundamental contributions to almost every area of pure and applied mathematics?especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics?to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory.
The narrative takes the reader from Euler’s childhood and education in Basel through his first period in St. Petersburg, 1727?41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Moving to Berlin, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, proposed a pulse theory of light, and faced Frederick the Great. Returning to St. Petersburg in 1766, Euler created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton’s dynamics, and published the best-selling Letters to a German Princess?all despite eye problems that ended in near-total blindness. In telling Euler’s remarkable story, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment.
Ronald S. Calinger is professor emeritus of history at the Catholic University of America and the founding chancellor of the Euler Society. His books include A Contextual History of Mathematics, Vita Mathematica, and Classics of Mathematics.
Series: Springer Proceedings in Mathematics & Statistics, Vol. 106
2014, XII, 526 p. 14 illus.
ISBN 978-4-431-55215-4
Provides classification problems and some new results in real and complex Grassmann manifolds
Introduces recent progress in geometric structures developed on Lagrangian submanifolds, Riemannian symmetric spaces, and Lorentzian manifolds
Presents investigations of several kinds of geometric properties on Riemannian manifolds by famous differential geometers from all over the world
Edited in collaboration with the Grassmann Research Group, this book contains many important articles delivered at the ICM 2014 Satellite Conference and the 18th International Workshop on Real and Complex Submanifolds, which was held at the National Institute for Mathematical Sciences, Daejeon, Republic of Korea, August 10?12, 2014.
The book covers various aspects of differential geometry focused on submanifolds, symmetric spaces, Riemannian and Lorentzian manifolds, and Kahler and Grassmann manifolds.
Content Level ≫ Research
Keywords ≫ Complex Submanifolds - Geometry - Hermitian Symmetric Space - Hypersurfaces - Real Submanifolds
Related subjects ≫ Geometry & Topology
Series: Probability Theory and Stochastic Modelling, Vol. 73
2015, VIII, 211 p.
ISBN 978-3-319-12852-8
Offers new material and a more general approach to the theory than in previous literature
Includes many different applications first treated by the authors
Presents interesting results for environmental sciences as well as financial mathematics and other fields where sudden and unexpected phenomena occur
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces.
The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results, and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis, and in particular the theory of operator semigroups. ?
Series: IMPA Monographs, Vol. 1
2015, X, 250 p. 35 illus.
Hardcover
ISBN 978-3-319-14309-5
Presents the birational classification of holomorphic foliations of surfaces
Discuss the theory introduced by L.G. Mendes and M. McQuillan
First book published in IMPA Monographs series
The text presents the birational classification of holomorphic foliations of surfaces. It discusses at length the theory developed by L.G. Mendes, M. McQuillan and the author to study foliations of surfaces in the spirit of the classification of complex algebraic surfaces.
Introduction: From Surfaces to Foliations.- Local Theory.- Foliations and Line Bundles.- Index Theorems.- Some Special Foliations.- Minimal Models.- Global 1-forms and Vector Fields.- The Rationality Criterion.- Numerical Kodaira Dimension.- Kodaira Dimension.- References.