Differential calculus and equations

This book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics.

Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences.

During the past three decades, the development of nonlinear analysis, dynamical systems and their applications to science and engineering has stimulated renewed enthusiasm for the theory of Ordinary Differential Equations (ODE).

New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 20 years, making a big impact on science and technology.

This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics.

This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle.

This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem.

This textbook is a self-contained introduction to partial differential equations.

Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth.

New Edition: The Nonlinear Workbook (6th Edition)The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology.

Inequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering.

This book presents a general approach to integration theory, as well as some advanced topics.

This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form.

This book provides an elementary introduction to classical analysis on normed spaces, with special attention paid to fixed points, calculus, and ordinary differential equations.

Complex analysis is a beautiful subject - perhaps the single most beautiful; and striking; in mathematics.

Stability and Time-Optimal Control of Hereditary Systems is the mathematical foundation and theory required for studying in depth the stability and optimal control of systems whose history is taken into account.

The Wiener Wintner ergodic theorem is a strengthening of Birkhoff pointwise ergodic theorem.

This is a concise textbook of complex analysis for undergraduate and graduate students.

This textbook is a self-contained introduction to partial differential equations.

This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.

In this new edition of An Introduction to Pseudo-Differential Operators, the style and scope of the original book are retained.

This book is about the theory and applications of Partial Differential Equations of First Order (PDEFO).

This textbook presents the most efficient analytical techniques in the local bifurcation theory of vector fields.

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers.

This book is a comprehensive introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations.

This is first course in mathematical analysis, for students who have some familiarity with calculus, but are not familiar with formal proofs.

This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations.

This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras.

This textbook in partial differential equations has been adopted as course material by the Moscow State University.

This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations.

This volume is an introductory text in several complex variables, using methods of integral representations and Hilbert space theory.

This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems.

This is a textbook for a first course in functions of complex variable, assuming a knowledge of freshman calculus.

This book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense.

This is a rigorous introduction to the theory of complex functions of one complex variable.

This collection of counter-examples highlights the theory of differential equations and related topics which is now playing an enormously important role in the area of science, engineering and mathematics.

The student of calculus is entitled to ask what calculus is and what it can be used for.

This book is intended for those having only a moderate background in mathematics, who need to increase their mathematical knowledge for development in their areas of work and to read the related mathematical literature.

This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations.

This book provides an introduction to those parts of analysis that are most useful in applications for graduate students.

This book is a self-contained introduction to the theory of periodic, progressive, permanent waves on the surface of incompressible inviscid fluid.

This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations.

Many books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom.

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds.

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces.

As an extensive collection of problems with detailed solutions in introductory and advanced matrix calculus, this self-contained book is ideal for both graduate and undergraduate mathematics students.

This book provides an introduction to elliptic and parabolic equations.

This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis.