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Introduction To Linear Algebra And Differential Equations

Author: John W. Dettman
Publisher: Courier Corporation
ISBN: 0486158314
Size: 70.66 MB
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View: 2008
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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.

Differential Equations With Linear Algebra

Author: Matthew R. Boelkins
Publisher: Oxford University Press
ISBN: 0199736669
Size: 27.47 MB
Format: PDF
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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 And Linear Algebra A Systems Approach

Author: Todd Kapitula
Publisher: SIAM
ISBN: 1611974097
Size: 15.24 MB
Format: PDF, Mobi
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Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course. Linear algebra is developed first, with an eye toward solving linear systems of ODEs. A computer algebra system is used for intermediate calculations (Gaussian elimination, complicated integrals, etc.); however, the text is not tailored toward a particular system.÷Ordinary Differential Equations and Linear Algebra: A Systems Approach÷systematically develops the linear algebra needed to solve systems of ODEs and includes over 15 distinct applications of the theory, many of which are not typically seen in a textbook at this level (e.g., lead poisoning, SIR models, digital filters). It emphasizes mathematical modeling and contains group projects at the end of each chapter that allow students to more fully explore the interaction between the modeling of a system, the solution of the model, and the resulting physical description.÷

Differential Equations Dynamical Systems And Linear Algebra

Author: Morris W. Hirsch
Publisher: Academic Press
ISBN: 0080873766
Size: 39.19 MB
Format: PDF, Docs
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This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

Differential Equations And Linear Algebra

Author: Stephen W. Goode
Publisher:
ISBN: 9780132637572
Size: 74.83 MB
Format: PDF, Mobi
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This very accessible guide offers a thorough introduction to the basics of differential equations and linear algebra. Expertly integrating the two topics, it explains concepts clearly and logically -without sacrificing level or rigor - and supports material with a vast array of problems of varying levels for readers to choose from. Promotes in-depth understanding (vs. rote memorization) - enabling readers to fully comprehend abstract concepts and finish with a solid and working knowledge of linear mathematics. Offers one of the most lucid and clearly written narratives on the subject, with material that is accessible to the average reader, yet challenging to all. Presents a greater emphasis on geometry to help users better visualize the abstract concepts, and illustrates all concepts with an ample amount of worked examples. Second Edition highlights include new discussions direction fields and Euler's method for first order differential equations; row space and column space of a matrix, and the rank-nullity theorem; non-linear systems of differential equations, including phase plane analysis; and change of variables for differential equations. Now features a chapter on second order linear differential equations that is not based on vector space methods to gives users a firmer grasp of the differential equation concept early on, and also on the solution techniques for this important class of differential equations.

Linear Algebra And Differential Equations

Author: Alexander Givental
Publisher: American Mathematical Soc.
ISBN: 9780821828502
Size: 70.41 MB
Format: PDF, ePub
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The material presented in this book corresponds to a semester-long course, ``Linear Algebra and Differential Equations'', taught to sophomore students at UC Berkeley. In contrast with typical undergraduate texts, the book offers a unifying point of view on the subject, namely that linear algebra solves several clearly-posed classification problems about such geometric objects as quadratic forms and linear transformations. This attractive viewpoint on the classical theory agrees well with modern tendencies in advanced mathematics and is shared by many research mathematicians. However, the idea of classification seldom finds its way to basic programs in mathematics, and is usually unfamiliar to undergraduates. To meet the challenge, the book first guides the reader through the entire agenda of linear algebra in the elementary environment of two-dimensional geometry, and prior to spelling out the general idea and employing it in higher dimensions, shows how it works in applications such as linear ODE systems or stability of equilibria. Appropriate as a text for regular junior and honors sophomore level college classes, the book is accessible to high school students familiar with basic calculus, and can also be useful to engineering graduate students.

Elementary Differential Equations With Linear Algebra

Author: Albert L. Rabenstein
Publisher: Academic Press
ISBN: 1483262375
Size: 12.59 MB
Format: PDF, ePub, Mobi
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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.