A Modern Introduction to Differential Equations

Author: Henry J. Ricardo

Publisher: Academic Press

ISBN: 0080886035

Category: Mathematics

Page: 536

View: 6827

A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equations and systems of differential equations; and systems of nonlinear equations. Each chapter concludes with a summary of the important concepts in the chapter. Figures and tables are provided within sections to help students visualize or summarize concepts. The book also includes examples and exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering. This book is designed for undergraduate students majoring in mathematics, the natural sciences, and engineering. However, students in economics, business, and the social sciences with the necessary background will also find the text useful. Student friendly readability- assessible to the average student Early introduction of qualitative and numerical methods Large number of exercises taken from biology, chemistry, economics, physics and engineering Exercises are labeled depending on difficulty/sophistication End of chapter summaries Group projects

A Modern Introduction to Differential Equations

Mathematics, Differential equations

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1478422653

Category: Education

Page: 20

View: 5807

Facts101 is your complete guide to A Modern Introduction to Differential Equations. In this book, you will learn topics such as The Numerical Approximation of Solutions, Second- and Higher-Order Equations, Systems of Linear Differential Equations, and The Laplace Transform plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Ordinary Differential Equations

Introduction to the Theory of Ordinary Differential Equations in the Real Domain

Author: J. Kurzweil

Publisher: Elsevier

ISBN: 1483297659

Category: Mathematics

Page: 440

View: 4511

The author, Professor Kurzweil, is one of the world's top experts in the area of ordinary differential equations - a fact fully reflected in this book. Unlike many classical texts which concentrate primarily on methods of integration of differential equations, this book pursues a modern approach: the topic is discussed in full generality which, at the same time, permits us to gain a deep insight into the theory and to develop a fruitful intuition. The basic framework of the theory is expanded by considering further important topics like stability, dependence of a solution on a parameter, Carathéodory's theory and differential relations. The book is very well written, and the prerequisites needed are minimal - some basics of analysis and linear algebra. As such, it is accessible to a wide circle of readers, in particular to non-mathematicians.

Introduction to Differential Equations with Dynamical Systems

Author: Stephen L. Campbell,Richard Haberman

Publisher: Princeton University Press

ISBN: 1400841321

Category: Mathematics

Page: 472

View: 5595

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.

Differential Equations with Boundary Value Problems

Modern Methods and Applications

Author: James R. Brannan,William E. Boyce

Publisher: N.A

ISBN: 9780470902141

Category: Boundary value problems

Page: 963

View: 2815

Unlike other books in the market, this second edition presents differential equations consistent with the way scientists and engineers use modern methods in their work. Technology is used freely, with more emphasis on modeling, graphical representation, qualitative concepts, and geometric intuition than on theoretical issues. It also refers to larger–scale computations that computer algebra systems and DE solvers make possible. And more exercises and examples involving working with data and devising the model provide scientists and engineers with the tools needed to model complex real–world situations.

Introduction to Linear Algebra and Differential Equations

Author: John W. Dettman

Publisher: Courier Corporation

ISBN: 0486158314

Category: Mathematics

Page: 432

View: 9042

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Introduction to Partial Differential Equations with MATLAB

Author: Jeffery Cooper

Publisher: Springer Science & Business Media

ISBN: 9780817639679

Category: Mathematics

Page: 540

View: 3490

The subject of partial differential equations has an unchanging core of material but is constantly expanding and evolving. Introduction to Partial Differential Equations with MATLAB is a careful integration of traditional core topics with modern topics, taking full advantage of the computational power of MATLAB to enhance the learning experience. This advanced text/reference is an introduction to partial differential equations covering the traditional topics within a modern context. To provide an up-to-date treatment, techniques of numerical computation have been included with carefully selected nonlinear topics, including nonlinear first order equations. Each equation studied is placed in the appropriate physical context. The analytical aspects of solutions are discussed in an integrated fashion with extensive examples and exercises, both analytical and computational. The book is excellent for classroom use and can be used for self-study purposes. Topic and Features: • Nonlinear equations including nonlinear conservation laws; • Dispersive wave equations and the Schrodinger equation; • Numerical methods for each core equation including finite difference methods, finite element methods, and the fast Fourier transform; • Extensive use of MATLAB programs in exercise sets. MATLAB m files for numerical and graphics programs available by ftp from this web site. This text/reference is an excellent resources designed to introduce advanced students in mathematics, engineering and sciences to partial differential equations. It is also suitable as a self-study resource for professionals and practitioners.

Differential Equations and Their Applications

An Introduction to Applied Mathematics

Author: Martin Braun

Publisher: Springer Science & Business Media

ISBN: 9780387978949

Category: Mathematics

Page: 578

View: 9746

Used in undergraduate classrooms across the USA, this is a clearly written, rigorous introduction to differential equations and their applications. Fully understandable to students who have had one year of calculus, this book distinguishes itself from other differential equations texts through its engaging application of the subject matter to interesting scenarios. This fourth edition incorporates earlier introductory material on bifurcation theory and adds a new chapter on Sturm-Liouville boundary value problems. Computer programs in C, Pascal, and Fortran are presented throughout the text to show readers how to apply differential equations towards quantitative problems.

An Introduction to Differential Equations

Order and Chaos

Author: Florin Diacu

Publisher: W H Freeman & Company

ISBN: 9780716732969

Category: Mathematics

Page: 399

View: 3398

The year 1215 saw a time of global upheaval from which the ripples can still be felt today - but it was also an age of domestic changes and the development of a way of life not entirely different from our own. From the oddest detail to the grandest political struggle, Danny Danzinger and John Gillingham paint an extraordinary picture of this fascinating age, featuring a cast of some of the most enduring names in history - Bad King John, Genghis Khan, St Francis of Assisi - as well as the thousands of ordinary people whose lives were affected by the historical events happening around them. The power struggles are balanced with the social issues of the day - fashion, communications, education, medicine, religion and sex - as the authors explore the attitudes and habits of a nation in flux, and the ways in which they sculpted the modern world.

Scientific Computing and Differential Equations

An Introduction to Numerical Methods

Author: Gene H. Golub,James M. Ortega

Publisher: Elsevier

ISBN: 0080516696

Category: Mathematics

Page: 344

View: 6605

Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level

Introduction to Differential Equations

Author: Michael Eugene Taylor

Publisher: American Mathematical Soc.

ISBN: 082185271X

Category: Mathematics

Page: 409

View: 2961

The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

Introduction to Partial Differential Equations

A Computational Approach

Author: Aslak Tveito,Ragnar Winther

Publisher: Springer Science & Business Media

ISBN: 0387227733

Category: Mathematics

Page: 392

View: 8046

Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

Introduction to Partial Differential Equations

Author: Donald Greenspan

Publisher: Courier Corporation

ISBN: 0486150933

Category: Mathematics

Page: 204

View: 2086

Designed for use in a 1-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, 2nd-order partial differential equations, wave equation, potential equation, heat equation, and more. Includes exercises. 1961 edition.

Ordinary Differential Equations

From Calculus to Dynamical Systems

Author: Virginia W. Noonburg

Publisher: The Mathematical Association of America

ISBN: 1939512042

Category: Mathematics

Page: 315

View: 5028

This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences. The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters. The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5. A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises. The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.

Introduction to Partial Differential Equations

Author: David Borthwick

Publisher: Springer

ISBN: 3319489364

Category: Mathematics

Page: 283

View: 9456

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.

Differential Equations

An Introduction to Basic Concepts, Results and Applications Third Edition

Author: Ioan I Vrabie

Publisher: World Scientific Publishing Company

ISBN: 981474980X

Category: Mathematics

Page: 528

View: 9882

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.