Differential Equations and Linear Algebra

Differential Equations and Linear Algebra
Author: Gilbert Strang
Publsiher: Wellesley-Cambridge Press
Total Pages: 510
Release: 2015-02-12
ISBN: 9780980232790
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations and Linear Algebra Book Excerpt:

Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.

Differential Equations and Linear Algebra

Differential Equations and Linear Algebra
Author: Stephen W. Goode,Scott A. Annin
Publsiher: Pearson
Total Pages: 888
Release: 2015-12-11
ISBN: 9780321964670
Category: Algebras, Linear
Language: EN, FR, DE, ES & NL

Differential Equations and Linear Algebra Book Excerpt:

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.

Differential Equations with Linear Algebra

Differential Equations with Linear Algebra
Author: Matthew R. Boelkins,Jack L. Goldberg,Merle C. Potter
Publsiher: Oxford University Press
Total Pages: 576
Release: 2009-11-05
ISBN: 0199736669
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations with Linear Algebra Book Excerpt:

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

Elementary Differential Equations with Linear Algebra

Elementary Differential Equations with Linear Algebra
Author: Albert L. Rabenstein
Publsiher: Academic Press
Total Pages: 528
Release: 2014-05-10
ISBN: 1483262375
Category: Mathematics
Language: EN, FR, DE, ES & NL

Elementary Differential Equations with Linear Algebra Book Excerpt:

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.

Differential Equations Dynamical Systems and Linear Algebra

Differential Equations  Dynamical Systems  and Linear Algebra
Author: Morris W. Hirsch,Robert L. Devaney,Stephen Smale
Publsiher: Academic Press
Total Pages: 358
Release: 1974-06-28
ISBN: 0080873766
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations Dynamical Systems and Linear Algebra Book Excerpt:

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.

Introduction to Linear Algebra and Differential Equations

Introduction to Linear Algebra and Differential Equations
Author: John W. Dettman
Publsiher: Courier Corporation
Total Pages: 432
Release: 2012-10-05
ISBN: 0486158314
Category: Mathematics
Language: EN, FR, DE, ES & NL

Introduction to Linear Algebra and Differential Equations Book Excerpt:

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.

Linear Algebra and Differential Equations

Linear Algebra and Differential Equations
Author: Anne C. Baker,Hugh L. Porteous
Publsiher: Prentice Hall
Total Pages: 440
Release: 1990
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Linear Algebra and Differential Equations Book Excerpt:

Differential Equations and Linear Algebra

Differential Equations and Linear Algebra
Author: Henry Edwards,David Penney,David Calvis
Publsiher: Pearson
Total Pages: 784
Release: 2017-01-25
ISBN: 0134661672
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations and Linear Algebra Book Excerpt:

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in Differential Equations and Linear Algebra . Concepts, methods, and core topics covering elementary differential equations and linear algebra through real-world applications In a contemporary introduction to differential equations and linear algebra, acclaimed authors Edwards and Penney combine core topics in elementary differential equations with concepts and methods of elementary linear algebra. Renowned for its real-world applications and blend of algebraic and geometric approaches, Differential Equations and Linear Algebra introduces you to mathematical modeling of real-world phenomena and offers the best problems sets in any differential equations and linear algebra textbook. The 4th Edition includes fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Additionally, an Expanded Applications website containing expanded applications and programming tools is now available.

Ordinary Differential Equations and Linear Algebra A Systems Approach

Ordinary Differential Equations and Linear Algebra  A Systems Approach
Author: Todd Kapitula
Publsiher: SIAM
Total Pages: 300
Release: 2015-11-17
ISBN: 1611974089
Category: Mathematics
Language: EN, FR, DE, ES & NL

Ordinary Differential Equations and Linear Algebra A Systems Approach Book Excerpt:

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.

Linear Algebra and Differential Equations

Linear Algebra and Differential Equations
Author: Gary L. Peterson,James S. Sochacki
Publsiher: Addison Wesley
Total Pages: 463
Release: 2002
ISBN: 9780201662122
Category: Mathematics
Language: EN, FR, DE, ES & NL

Linear Algebra and Differential Equations Book Excerpt:

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.

Elementary Differential Equations with Linear Algebra

Elementary Differential Equations with Linear Algebra
Author: David L. Powers
Publsiher: Prindle Weber & Schmidt
Total Pages: 573
Release: 1986
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Elementary Differential Equations with Linear Algebra Book Excerpt:

Ordinary Differential Equations with Linear Algebra

Ordinary Differential Equations with Linear Algebra
Author: David Lomen,James Mark
Publsiher: Prentice Hall
Total Pages: 350
Release: 1986
ISBN: 1928374650XXX
Category: Mathematics
Language: EN, FR, DE, ES & NL

Ordinary Differential Equations with Linear Algebra Book Excerpt:

Differential Equations

Differential Equations
Author: Anindya Dey
Publsiher: CRC Press
Total Pages: 626
Release: 2021-09-26
ISBN: 1000436780
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations Book Excerpt:

Differential Equations: A Linear Algebra Approach follows an innovative approach of inculcating linear algebra and elementary functional analysis in the backdrop of even the simple methods of solving ordinary differential equations. The contents of the book have been made user-friendly through concise useful theoretical discussions and numerous illustrative examples practical and pathological.

Linear Algebra and Ordinary Differential Equations softcover

Linear Algebra and Ordinary Differential Equations  softcover
Author: Alan Jeffrey
Publsiher: CRC Press
Total Pages: 1136
Release: 1991-03-03
ISBN: 9780865421141
Category: Mathematics
Language: EN, FR, DE, ES & NL

Linear Algebra and Ordinary Differential Equations softcover Book Excerpt:

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 Algebra to Differential Equations

Linear Algebra to Differential Equations
Author: J. Vasundhara Devi,Sadashiv G. Deo,Ramakrishna Khandeparkar
Publsiher: CRC Press
Total Pages: 416
Release: 2021-09-27
ISBN: 1351014943
Category: Mathematics
Language: EN, FR, DE, ES & NL

Linear Algebra to Differential Equations Book Excerpt:

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.

Ordinary Differential Equations and Linear Algebra A Systems Approach

Ordinary Differential Equations and Linear Algebra  A Systems Approach
Author: Todd Kapitula
Publsiher: SIAM
Total Pages: 300
Release: 2015-11-17
ISBN: 1611974097
Category: Mathematics
Language: EN, FR, DE, ES & NL

Ordinary Differential Equations and Linear Algebra A Systems Approach Book Excerpt:

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.√∑

Multivariable Calculus Linear Algebra and Differential Equations

Multivariable Calculus  Linear Algebra  and Differential Equations
Author: Stanley I. Grossman
Publsiher: Academic Press
Total Pages: 992
Release: 2014-05-10
ISBN: 1483218031
Category: Mathematics
Language: EN, FR, DE, ES & NL

Multivariable Calculus Linear Algebra and Differential Equations Book Excerpt:

Multivariable Calculus, Linear Algebra, and Differential Equations, Second Edition contains a comprehensive coverage of the study of advanced calculus, linear algebra, and differential equations for sophomore college students. The text includes a large number of examples, exercises, cases, and applications for students to learn calculus well. Also included is the history and development of calculus. The book is divided into five parts. The first part includes multivariable calculus material. The second part is an introduction to linear algebra. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem, and the implicit function theorem. The fourth section contains detailed discussions of first-order and linear second-order equations. Also included are optional discussions of electric circuits and vibratory motion. The final section discusses Taylor's theorem, sequences, and series. The book is intended for sophomore college students of advanced calculus.

Differential Equations and Linear Algebra Global Edition

Differential Equations and Linear Algebra  Global Edition
Author: C. Henry Edwards,David E. Penney,David Calvis
Publsiher: Pearson Higher Ed
Total Pages: 757
Release: 2020-06-25
ISBN: 1292356987
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Equations and Linear Algebra Global Edition Book Excerpt:

For courses in Differential Equations and Linear Algebra. The right balance between concepts, visualisation, applications, and skills Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications. The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout. The full text downloaded to your computer With eBooks you can: search for key concepts, words and phrases make highlights and notes as you study share your notes with friends eBooks are downloaded to your computer and accessible either offline through the Bookshelf (available as a free download), available online and also via the iPad and Android apps. Upon purchase, you'll gain instant access to this eBook. Time limit The eBooks products do not have an expiry date. You will continue to access your digital ebook products whilst you have your Bookshelf installed.

Linear Algebra

Linear Algebra
Author: Tom M. Apostol
Publsiher: John Wiley & Sons
Total Pages: 347
Release: 2014-08-22
ISBN: 1118626184
Category: Mathematics
Language: EN, FR, DE, ES & NL

Linear Algebra Book Excerpt:

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.

Differential Equations

Differential Equations
Author: Allan Struthers,Merle Potter
Publsiher: Springer
Total Pages: 514
Release: 2019-07-31
ISBN: 3030205061
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Differential Equations Book Excerpt:

This book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, including a number of physical applications, and goes on to discuss first-order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms, nonlinear systems of differential equations, and numerical methods used in solving differential equations. The style of presentation of the book ensures that the student with a minimum of assistance may apply the theorems and proofs presented. Liberal use of examples and homework problems aids the student in the study of the topics presented and applying them to numerous applications in the real scientific world. This textbook focuses on the actual solution of ordinary differential equations preparing the student to solve ordinary differential equations when exposed to such equations in subsequent courses in engineering or pure science programs. The book can be used as a text in a one-semester core course on differential equations, alternatively it can also be used as a partial or supplementary text in intensive courses that cover multiple topics including differential equations.