Elementary Differential Equations with Linear Algebra

Author: Albert L. Rabenstein

Publisher: Academic Press

ISBN: 1483262375

Category: Mathematics

Page: 528

View: 7896

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Elementary Differential Equations with Linear Algebra, Third Edition provides an introduction to differential equation and linear algebra. This book includes topics on numerical methods and Laplace transforms. Organized into nine chapters, this edition begins with an overview of an equation that involves a single unknown function of a single variable and some finite number of its derivatives. This text then examines a linear system of two equations with two unknowns. Other chapters consider a class of linear transformations that are defined on spaces of functions wherein these transformations are essential in the study of linear differential equations. This book discusses as well the linear differential equations whose coefficients are constant functions. The final chapter deals with the properties of Laplace transform in detail and examine as well the applications of Laplace transforms to differential equations. This book is a valuable resource for mathematicians, students, and research workers.
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Differential Equations & Linear Algebra

Author: Charles Henry Edwards,David E. Penney,David Calvis

Publisher: N.A

ISBN: 9780138141028

Category: Algebras, Linear

Page: 762

View: 4247

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For courses in Differential Equations and Linear Algebra. Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed-yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.
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Differential Equations and Linear Algebra: Pearson New International Edition

Author: C. Henry Edwards,David E. Penney

Publisher: Pearson Higher Ed

ISBN: 1292052805

Category: Mathematics

Page: 696

View: 9652

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For courses in Differential Equations and Linear Algebra. Acclaimed authors Edwards and Penney combine core topics in elementary differential equations with those concepts and methods of elementary linear algebra needed for a contemporary combined introduction to differential equations and linear algebra. Known for its real-world applications and its blend of algebraic and geometric approaches, this text discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. In the Third Edition, new graphics and narrative have been added as needed—yet the proven chapter and section structure remains unchanged, so that class notes and syllabi will not require revision for the new edition.
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Applied Linear Algebra and Matrix Analysis

Author: Thomas S. Shores

Publisher: Springer Science & Business Media

ISBN: 9780387331959

Category: Mathematics

Page: 384

View: 6383

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This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises.
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Differential Equations and Linear Algebra

Author: Stephen W. Goode,Scott A. Annin

Publisher: Pearson Higher Ed

ISBN: 0130457949

Category: Mathematics

Page: 804

View: 1151

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For combined differential equations and linear algebra courses teaching students who have successfully completed three semesters of calculus. This complete introduction to both differential equations and linear algebra presents a carefully balanced and sound integration of the two topics. It promotes in-depth understanding rather than rote memorization, enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. A vast array of problems supports the material, with varying levels from which students/instructors can choose.
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Differential Equations with Applications and Historical Notes, Third Edition

Author: George F. Simmons

Publisher: CRC Press

ISBN: 1498702627

Category: Mathematics

Page: 764

View: 1236

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Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.
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Math Refresher for Scientists and Engineers

Author: John R. Fanchi

Publisher: John Wiley & Sons

ISBN: 0471791547

Category: Mathematics

Page: 330

View: 7937

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Expanded coverage of essential math, including integral equations,calculus of variations, tensor analysis, and specialintegrals Math Refresher for Scientists and Engineers, Third Edition isspecifically designed as a self-study guide to help busyprofessionals and students in science and engineering quicklyrefresh and improve the math skills needed to perform their jobsand advance their careers. The book focuses on practicalapplications and exercises that readers are likely to face in theirprofessional environments. All the basic math skills needed tomanage contemporary technology problems are addressed and presentedin a clear, lucid style that readers familiar with previouseditions have come to appreciate and value. The book begins with basic concepts in college algebra andtrigonometry, and then moves on to explore more advanced conceptsin calculus, linear algebra (including matrices), differentialequations, probability, and statistics. This Third Edition has beengreatly expanded to reflect the needs of today's professionals. Newmaterial includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skillsneeded by scientists and engineers. The wide range of topicscovered in one title is unique. All chapters provide a review ofimportant principles and methods. Examples, exercises, andapplications are used liberally throughout to engage the readersand assist them in applying their new math skills to actualproblems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams,readers will find this self-study guide enables them to quicklymaster the math they need. It can additionally be used as atextbook for advanced-level undergraduates in physics andengineering.
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The Numerical Solution of Ordinary and Partial Differential Equations

Author: Granville Sewell

Publisher: World Scientific

ISBN: 9814635111

Category: Mathematics

Page: 348

View: 5663

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This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A. The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions. Contents:Direct Solution of Linear SystemsInitial Value Ordinary Differential EquationsThe Initial Value Diffusion ProblemThe Initial Value Transport and Wave ProblemsBoundary Value ProblemsThe Finite Element MethodsAppendix A — Solving PDEs with PDE2DAppendix B — The Fourier Stability MethodAppendix C — MATLAB ProgramsAppendix D — Answers to Selected Exercises Readership: Undergraduate, graduate students and researchers. Key Features:The discussion of stability, absolute stability and stiffness in Chapter 1 is clearer than in other textsStudents will actually learn to write programs solving a range of simple PDEs using the finite element method in chapter 5In Appendix A, students will be able to solve quite difficult PDEs, using the author's software package, PDE2D. (a free version is available which solves small to moderate sized problems)Keywords:Differential Equations;Partial Differential Equations;Finite Element Method;Finite Difference Method;Computational Science;Numerical AnalysisReviews: "This book is very well written and it is relatively easy to read. The presentation is clear and straightforward but quite rigorous. This book is suitable for a course on the numerical solution of ODEs and PDEs problems, designed for senior level undergraduate or beginning level graduate students. The numerical techniques for solving problems presented in the book may also be useful for experienced researchers and practitioners both from universities or industry." Andrzej Icha Pomeranian Academy in Słupsk Poland
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