Introduction To Piecewise Differentiable Equations

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Introduction To Piecewise Differentiable Equations

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Author : Stefan Scholtes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-01

Introduction To Piecewise Differentiable Equations written by Stefan Scholtes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-01 with Mathematics categories.

​​​​​​​ This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.

Introduction To Differential Equations With Dynamical Systems

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Author : Stephen L. Campbell
language : en
Publisher: Princeton University Press
Release Date : 2011-10-14

Introduction To Differential Equations With Dynamical Systems written by Stephen L. Campbell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.

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.

Introduction To Inverse Problems For Differential Equations

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Author : Alemdar Hasanov Hasanoğlu
language : en
Publisher: Springer Nature
Release Date : 2021-08-02

Introduction To Inverse Problems For Differential Equations written by Alemdar Hasanov Hasanoğlu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Mathematics categories.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

An Introduction To Partial Differential Equations With Matlab

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Author : Matthew P. Coleman
language : en
Publisher: CRC Press
Release Date : 2016-04-19

An Introduction To Partial Differential Equations With Matlab written by Matthew P. Coleman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

An Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,

Differential Equations An Introduction To Basic Concepts Results And Applications Third Edition

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Author : Ioan I Vrabie
language : en
Publisher: World Scientific Publishing Company
Release Date : 2016-05-30

Differential Equations An Introduction To Basic Concepts Results And Applications Third Edition written by Ioan I Vrabie and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-30 with Mathematics categories.

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. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems.In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.

An Introduction To The Finite Element Method For Differential Equations

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Author : Mohammad Asadzadeh
language : en
Publisher: John Wiley & Sons
Release Date : 2020-08-27

An Introduction To The Finite Element Method For Differential Equations written by Mohammad Asadzadeh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Mathematics categories.

Master the finite element method with this masterful and practical volume An Introduction to the Finite Element Method (FEM) for Differential Equations provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases. The book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, An Introduction to the Finite Element Method covers topics including: An introduction to basic ordinary and partial differential equations The concept of fundamental solutions using Green's function approaches Polynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations Higher-dimensional interpolation procedures Stability and convergence analysis of FEM for differential equations This book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.

Introduction To Partial Differential Equations With Matlab

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Author : Jeffery Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-18

Introduction To Partial Differential Equations With Matlab written by Jeffery Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-18 with Computers categories.

Intended for undergraduate students in math, science, and engineering, this text uses MATLAB software to expand the introduction of differential equations from the core topics of solution techniques for boundary value problems with constant coefficients to topics less common for an introductory text such as nonlinear problems and brief discussions of numerical methods. The Schrodinger equation is dicussed as a dispersive equation and the LaPlace and Poisson equations are treated. Finite difference schemes are used to compute solutions. Some mfiles to implement basic finite difference schemes have been included. Annotation copyrighted by Book News, Inc., Portland, OR

Introduction To Partial Differential Equations

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Author : David Borthwick
language : en
Publisher: Springer
Release Date : 2017-01-12

Introduction To Partial Differential Equations written by David Borthwick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-12 with Mathematics categories.

This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise. Within each section the author creates a narrative that answers the five questions: What is the scientific problem we are trying to understand? How do we model that with PDE? What techniques can we use to analyze the PDE? How do those techniques apply to this equation? What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

Introductory Differential Equations

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Author : Martha L. Abell
language : en
Publisher: Academic Press
Release Date : 2009-09-09

Introductory Differential Equations written by Martha L. Abell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-09 with Mathematics categories.

This text is for courses that are typically called (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems. The text is appropriate for two semester courses: the first typically emphasizes ordinary differential equations and their applications while the second emphasizes special techniques (like Laplace transforms) and partial differential equations. The texts follows a "traditional" curriculum and takes the "traditional" (rather than "dynamical systems") approach. Introductory Differential Equations is a text that follows a traditional approach and is appropriate for a first course in ordinary differential equations (including Laplace transforms) and a second course in Fourier series and boundary value problems. Note that some schools might prefer to move the Laplace transform material to the second course, which is why we have placed the chapter on Laplace transforms in its location in the text. Ancillaries like Differential Equations with Mathematica and/or Differential Equations with Maple would be recommended and/or required ancillaries depending on the school, course, or instructor. - Technology Icons - These icons highlight text that is intended to alert students that technology may be used intelligently to solve a problem, encouraging logical thinking and application - Think About It Icons and Examples - Examples that end in a question encourage students to think critically about what to do next, whether it is to use technology or focus on a graph to determine an outcome - Differential Equations at Work - These are projects requiring students to think critically by having students answer questions based on different conditions, thus engaging students

Introduction To Partial Differential Equations

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Author : Arne Broman
language : en
Publisher: Courier Corporation
Release Date : 2012-04-27

Introduction To Partial Differential Equations written by Arne Broman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-27 with Mathematics categories.

The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.