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Stochastic Differential Equations
This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new …
An Introduction to Infinite-Dimensional Analysis
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic …
Sheaves in Topology
Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. …
Elementary Number Theory, Cryptography and Codes
In this volume one finds basic techniques from algebra and number theory (e.g. congruences, unique factorization domains, finite fields, quadratic residues, primality tests, …
Mathematical Analysis II
An entire generation of mathematicians has grown up during the time - tween the appearance of the ?rst edition of this textbook and the publication of the fourth edition, a …
Frontiers of Numerical Analysis
TheEleventh LMS-EPSRCComputational MathematicsandScienti?cC- puting Summer School was held at the University of Durham, UK, from the 4th of July to the 9th of July 2004. This was …
Analysis I
Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a …
Qualitative Theory of Planar Differential Systems
Our aim is to study ordinary di?erential equations or simply di?erential s- tems in two real variables x ? = P(x,y), (0.1) y? = Q(x,y), r 2 where P and Q are C functions de?ned on …
Points and Lines
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. …
The Homotopy Index and Partial Differential Equations
The homotopy index theory was developed by Charles Conley for two sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi cal measure of …
Notes on Geometry
In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its …
Bifurcations and Catastrophes
Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and …