Differential calculus and equations

Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications.

Optimal control theory has numerous applications in both science and engineering.

This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.

Mathematical Physics with Partial Differential Equations is for advanced undergraduate and beginning graduate students taking a course on mathematical physics taught out of math departments.

This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences.

This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids.

Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation.

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations.

Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems.

Stochastic Differential Equations and Diffusion Processes

Delay Differential Equations emphasizes the global analysis of full nonlinear equations or systems.

This book provides an introduction to the structure and stability properties of solutions of functional differential equations.

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems.

Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs).

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations.

Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology.

The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications.

Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions.

Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations.

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It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner.

This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e.

A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations.

Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations.

This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences.

Basic Linear Partial Differential Equations

Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations.

The analysis of differential equations in domains and on manifolds with singularities belongs to the main streams of recent developments in applied and pure mathematics.

Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc.

The objective of this book is to report the results of investigations made by the authors into certain hydrodynamical models with nonlinear systems of partial differential equations.

Scattering Theory for dissipative and time-dependent systems has been intensively studied in the last fifteen years.

Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations.

Part I of this volume surveys the developments in the analysis of nonlinear phenomena in Japan during the past decade, while Part II consists of up-to-date original papers concerning qualitative theories and their applications.

The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.

Introduction to the Theory of Linear Partial Differential Equations

Spectral Transform and Solitons

Asymptotic Analysis of Singular Perturbations

This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups.

This is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions).

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades.

The problems treated in this volume concern nonlinear partial differential equations occurring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics.

An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research.

The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems.

This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations.

This volume is the result of lectures delivered at the second meeting on the subject of nonlinear partial differential equations, held at Tohoku University, 27-29 February 1984.

Transmutation Theory and Applications

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al.