Introduction to Linear Algebra and Differential Equations

6 LINEAR DIFFERENTIAL EQUATIONS 6.1 INTRODUCTION This chapter deals with higher order linear differential equations . The second section deals with general theorems about solutions of the nonsingular initialvalue problem ( leading ...

Author: John W. Dettman

Publisher: Courier Corporation

ISBN: 0486651916

Category: Mathematics

Page: 404

View: 162

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Excellent introductory text for students with one year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. Includes 48 black-and-white illustrations. Exercises with solutions. Index.
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Introduction to Linear Algebra and Differential Equations

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.

Author: John W. Dettman

Publisher: Courier Corporation

ISBN: 9780486158310

Category: Mathematics

Page: 432

View: 186

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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.
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Linear Algebra and Differential Equations

This book has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations.

Author: Gary L. Peterson

Publisher: Addison Wesley

ISBN: 0201662124

Category: Mathematics

Page: 463

View: 732

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This book has been written for a one-semester combined linear algebra and differential equations course, yet it contains enough material for a two-term sequence in linear algebra and differential equations. By introducing matrices, determinants, and vector spaces early in the course, the authors are able to fully develop the connections between linear algebra and differential equations. The book is flexible enough to be easily adapted to fit most syllabi, including courses that cover differential equations first. Technology is fully integrated where appropriate, and the text offers fresh and relevant applications to motivate student interest. Matrices and Determinants; Vector Spaces; First Order Ordinary Differential Equations; Linear Differential Equations; Linear Transformations and Eigenvalues and Eigenvectors; Systems of Differential Equations; The Laplace Transform; Power Series Solutions to Linear Differential Equations; Inner Product Spaces For all readers interested in linear algebra and differential equations.
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Differential Equations and Linear Algebra

The Fourth Edition includes many updated problems to support the material, with varying difficulty levels from which students/instructors can choose.

Author: Stephen W. Goode

Publisher: Pearson

ISBN: 0321964675

Category: Algebras, Linear

Page: 888

View: 629

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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 Linear Algebra

In particular, linear algebra is a fundamental subject that plays a key role in the study of much higher level mathematics; through its study, as well as our investigations of differential equations, we aim to provide a foundation for ...

Author: Matthew R. Boelkins

Publisher: Oxford University Press

ISBN: 9780199736669

Category: Mathematics

Page: 576

View: 885

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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
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Elementary Differential Equations with Linear Algebra

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.

Author: Albert L. Rabenstein

Publisher: Academic Press

ISBN: 9781483262376

Category: Mathematics

Page: 528

View: 360

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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 Dynamical Systems and Linear Algebra

This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics.

Author: Morris W. Hirsch

Publisher: Academic Press

ISBN: 9780080873763

Category: Mathematics

Page: 358

View: 847

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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.
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Linear Algebra to Differential Equations

[1] H. Anton, C. Rorres, Elementary Linear Algebra with Applications, (10th Edition), Wiley Publication, USA. [2] S. Barnet, Matrix Differential Equations and Kronecker Products, SIAM J. Appl. Math. 24, No 1(1973) pp1–5.

Author: J. Vasundhara Devi

Publisher: CRC Press

ISBN: 9781351014946

Category: Mathematics

Page: 416

View: 996

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Linear Algebra to Differential Equations concentrates on the essential topics necessary for all engineering students in general and computer science branch students, in particular. Specifically, the topics dealt will help the reader in applying linear algebra as a tool. The advent of high-speed computers has paved the way for studying large systems of linear equations as well as large systems of linear differential equations. Along with the standard numerical methods, methods that curb the progress of error are given for solving linear systems of equations. The topics of linear algebra and differential equations are linked by Kronecker products and calculus of matrices. These topics are useful in dealing with linear systems of differential equations and matrix differential equations. Differential equations are treated in terms of vector and matrix differential systems, as they naturally arise while formulating practical problems. The essential concepts dealing with the solutions and their stability are briefly presented to motivate the reader towards further investigation. This book caters to the needs of Engineering students in general and in particular, to students of Computer Science & Engineering, Artificial Intelligence, Machine Learning and Robotics. Further, the book provides a quick and complete overview of linear algebra and introduces linear differential systems, serving the basic requirements of scientists and researchers in applied fields. Features Provides complete basic knowledge of the subject Exposes the necessary topics lucidly Introduces the abstraction and at the same time is down to earth Highlights numerical methods and approaches that are more useful Essential techniques like SVD and PCA are given Applications (both classical and novel) bring out similarities in various disciplines: Illustrative examples for every concept: A brief overview of techniques that hopefully serves the present and future needs of students and scientists.
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Linear Algebra

Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization.

Author: Tom M. Apostol

Publisher: John Wiley & Sons

ISBN: 9781118626184

Category: Mathematics

Page: 347

View: 124

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Developed from the author's successful two-volume Calculus text this book presents Linear Algebra without emphasis on abstraction or formalization. To accommodate a variety of backgrounds, the text begins with a review of prerequisites divided into precalculus and calculus prerequisites. It continues to cover vector algebra, analytic geometry, linear spaces, determinants, linear differential equations and more.
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