Ordinary Differential Equations And Linear Algebra

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Ordinary Differential Equations And Linear Algebra A Systems Approach

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Author : Todd Kapitula
language : en
Publisher: SIAM
Release Date : 2015-11-17

Ordinary Differential Equations And Linear Algebra A Systems Approach written by Todd Kapitula and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-17 with Mathematics categories.

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 With Linear Algebra

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Author : Matthew R. Boelkins
language : en
Publisher: Oxford University Press
Release Date : 2009-11-05

Differential Equations With Linear Algebra written by Matthew R. Boelkins and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-05 with Mathematics categories.

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 With Linear Algebra

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Author : David Lomen
language : en
Publisher: Prentice Hall
Release Date : 1986

Ordinary Differential Equations With Linear Algebra written by David Lomen and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

Linear Algebra And Differential Equations

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Author : Alexander Givental
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Linear Algebra And Differential Equations written by Alexander Givental and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Algebras, Linear categories.

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.

A Course In Ordinary Differential Equations

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Author : Stephen A. Wirkus
language : en
Publisher: CRC Press
Release Date : 2006-10-23

A Course In Ordinary Differential Equations written by Stephen A. Wirkus and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-23 with Mathematics categories.

The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB, Mathematica, and Maple A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field o

Linear Algebra And Ordinary Differential Equations Softcover

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Author : Alan Jeffrey
language : en
Publisher: CRC Press
Release Date : 1991-03-03

Linear Algebra And Ordinary Differential Equations Softcover written by Alan Jeffrey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-03 with Mathematics categories.

This book, written for undergraduate engineering and applied mathematics students, incorporates a broad coverage of essential standard topics in differential equations with material important to the engineering and applied mathematics fields. Because linear differential equations and systems play an essential role in many applications, the book presents linear algebra using a detailed development of matrix algebra, preceded by a short discussion of the algebra of vectors. New ideas are introduced with carefully chosen illustrative examples, which in turn are reinforced by the problem sets at the end of each section. The problem sets are divided into two parts. The first part contains straightforward problems similar to those in the text that are designed to emphasize key concepts and develop manipulative skills. The second part provides a more difficult group of problems that both extend the text and provide a deeper insight into the subject.

Linear Ordinary Differential Equations

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Author : Earl A. Coddington
language : en
Publisher: SIAM
Release Date : 1997-01-01

Linear Ordinary Differential Equations written by Earl A. Coddington and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.

Linear Ordinary Differential Equations, a text for advanced undergraduate or beginning graduate students, presents a thorough development of the main topics in linear differential equations. A rich collection of applications, examples, and exercises illustrates each topic. The authors reinforce students' understanding of calculus, linear algebra, and analysis while introducing the many applications of differential equations in science and engineering. Three recurrent themes run through the book. The methods of linear algebra are applied directly to the analysis of systems with constant or periodic coefficients and serve as a guide in the study of eigenvalues and eigenfunction expansions. The use of power series, beginning with the matrix exponential function leads to the special functions solving classical equations. Techniques from real analysis illuminate the development of series solutions, existence theorems for initial value problems, the asymptotic behavior solutions, and the convergence of eigenfunction expansions.

Ordinary Differential Equations

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Author : Wolfgang Walter
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-11

Ordinary Differential Equations written by Wolfgang Walter 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 2013-03-11 with Mathematics categories.

Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

Elementary Differential Equations With Linear Algebra

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Author : Albert L. Rabenstein
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Elementary Differential Equations With Linear Algebra written by Albert L. Rabenstein and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

Linear Algebra And Ordinary Differential Equations

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Author : Alan Jeffrey
language : en
Publisher: CRC Press
Release Date : 1991-03-01

Linear Algebra And Ordinary Differential Equations written by Alan Jeffrey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-01 with categories.