Differential calculus and equations Books

Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér,...

This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this second volume, special emphasis is placed on functional analytic methods...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.In this first volume, special emphasis is placed on geometric and complex variable...

The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions.This book...

Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for...

"Hypernumbers and Extrafunctions" presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite...

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful...

This book is intended to be an introduction to Delay Differential Equations for upper level undergraduates or beginning graduate mathematics students who have a reasonable background in ordinary differential equations and who would like to get to the...

For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with...

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere...

This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular...

This textbook gives an introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodi?erential methods are introduced. Distributiontheoryhasbeen...

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics...

In the last century many problems which arose in the science, engineer­ ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ­ ential...

It is generally acknowledged that deterministic formulations of dy­ namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe­ nomena typically...

Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most...

""Einleitung in die Theorie der linearen Differentialgleichungen mit einer unabh�����ngigen Variablen"" ist ein Buch von Lothar Heffter, das im Jahr 1894 ver������ffentlicht wurde. Es ist ein Lehrbuch, das sich mit der Theorie der linearen...

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. This book includes a collection of related topics...

This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can be...

In most physical, chemical, biological and economic phenomena it is quite natural to assume that the system not only depends on the present state but also on past occurrences. These circumstances are mathematically described by partial differential...

This book is directed to the computer-based modeling of chemotaxis inflammation, typically resulting from an infection by a pathogen (e.g., bacteria, viruses). The book has particular relevance to the coronavirus pandemic since long-Covid neurological...

This series on the International Conference on Difference Equations and Applications has established a tradition within the mathematical community. It brings together scientists from many different areas of research to highlight current interests,...

Differential Equations in Engineering: Research and Applications describes advanced research in the field of the applications of differential equations in engineering and the sciences, and offers a sound theoretical background, along with case studies.It...

Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of...

This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates...

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into...

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving...

Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations.- Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations #x2013; Some Constructive Approaches.- Self-Similar Solutions as Large Time Asymptotics...

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Throughout Geometry, Complex Dimensions and Zeta Functions, Second...

Preface.- 1. Introduction.- 2. Preliminaries.- 3. Degenerate and Singular Parabolic Equations.- 4. Expansion of Positivity.- 5. The Harnack Inequality for Degenerate Equations.- 6. The Harnack Inequality for Singular Equations.- 7. Homogeneous Monotone...

This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering...

Preface.- Control of Systems Described by Elliptic-Type Partial-Differential Equations Under Conjugation Conditions.- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation Under Conjugation Conditions.-...

Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs). Students and...

Preliminaries.- Schechter-Tintarev Linking.- Sign-Changing Saddle Point.- On a Brezis-Nirenberg Theorem.- Even Functionals.- Parameter Dependence.- On a Bartsch-Chang-Wang-Weth Theory.

In this book the author presents the Opial, Poincaré, Sobolev, Hilbert, and Ostrowski fractional differentiation inequalities. Results for the above are derived using three different types of fractional derivatives, namely by...

Structural Stability.- Spatial Decay.- Convection in Porous Media.- Stability of Other Porous Flows.- Fluid - Porous Interface Problems.- Elastic Materials with Voids.- Poroacoustic Waves.- Numerical Solution of Eigenvalue Problems.

This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new...

This book is drawn from across many active fields of mathematics and physics. It has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods...

INTRODUCTION.- CHAPTER 1: Infinite Products & Elementary Functions.- 1.1 Classical Euler representations.- 1.2 Alternative derivations.- 1.3 Other elementary functions.- 1.4 Chapter exercises.- CHAPTER 2: Green's Functions for the Laplace Equation.-...

1 Introduction.- 2 The Dolbeault-Dirac Operator.- 3 Clifford Modules.- 4 The Spin Group and the Spin-c Group.- 5 The Spin-c Dirac Operator.- 6 Its Square.- 7 The Heat Kernel Method.- 8 The Heat Kernel Expansion.- 9 The Heat Kernel on a Principal Bundle.-...

This textbook introduces variational methods and their applications to differential equations to graduate students and researchers interested in differential equations and nonlinear analysis. It serves as a sampling of topics...

Overview The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. The core consists of solution methods, mainly separation of variables, for boundary value...

This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the...

A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or...