Differential Equations With Linear Algebra

Author : Gilbert Strang
Publisher : Wellesley-Cambridge Press
Page : 0 pages
File Size : 45,9 Mb
Release : 2015-02-12
Category : Mathematics
ISBN : 0980232791

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Differential Equations and Linear Algebra by Gilbert Strang Pdf

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.

Author : Anindya Dey
Publisher : CRC Press
Page : 522 pages
File Size : 50,6 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9781000436792

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Differential Equations by Anindya Dey Pdf

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.

Author : Todd Kapitula
Publisher : SIAM
Page : 308 pages
File Size : 49,5 Mb
Release : 2015-11-17
Category : Mathematics
ISBN : 9781611974096

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Ordinary Differential Equations and Linear Algebra by Todd Kapitula Pdf

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.?

Author : John W. Dettman
Publisher : Courier Corporation
Page : 432 pages
File Size : 42,7 Mb
Release : 2012-10-05
Category : Mathematics
ISBN : 9780486158310

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Introduction to Linear Algebra and Differential Equations by John W. Dettman Pdf

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.

Author : Charles Henry Edwards,David E. Penney
Publisher : Prentice Hall
Page : 0 pages
File Size : 52,6 Mb
Release : 2010
Category : Algebras, Linear
ISBN : 0136054250

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Differential Equations and Linear Algebra by Charles Henry Edwards,David E. Penney Pdf

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 book discusses mathematical modeling of real-world phenomena, with a fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. First-Order Differential Equations; Mathematical Models and Numerical Methods; Linear Systems and Matrices; Vector Spaces; Higher-Order Linear Differential Equations; Eigenvalues and Eigenvectors; Linear Systems of Differential Equations; Matrix Exponential Methods; Nonlinear Systems and Phenomena; Laplace Transform Methods; Power Series Methods. For future math majors, engineers, or scientists that have taken two or three semesters of Calculus.

Author : Matthew R. Boelkins,Jack L. Goldberg,Merle C. Potter
Publisher : OUP USA
Page : 572 pages
File Size : 52,5 Mb
Release : 2009-11-05
Category : Mathematics
ISBN : 9780195385861

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Differential Equations with Linear Algebra by Matthew R. Boelkins,Jack L. Goldberg,Merle C. Potter Pdf

Differential Equations with Linear Algebra explores the interplay between linear algebra and differential equations by examining fundamental problems in elementary differential equations. With an example-first style, the text is accessible to students who have completed multivariable calculus and is appropriate for courses in mathematics and engineering that study systems of differential equations.

Author : Alan Jeffrey
Publisher : CRC Press
Page : 1136 pages
File Size : 45,7 Mb
Release : 1991-03-03
Category : Mathematics
ISBN : 0865421145

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Linear Algebra and Ordinary Differential Equations (softcover) by Alan Jeffrey Pdf

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.

Author : Jason Brownlee
Publisher : Machine Learning Mastery
Page : 211 pages
File Size : 43,5 Mb
Release : 2018-01-24
Category : Computers
ISBN : 8210379456XXX

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Basics of Linear Algebra for Machine Learning by Jason Brownlee Pdf

Linear algebra is a pillar of machine learning. You cannot develop a deep understanding and application of machine learning without it. In this laser-focused Ebook, you will finally cut through the equations, Greek letters, and confusion, and discover the topics in linear algebra that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover what linear algebra is, the importance of linear algebra to machine learning, vector, and matrix operations, matrix factorization, principal component analysis, and much more.

Author : Albert L. Rabenstein
Publisher : Academic Press
Page : 529 pages
File Size : 44,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262376

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Elementary Differential Equations with Linear Algebra by Albert L. Rabenstein Pdf

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.

Author : Alexander Givental
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 55,6 Mb
Release : 2001
Category : Algebras, Linear
ISBN : 0821828509

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Linear Algebra and Differential Equations by Alexander Givental Pdf

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.

Author : Kuldeep Singh
Publisher : Oxford University Press
Page : 617 pages
File Size : 53,5 Mb
Release : 2013-10
Category : Mathematics
ISBN : 9780199654444

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Linear Algebra by Kuldeep Singh Pdf

"This book is intended for first- and second-year undergraduates arriving with average mathematics grades ... The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to all of the set problems freely available online http://www.oup.co.uk/companion/singh" -- From preface.

Author : Ross L. Finney,Donald R. Ostberg,Robert Garlin Kuller
Publisher : Addison Wesley Publishing Company
Page : 536 pages
File Size : 43,5 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015016357900

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Elementary Differential Equations with Linear Algebra by Ross L. Finney,Donald R. Ostberg,Robert Garlin Kuller Pdf

Author : Morris W. Hirsch,Robert L. Devaney,Stephen Smale
Publisher : Academic Press
Page : 358 pages
File Size : 47,7 Mb
Release : 1974-06-28
Category : Mathematics
ISBN : 9780080873763

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Differential Equations, Dynamical Systems, and Linear Algebra by Morris W. Hirsch,Robert L. Devaney,Stephen Smale Pdf

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.

Author : Anne C. Baker,Hugh L. Porteous
Publisher : Unknown
Page : 440 pages
File Size : 45,9 Mb
Release : 1990
Category : Algebras, Linear
ISBN : UCSC:32106009603405

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Linear Algebra and Differential Equations by Anne C. Baker,Hugh L. Porteous Pdf

Author : J. Vasundhara Devi,Sadashiv G. Deo,Ramakrishna Khandeparkar
Publisher : Chapman & Hall/CRC
Page : 416 pages
File Size : 54,7 Mb
Release : 2021
Category : Mathematics
ISBN : 1351014951

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Linear Algebra to Differential Equations by J. Vasundhara Devi,Sadashiv G. Deo,Ramakrishna Khandeparkar Pdf

"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"--