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Differential Equations And Linear Algebra

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Differential Equations and Linear Algebra

Differential Equations and Linear Algebra Book
Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Release : 2015-02-12
ISBN : 9780980232790
Language : En, Es, Fr & De

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Book Description :

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

Differential Equations Book
Author : Anindya Dey
Publisher : CRC Press
Release : 2021-09-27
ISBN : 1000436799
Language : En, Es, Fr & De

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Book Description :

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 to Differential Equations

Linear Algebra to Differential Equations Book
Author : J. Vasundhara Devi,Sadashiv G. Deo,Ramakrishna Khandeparkar
Publisher : CRC Press
Release : 2021-09-27
ISBN : 1351014943
Language : En, Es, Fr & De

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Book Description :

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.

Differential Equations with Linear Algebra

Differential Equations with Linear Algebra Book
Author : Matthew R. Boelkins,Jack L. Goldberg,Merle C. Potter
Publisher : Oxford University Press
Release : 2009-11-05
ISBN : 0199736669
Language : En, Es, Fr & De

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Book Description :

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

Ordinary Differential Equations and Linear Algebra  A Systems Approach Book
Author : Todd Kapitula
Publisher : SIAM
Release : 2015-11-17
ISBN : 1611974097
Language : En, Es, Fr & De

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Book Description :

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 and Linear Algebra

Differential Equations and Linear Algebra Book
Author : Charles Henry Edwards,David E. Penney
Publisher : Pearson
Release : 2013-08-27
ISBN : 9781292039084
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Calculus Linear Algebra and Differential Equations

Multivariable Calculus  Linear Algebra  and Differential Equations Book
Author : Stanley I. Grossman
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483218031
Language : En, Es, Fr & De

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Book Description :

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.

Introduction to Linear Algebra and Differential Equations

Introduction to Linear Algebra and Differential Equations Book
Author : John W. Dettman
Publisher : Courier Corporation
Release : 2012-10-05
ISBN : 0486158314
Language : En, Es, Fr & De

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Book Description :

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 and Linear Algebra

Differential Equations and Linear Algebra Book
Author : Henry Edwards
Publisher : Pearson College Division
Release : 2008-12-01
ISBN : 9780136054276
Language : En, Es, Fr & De

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Book Description :

Download Differential Equations and Linear Algebra book written by Henry Edwards, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Differential Equations and Linear Algebra Global Edition

Differential Equations and Linear Algebra  Global Edition Book
Author : C. HENRY. PENNEY EDWARDS (DAVID E.. CALVIS, DAVID.),David E. Penney,David Calvis
Publisher : Unknown
Release : 2020-07-08
ISBN : 9781292356952
Language : En, Es, Fr & De

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Book Description :

Download Differential Equations and Linear Algebra Global Edition book written by C. HENRY. PENNEY EDWARDS (DAVID E.. CALVIS, DAVID.),David E. Penney,David Calvis, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Elementary Differential Equations with Linear Algebra

Elementary Differential Equations with Linear Algebra Book
Author : Ross L. Finney,Donald R. Ostberg,Robert Garlin Kuller
Publisher : Addison-Wesley
Release : 1976
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Elementary Differential Equations with Linear Algebra book written by Ross L. Finney,Donald R. Ostberg,Robert Garlin Kuller, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Linear Algebra and Differential Equations

Linear Algebra and Differential Equations Book
Author : Alexander Givental
Publisher : American Mathematical Soc.
Release : 2001
ISBN : 9780821828502
Language : En, Es, Fr & De

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Book Description :

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.

Differential Equations Dynamical Systems and Linear Algebra

Differential Equations  Dynamical Systems  and Linear Algebra Book
Author : Morris W. Hirsch,Robert L. Devaney,Stephen Smale
Publisher : Academic Press
Release : 1974-06-28
ISBN : 0080873766
Language : En, Es, Fr & De

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Book Description :

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.

Linear Algebra and Ordinary Differential Equations softcover

Linear Algebra and Ordinary Differential Equations  softcover  Book
Author : Alan Jeffrey
Publisher : CRC Press
Release : 1991-03-03
ISBN : 9780865421141
Language : En, Es, Fr & De

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Book Description :

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.

Multivariable Mathematics

Multivariable Mathematics Book
Author : Richard E. Williamson,Hale F. Trotter
Publisher : Pearson
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This book explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. Unique coverage including, the introduction of vector geometry and matrix algrebra, the early introduction of the gradient vector as the key to differentiability, optional numerical methods. For any reader interested in learning more about this discipline.

Differential Equations Linear Algebra

Differential Equations   Linear Algebra Book
Author : Michael D. Greenberg
Publisher : Unknown
Release : 2001
ISBN : 9780130111180
Language : En, Es, Fr & De

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Book Description :

Written by a mathematician/engineer/scientist author who brings all three perspectives to the book. This volume offers an extremely easy-to-read and easy-to-comprehend exploration of both ordinary differential equations and linear algebra--motivated throughout by high-quality applications to science and engineering. Features many optional sections and subsections that allow topics to be covered comprehensively, moderately, or minimally, and includes supplemental coverage of Maple at the end of most sections. For anyone interested in Differential Equations and Linear Algebra.

Linear Algebra

Linear Algebra Book
Author : Tom M. Apostol
Publisher : John Wiley & Sons
Release : 2014-08-22
ISBN : 1118626184
Language : En, Es, Fr & De

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Book Description :

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.

Introduction to Applied Linear Algebra

Introduction to Applied Linear Algebra Book
Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Release : 2018-06-07
ISBN : 1316518965
Language : En, Es, Fr & De

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Book Description :

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Differential Equations and Linear Algebra

Differential Equations and Linear Algebra Book
Author : Stephen W. Goode,Scott A. Annin
Publisher : Pearson Higher Ed
Release : 2013-08-29
ISBN : 1292037725
Language : En, Es, Fr & De

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Book Description :

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

Differential Equations Book
Author : Clay C. Ross
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475739494
Language : En, Es, Fr & De

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Book Description :

The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.