# Differential Equations

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## Lectures on Partial Differential Equations

Author | : I. G. Petrovsky |

Publsiher | : Courier Corporation |

Total Pages | : 272 |

Release | : 2012-12-13 |

ISBN | : 0486155080 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Lectures on Partial Differential Equations Book Excerpt:**

Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.

## Differential Equations with Linear Algebra

Author | : Matthew R. Boelkins,Jack L. Goldberg,Merle C. Potter |

Publsiher | : Oxford University Press |

Total Pages | : 573 |

Release | : 2009-11-05 |

ISBN | : 0199736669 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Differential Equations with Linear Algebra Book Excerpt:**

Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, the book is appropriate for courses for majors in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with a full chapter devoted to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the chapter on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. This chapter enables students to quickly learn enough linear algebra to appreciate the structure of solutions to linear differential equations and systems thereof in subsequent study and to apply these ideas regularly. The book offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The following chapter develops the mathematics necessary to solve these problems and explores related topics further. Even in more theoretical developments, we use an example-first style to build intuition and understanding before stating or proving general results. Over 100 figures provide visual demonstration of key ideas; the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and support students' use of technology in solving problems. Each chapter closes with several substantial projects for further study, many of which are based in applications. Errata sheet available at: www.oup.com/us/companion.websites/9780195385861/pdf/errata.pdf

## Ordinary Differential Equations

Author | : Morris Tenenbaum,Harry Pollard |

Publsiher | : Courier Corporation |

Total Pages | : 852 |

Release | : 1985-10-01 |

ISBN | : 0486649407 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

## Ordinary Differential Equations

Author | : Radu Precup |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 234 |

Release | : 2018-01-22 |

ISBN | : 3110447509 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ordinary Differential Equations Book Excerpt:**

This introductory text combines models from physics and biology with rigorous reasoning in describing the theory of ordinary differential equations along with applications and computer simulations with Maple. Offering a concise course in the theory of ordinary differential equations, it also enables the reader to enter the field of computer simulations. Thus, it is a valuable read for students in mathematics as well as in physics and engineering. It is also addressed to all those interested in mathematical modeling with ordinary differential equations and systems. Contents Part I: Theory Chapter 1 First-Order Differential Equations Chapter 2 Linear Differential Systems Chapter 3 Second-Order Differential Equations Chapter 4 Nonlinear Differential Equations Chapter 5 Stability of Solutions Chapter 6 Differential Systems with Control Parameters Part II: Exercises Seminar 1 Classes of First-Order Differential Equations Seminar 2 Mathematical Modeling with Differential Equations Seminar 3 Linear Differential Systems Seminar 4 Second-Order Differential Equations Seminar 5 Gronwall’s Inequality Seminar 6 Method of Successive Approximations Seminar 7 Stability of Solutions Part III: Maple Code Lab 1 Introduction to Maple Lab 2 Differential Equations with Maple Lab 3 Linear Differential Systems Lab 4 Second-Order Differential Equations Lab 5 Nonlinear Differential Systems Lab 6 Numerical Computation of Solutions Lab 7 Writing Custom Maple Programs Lab 8 Differential Systems with Control Parameters

## Non Instantaneous Impulses in Differential Equations

Author | : Ravi Agarwal,Snezhana Hristova,Donal O'Regan |

Publsiher | : Springer |

Total Pages | : 251 |

Release | : 2017-10-27 |

ISBN | : 3319663844 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Non Instantaneous Impulses in Differential Equations Book Excerpt:**

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case)- Fractional differential equations with non-instantaneous impulses (with Caputo fractional derivatives of order q ε (0, 1))- Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution) Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliography is included. Graduate students at various levels as well as researchers in differential equations and related fields will find this a valuable resource of both introductory and advanced material.

## Theory of Differential Equations with Unbounded Delay

Author | : V. Lakshmikantham,Lizhi Wen,Binggen Zhang |

Publsiher | : Springer Science & Business Media |

Total Pages | : 386 |

Release | : 2013-11-27 |

ISBN | : 146152606X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Theory of Differential Equations with Unbounded Delay Book Excerpt:**

Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research. It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems. It is the first book that: (i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay; (ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them; (iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and (iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions. This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.

## Introduction to Differential Equations with Dynamical Systems

Author | : Stephen L. Campbell,Richard Haberman |

Publsiher | : Princeton University Press |

Total Pages | : 472 |

Release | : 2011-10-14 |

ISBN | : 1400841321 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Introduction to Differential Equations with Dynamical Systems Book Excerpt:**

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

## Stochastic Partial Differential Equations with L vy Noise

Author | : S. Peszat,J. Zabczyk |

Publsiher | : Cambridge University Press |

Total Pages | : 432 |

Release | : 2007-10-11 |

ISBN | : 0521879892 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Stochastic Partial Differential Equations with L vy Noise Book Excerpt:**

Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

## A treatise on differential equations

Author | : Andrew Russell Forsyth |

Publsiher | : Unknown |

Total Pages | : 135 |

Release | : 1885 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**A treatise on differential equations Book Excerpt:**

## Examples of Differential Equations

Author | : George Abbott Osborne |

Publsiher | : Unknown |

Total Pages | : 78 |

Release | : 1886 |

ISBN | : 1928374650XXX |

Category | : Differential equations |

Language | : EN, FR, DE, ES & NL |

**Examples of Differential Equations Book Excerpt:**

## A Treatise on Differential Equations

Author | : George Boole |

Publsiher | : Unknown |

Total Pages | : 735 |

Release | : 1859 |

ISBN | : 1928374650XXX |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**A Treatise on Differential Equations Book Excerpt:**

## Almost Periodic Solutions of Differential Equations in Banach Spaces

Author | : Yoshiyuki Hino,Toshiki Naito,Nguyen VanMinh,Jong Son Shin |

Publsiher | : CRC Press |

Total Pages | : 264 |

Release | : 2001-10-25 |

ISBN | : 1482263165 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Almost Periodic Solutions of Differential Equations in Banach Spaces Book Excerpt:**

This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.

## A Treatise on Linear Differential Equations

Author | : Thomas Craig |

Publsiher | : Unknown |

Total Pages | : 540 |

Release | : 1889 |

ISBN | : 1928374650XXX |

Category | : Differential equations, Linear |

Language | : EN, FR, DE, ES & NL |

**A Treatise on Linear Differential Equations Book Excerpt:**

## Differential Equations and Vector Calculus

Author | : Dr T.K.V. Iyengar & Dr B. Krishna Gandhi & S. Ranganadham & Dr M.V.S.S.N. Prasad |

Publsiher | : S. Chand Publishing |

Total Pages | : 135 |

Release | : 2022 |

ISBN | : 9352838262 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Differential Equations and Vector Calculus Book Excerpt:**

In this book, how to solve such type equations has been elaborately described. In this book, vector differential calculus is considered, which extends the basic concepts of (ordinary) differential calculus, such as, continuity and differentiability to vector functions in a simple and natural way. This book comprises previous question papers problems at appropriate places and also previous GATE questions at the end of each chapter for the

## Delay And Differential Equations Proceedings In Honor Of George Seifert On His Retirement

Author | : Fink Arlington M,Kliemann Wolfgang,Miller Richard K |

Publsiher | : World Scientific |

Total Pages | : 184 |

Release | : 1992-02-28 |

ISBN | : 9814555274 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Delay And Differential Equations Proceedings In Honor Of George Seifert On His Retirement Book Excerpt:**

This is a collection of lectures by leading research mathematicians on the very latest work on qualitative theory of solutions of dynamical systems, ordinary differential equations, delay-differential equations, Volterra integrodifferential equations and partial differential equations.

## New Developments in Differential Equations

Author | : Anonim |

Publsiher | : Elsevier |

Total Pages | : 247 |

Release | : 1976-01-01 |

ISBN | : 9780080871325 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**New Developments in Differential Equations Book Excerpt:**

New Developments in Differential Equations

## Differential Equations and Asymptotic Theory in Mathematical Physics

Author | : Chen Hua,Roderick Wong |

Publsiher | : World Scientific |

Total Pages | : 388 |

Release | : 2004-10-18 |

ISBN | : 9814481688 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Differential Equations and Asymptotic Theory in Mathematical Physics Book Excerpt:**

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Orthogonal Polynomials (M E H Ismail)Gevrey Asymptotics and Applications to Holomorphic Ordinary Differential Equations (J-P Ramis)Spikes for Singularly Perturbed Reaction-Diffusion Systems and Carrier's Problem (M J Ward)Five Lectures on Asymptotic Theory (R S C Wong)A Perturbation Model for the Growth of Type III-V Compound Crystals (C S Bohun et al.)Asymptotic Behaviour of the Trace for Schrödinger Operator on Irregular Domains (H Chen & C Yu)Limitations and Modifications of Black-Scholes Model (L S Jiang & X M Ren)Exact Boundary Controllability of Unsteady Flows in a Network of Open Canals (T T Li)Hierarchy of Partial Differential Equations and Fundamental Solutions Associated with Summable Formal Solutions of a Partial Differential Equations of non Kowalevski Type (M Miyake & K Ichinobe)On the Singularities of Solutions of Nonlinear Partial Differential Equations in the Complex Domain, II (H Tahara)Identifying Corrosion Boundary by Perturbation Method (Y J Tan & X X Chen)Existence and Stability of Lamellar and Wriggled Lamellar Solutions in the Diblock Copolymer Problem (J C Wei) Readership: Graduate students, researchers, academics and lecturers in mathematical physics. Keywords:Asymptotic Theory;Special Functions;Orthogonal Polynomials;Singular Perturbations;Reaction Diffusion Equations;Gevrey Asymptotics;Stationary Phase Approximation;WKB Method

## Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Author | : Stefan Bergman,Menahem Schiffer |

Publsiher | : Courier Corporation |

Total Pages | : 450 |

Release | : 2005-09-01 |

ISBN | : 0486445534 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Kernel Functions and Elliptic Differential Equations in Mathematical Physics Book Excerpt:**

This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.

## Introduction to Numerical Methods for Time Dependent Differential Equations

Author | : Heinz-Otto Kreiss,Omar Eduardo Ortiz |

Publsiher | : John Wiley & Sons |

Total Pages | : 192 |

Release | : 2014-04-24 |

ISBN | : 1118838912 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Introduction to Numerical Methods for Time Dependent Differential Equations Book Excerpt:**

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

## Nonlinear Partial Differential Equations in Engineering and Applied Science

Author | : Robert L. Sternberg |

Publsiher | : Routledge |

Total Pages | : 303 |

Release | : 2017-10-02 |

ISBN | : 1351428055 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Partial Differential Equations in Engineering and Applied Science Book Excerpt:**

In this volume are twenty-eight papers from the Conference on Nonlinear Partial Differential Equationsin Engineering and Applied Science, sponsored by the Office of Naval Research and held at the Universityof Rhode Island in June, 1979. Included are contributions from an international group of distinguishedmathematicians, scientists, and engineers coming from a wide variety of disciplines and having a commoninterest in the application of mathematics, particularly nonlinear partial differential equations, to realworld problems.The subject matter ranges from almost purely mathematical topics in numerical analysis and bifurcationtheory to a host of practical applications that involve nonlinear partial differential equations, suchas fluid dynamics, nonlinear waves, elasticity, viscoelasticity, hyperelasticity, solitons, metallurgy, shocklessairfoil design, quantum fields, and Darcy's law on flows in porous media.Non/inear Partial Differential Equations in Engineering and Applied Science focuses on a variety oftopics of specialized, contemporary concern to mathematicians, physical and biological scientists, andengineers who work with phenomena that can be described by nonlinear partial differential equations.