Book description
For courses in Differential Equations and Linear Algebra.
The right balance between concepts, visualization, applications, and skills Differential Equations and Linear Algebra provides the conceptual development and geometric visualization 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, computerbased 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 realworld phenomena, evident in figures, examples, problems, and applications throughout.
For the first time, MyLab™ Math is available for this text, providing online homework with immediate feedback, the complete eText, and more.
Additionally, new presentation slides created by author David Calvis are available in Beamer (LaTeX) and PDF formats.
The slides are ideal for classroom lectures and student review, and combined with Calvis’ superlative instructional videos offer a level of support not found in any other Differential Equations course.
Also available with MyLab Math
MyLab Math is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab Math personalizes the learning experience and improves results for each student.
Table of contents
 Differential Equations & Linear Algebra
 Contents
 Application Modules
 Preface
 1 FirstOrder Differential Equations
 2 Mathematical Models and Numerical Methods
 3 Linear Systems and Matrices
 4 Vector Spaces

5 HigherOrder Linear Differential Equations
 5.1 Introduction: SecondOrder Linear Equations
 5.2 General Solutions of Linear Equations
 5.3 Homogeneous Equations with Constant Coefficients
 5.4 Mechanical Vibrations
 5.5 Nonhomogeneous Equations and Undetermined Coefficients
 5.6 Forced Oscillations and Resonance
 6 Eigenvalues and Eigenvectors

7 Linear Systems of Differential Equations
 7.1 FirstOrder Systems and Applications
 7.2 Matrices and Linear Systems
 7.3 The Eigenvalue Method for Linear Systems

7.4 A Gallery of Solution Curves of Linear Systems
 Systems of Dimension n=2
 Real Eigenvalues
 Saddle Points
 Nodes: Sinks and Sources
 Zero Eigenvalues and StraightLine Solutions
 Repeated Eigenvalues; Proper and Improper Nodes
 The Special Case of a Repeated Zero Eigenvalue
 Complex Conjugate Eigenvalues and Eigenvectors
 Pure Imaginary Eigenvalues: Centers and Elliptical Orbits
 Complex Eigenvalues: Spiral Sinks and Sources
 A 3Dimensional Example
 7.4 Problems
 7.4 Application Dynamic Phase Plane Graphics
 7.5 SecondOrder Systems and Mechanical Applications*
 7.6 Multiple Eigenvalue Solutions
 7.7 Numerical Methods for Systems
 7.7 Application Comets and Spacecraft
 8 Matrix Exponential Methods

9 Nonlinear Systems and Phenomena
 9.1 Stability and the Phase Plane
 9.2 Linear and Almost Linear Systems
 9.3 Ecological Models: Predators and Competitors
 9.4 Nonlinear Mechanical Systems
 10 Laplace Transform Methods
 11 Power Series Methods
 References for Further Study
 APPENDIX A Existence and Uniqueness of Solutions
 APPENDIX B Theory of Determinants
 Answers to Selected Problems
 Index
Product information
 Title: Differential Equations and Linear Algebra, 4th Edition
 Author(s):
 Release date: January 2017
 Publisher(s): Pearson
 ISBN: 9780136739692
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