Calculus and mathematical analysis

A unifying approach suitable for graduate students and mathematicians.

A careful exposition of the most fundamental questions in the theory of nonlinear Markov processes.

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

This introductory text on complex variable methods has been updated with even more examples and exercises.

A systematic and comprehensive introduction to ordinary differential equations for engineering students and practitioners.

This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.

The first comprehensive, unified development of the theory of p-adic differential equations.

A comprehensive, self-contained treatment of non-Archimedean functional analysis, with an emphasis on locally convex space theory.

Moving frames explained in the language of undergraduate calculus, suitable for graduate students.

First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.

An introduction to rough path theory and its applications to stochastic analysis, written for graduate students and researchers.

A 2003 textbook on Fourier and Laplace transforms for undergraduate and graduate students.

Presents new algorithms for determining orbits; ideal for graduate students and researchers in applied mathematics, physics, astronomy and aerospace engineering.

First book on the fast multipole BEM, bringing together classical theory in BEM formulations and the fast multipole method.

The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators.

An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.

A fully revised and appended edition of this unique volume, which develops together these two important subjects.

A treatment of positive characteristic phenomena from an analytic viewpoint.

Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.

An extensively updated second edition including new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients.

This book provides probabilists with sufficient background to begin applying PDEs to probability theory and probability theory to PDEs.

Presents the major mathematical tools necessary for the study of complex dynamics.

Detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions.

This book concerns partial differential equations applied to fluids problems in science and engineering.

Presents concepts of chaotic systems for researchers and graduate students in statistical mechanics and chaos.

A self-contained and elementary presentation of Lie group theory, with numerous exercises and worked examples ideal for a graduate course.

An update of this popular introduction to probability theory and information theory with new material on Markov chains.

An introduction to harmonic measure on plane domains and careful discussion of the work of Makarov, Carleson, Jones and others.

This edition of this successful text includes chapters on hyperelastic plastic behaviour and updates to FLagSHyP web program.

Self-contained text, ideal for graduate students new to the area and researchers.

The main tools of involutive systems of complex vector fields together with the major results from last twenty five years.

This 2007 textbook uses examples, exercises, diagrams, and unambiguous proof, to help students make the link between classical and differential geometries.

Monograph exploring the connections that forcing makes with descriptive set theory and other areas of mathematics.

This book introduces applied mathematics through Fourier analysis, with applications to studying sampling theory, PDEs, probability, diffraction, musical tones, and wavelets.

This book uses mathematical arguments to obtain insights into random graphs.

A student-friendly Analysis textbook suitable as an undergraduate course book or for self-study.

A reference/advanced text on part of applied analysis with applications in numerical analysis and computer-aided geometric design.

This book contains a wealth of inequalities used in linear analysis, explaining in detail how they are used.

Authoritative text presenting a broad view of the spectral theory of non-self-adjoint linear operators.

This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models of complex systems.

This thoroughly revised 2007 third edition updates the definitive introduction to finite element methods.

Surveys topics in the theory and applications of dynamical systems subject to random shocks.

Details the interaction between the two vigorous fields of non-commutative geometry and quantum stochastic processes.

This book, first published in 2007, is for the applied researcher performing data analysis using linear and nonlinear regression and multilevel models.

Graduate text explaining how methods of nonlinear analysis can be used to tackle nonlinear differential equations.

Introduction to singularity theory based on MSc course taught by author; novel synthesis, with new results not found elsewhere.

Graduate text/reference in number theory.

An introduction for graduate students, a guide for users, and a comprehensive resource for experts.

Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism.

A self-contained introduction to the theory of scattered data approximation, suitable for graduates and researchers.