Download or read book Introduction to Piecewise Differentiable Equations written by Stefan Scholtes and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction To Partial Differential Equations With Maple An A Concise Course written by Zhilin Li and published by World Scientific. This book was released on 2021-09-23 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations.The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm-Liouville eigenvalue problems and series solutions.The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area.
Download or read book Introduction to Partial Differential Equations for Scientists and Engineers Using Mathematica written by Kuzman Adzievski and published by CRC Press. This book was released on 2016-04-19 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: With special emphasis on engineering and science applications, this textbook provides a mathematical introduction to the field of partial differential equations (PDEs). The text represents a new approach to PDEs at the undergraduate level by presenting computation as an integral part of the study of differential equations. The authors use the computer software Mathematica (R) along with graphics to improve understanding and interpretation of concepts. The book also presents solutions to selected examples as well as exercises in each chapter. Topics include Laplace and Fourier transforms as well as Sturm-Liuville Boundary Value Problems.
Download or read book Introduction to the Qualitative Theory of Differential Systems written by Jaume Llibre and published by Springer Science & Business Media. This book was released on 2013-10-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with continuous piecewise linear differential systems in the plane with three pieces separated by a pair of parallel straight lines. Moreover, these differential systems are symmetric with respect to the origin of coordinates. This class of systems driven by concrete applications is of interest in engineering, in particular in control theory and the design of electric circuits. By studying these particular differential systems we will introduce the basic tools of the qualitative theory of ordinary differential equations, which allow us to describe the global dynamics of these systems including the infinity. The behavior of their solutions, their parametric stability or instability and their bifurcations are described. The book is very appropriate for a first course in the qualitative theory of differential equations or dynamical systems, mainly for engineers, mathematicians, and physicists.
Download or read book Introduction to Ordinary Differential Equations written by Albert L. Rabenstein and published by Academic Press. This book was released on 2014-05-12 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.
Download or read book An Introduction to Partial Differential Equations with MATLAB written by Matthew P. Coleman and published by CRC Press. This book was released on 2024-08-01 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two editions of An Introduction to Partial Differential Equations with MATLAB® gained popularity among instructors and students at various universities throughout the world. Plain mathematical language is used in a friendly manner to provide a basic introduction to partial differential equations (PDEs). Suitable for a one- or two-semester introduction to PDEs and Fourier series, the book strives to provide physical, mathematical, and historical motivation for each topic. Equations are studied based on method of solution, rather than on type of equation. This third edition of this popular textbook updates the structure of the book by increasing the role of the computational portion, compared to previous editions. The redesigned content will be extremely useful for students of mathematics, physics, and engineering who would like to focus on the practical aspects of the study of PDEs, without sacrificing mathematical rigor. The authors have maintained flexibility in the order of topics. In addition, students will be able to use what they have learned in some later courses (for example, courses in numerical analysis, optimization, and PDE-based programming). Included in this new edition is a substantial amount of material on reviewing computational methods for solving ODEs (symbolically and numerically), visualizing solutions of PDEs, using MATLAB®'s symbolic programming toolbox, and applying various schemes from numerical analysis, along with suggestions for topics of course projects. Students will use sample MATLAB® or Python codes available online for their practical experiments and for completing computational lab assignments and course projects.
Download or read book Introduction to Differential Equations with Dynamical Systems written by Stephen L. Campbell and published by Princeton University Press. This book was released on 2011-10-14 with total page 445 pages. Available in PDF, EPUB and Kindle. 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.
Download or read book Partial Differential Equations An Introduction With Matematica And Maple written by Ioannis P Stavroulakis and published by World Scientific Publishing Company. This book was released on 1999-12-13 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained introduction to partial differential equations. It is designed for undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered. The material is illustrated with model examples. Mathematics software products such as Mathematica and Maple in ScientificWorkPlace are used in both graphical and computational aspects.
Download or read book Partial Differential Equations written by Ioannis P. Stavroulakis and published by World Scientific. This book was released on 2004 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a self-contained introduction to partial differential equations.It has been designed for undergraduates and first year graduate students majoring in mathematics, physics, engineering, or science.The text provides an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered.
Download or read book Applied Partial Differential Equations An Introduction written by Alan Jeffrey and published by Academic Press. This book was released on 2003 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks. This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market. * Includes new and important materials necessary to meet current demands made by diverse applications * Very detailed solutions to odd numbered problems to help students * Instructor's Manual Available
Download or read book An Introduction to Partial Differential Equations with MATLAB Second Edition written by Matthew P. Coleman and published by CRC Press. This book was released on 2013-06-26 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.
Download or read book Introduction to Partial Differential Equations written by Arne Broman and published by Courier Corporation. This book was released on 2012-04-27 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Inverse Problems for Differential Equations written by Alemdar Hasanov Hasanoğlu and published by Springer Nature. This book was released on 2021-08-02 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Numerical Methods in Differential Equations written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Download or read book Introduction to Ordinary Differential Equations written by Albert L. Rabenstein and published by Academic Press. This book was released on 2014-05-10 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Ordinary Differential Equations, Second Edition provides an introduction to differential equations. This book presents the application and includes problems in chemistry, biology, economics, mechanics, and electric circuits. Organized into 12 chapters, this edition begins with an overview of the methods for solving single differential equations. This text then describes the important basic properties of solutions of linear differential equations and explains higher-order linear equations. Other chapters consider the possibility of representing the solutions of certain linear differential equations in terms of power series. This book discusses as well the important properties of the gamma function and explains the stability of solutions and the existence of periodic solutions. The final chapter deals with the method for the construction of a solution of the integral equation and explains how to establish the existence of a solution of the initial value system. This book is a valuable resource for mathematicians, students, and research workers.
Download or read book Differential Equations An Introduction To Basic Concepts Results And Applications Third Edition written by Ioan I Vrabie and published by World Scientific Publishing Company. This book was released on 2016-05-30 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.