Differential Equations and Linear Algebra, 4th edition

Published by Do not use (January 4, 2017) © 2018

  • C Henry Edwards University of Georgia, Athens
  • David E. Penney University of Georgia, Athens
  • David Calvis Baldwin Wallace University

eTextbook

per month

  • Anytime, anywhere learning with the Pearson+ app
  • Easy-to-use search, navigation and notebook
  • Simpler studying with flashcards
from$143.99

  • Hardcover, paperback or looseleaf edition
  • Affordable rental option for select titles
  • Free shipping on looseleafs and traditional textbooks

MyLab

from$89.99

  • Reach every student with personalized support
  • Customize courses with ease
  • Optimize learning with dynamic study tools

For courses in Differential Equations and Linear Algebra.

The right balance between concepts, visualization, applications and skills 

Differential Equations and Linear Algebra, 4th Edition combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It provides the conceptual development and geometric visualization of a modern differential equations and linear algebra course that is essential to science and engineering students. The authors balance traditional manual methods with the computer-based methods that illuminate qualitative phenomena; this comprehensive approach makes accessible a wider range of more realistic applications.

Hallmark features of this title

  • Numerical methods emphasis includes early introduction of numerical solution techniques, mathematical modeling, stability and qualitative properties of differential equations.
  • 44 Application Modules follow key sections. Most provide computing projects that illustrate the corresponding text sections.
  • Approximately 2000 problems range from computational problems to applied and conceptual problems. 
  • The expansive answer section offers answers to most odd-numbered and many even-numbered problems. 
  • Emphasis on the intersection of technology and ODEs instructs students in newer methods of computing differential equations.
  • Software systems tailored specifically to differential equations are covered as well as the widely used Maple, Mathematica and MATLAB.

New and updated features of this title

  • New text and graphics have been inserted in a number of sections to enhance student understanding. Nearly 80 new figures illustrate interactive computer applications.
  • Now includes Python, the popular computer platform that is freely available online and an all-purpose scientific computing environment.
  • Online Expanded Applications enhance the text's applications material and provide detailed coverage of Maple, Mathematica and MATLAB techniques.
  • Chapter 7 (Linear Systems of Differential Equations) has a new section devoted to the construction of a “gallery” of phase plane portraits illustrating all the possible geometric behaviors of solutions of the 2-dimensional linear system x' = Ax.
  • Chapter 9 (Nonlinear Systems and Phenomena) now contains a new biological application which includes a substantial investigation of the nonlinear FitzHugh-Nagumo equations of neuroscience.

Highlights of the DIGITAL UPDATE for MyLab Math 

Instructors, contact your sales rep to ensure you have the most recent version of the course.  

In this Digital Update, MyLab Math is available for the first time with this text, providing online homework with immediate feedback, the complete eText and more.

Features of MyLab Math for the 4th Edition

  • Nearly 700 assignable exercises are based on the textbook exercises and regenerate algorithmically. Most include learning aids such as guided solutions, sample problems and extra help at point-of-use, with helpful feedback.
  • The Additional Review for Differential Equations chapter addresses gaps in prerequisite skills, with remediation of key calculus and precalculus objectives.
  • Instructional videos created by the authors are available as learning aids within exercises and for self-study.
  • Presentation slides created by author David Calvis are available in Beamer and PDF formats. Ideal for classroom lecture and student review, and combined with Calvis' superlative videos, they offer a level of support not found in any other DE course.
  • The Instructor Solution Manual within MyLab Math provides worked-out solutions for most of the text's problems. The Student Solution Manual, available within MyLab Math and in print, contains solutions for most of the odd-numbered problems.
  1. First-Order Differential Equations
    • 1.1 Differential Equations and Mathematical Models
    • 1.2 Integrals as General and Particular Solutions
    • 1.3 Slope Fields and Solution Curves
    • 1.4 Separable Equations and Applications
    • 1.5 Linear First-Order Equations
    • 1.6 Substitution Methods and Exact Equations
  2. Mathematical Models and Numerical Methods
    • 2.1 Population Models
    • 2.2 Equilibrium Solutions and Stability
    • 2.3 Acceleration - Velocity Models
    • 2.4 Numerical Approximation: Euler's Method
    • 2.5 A Closer Look at the Euler Method
    • 2.6 The Runge - Kutta Method
  3. Linear Systems and Matrices
    • 3.1 Introduction to Linear Systems
    • 3.2 Matrices and Gaussian Elimination
    • 3.3 Reduced Row-Echelon Matrices
    • 3.4 Matrix Operations
    • 3.5 Inverses of Matrices
    • 3.6 Determinants
    • 3.7 Linear Equations and Curve Fitting
  4. Vector Spaces
    • 4.1 The Vector Space R3
    • 4.2 The Vector Space Rn and Subspaces
    • 4.3 Linear Combinations and Independence of Vectors
    • 4.4 Bases and Dimension for Vector Spaces
    • 4.5 Row and Column Spaces
    • 4.6 Orthogonal Vectors in Rn
    • 4.7 General Vector Spaces
  5. Higher-Order Linear Differential Equations
    • 5.1 Introduction: Second-Order 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
    • 6.1 Introduction to Eigenvalues
    • 6.2 Diagonalization of Matrices
    • 6.3 Applications Involving Powers of Matrices
  7. Linear Systems of Differential Equations
    • 7.1 First-Order 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
    • 7.5 Second-Order Systems and Mechanical Applications
    • 7.6 Multiple Eigenvalue Solutions
    • 7.7 Numerical Methods for Systems
  8. Matrix Exponential Methods
    • 8.1 Matrix Exponentials and Linear Systems
    • 8.2 Nonhomogeneous Linear Systems
    • 8.3 Spectral Decomposition 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
    • 10.1 Laplace Transforms and Inverse Transforms
    • 10.2 Transformation of Initial Value Problems
    • 10.3 Translation and Partial Fractions
    • 10.4 Derivatives, Integrals, and Products of Transforms
    • 10.5 Periodic and Piecewise Continuous Input Functions
  11. Power Series Methods
    • 11.1 Introduction and Review of Power Series
    • 11.2 Power Series Solutions
    • 11.3 Frobenius Series Solutions
    • 11.4 Bessel Functions

    Appendices

    • A: Existence and Uniqueness of Solutions
    • B: Theory of Determinants

        

APPLICATION MODULES

The modules listed below follow the indicated sections in the text. Most provide computing projects that illustrate the corresponding text sections. Many of these modules are enhanced by the supplementary material found at the new Expanded Applications website.

    • 1.3 Computer-Generated Slope Fields and Solution Curves
    • 1.4 The Logistic Equation
    • 1.5 Indoor Temperature Oscillations
    • 1.6 Computer Algebra Solutions
    • 2.1 Logistic Modeling of Population Data
    • 2.3 Rocket Propulsion
    • 2.4 Implementing Euler's Method
    • 2.5 Improved Euler Implementation
    • 2.6 Runge-Kutta Implementation
    • 3.2 Automated Row Operations
    • 3.3 Automated Row Reduction
    • 3.5 Automated Solution of Linear Systems
    • 5.1 Plotting Second-Order Solution Families
    • 5.2 Plotting Third-Order Solution Families
    • 5.3 Approximate Solutions of Linear Equations
    • 5.5 Automated Variation of Parameters
    • 5.6 Forced Vibrations and Resonance
    • 7.1 Gravitation and Kepler's Laws of Planetary Motion
    • 7.3 Automatic Calculation of Eigenvalues and Eigenvectors
    • 7.4 Dynamic Phase Plane Graphics
    • 7.5 Earthquake-Induced Vibrations of Multistory Buildings
    • 7.6 Defective Eigenvalues and Generalized Eigenvectors
    • 7.7 Comets and Spacecraft
    • 8.1 Automated Matrix Exponential Solutions
    • 8.2 Automated Variation of Parameters
    • 9.1 Phase Portraits and First-Order Equations
    • 9.2 Phase Portraits of Almost Linear Systems
    • 9.3 Your Own Wildlife Conservation Preserve
    • 9.4 The Rayleigh and van der Pol Equations

About our authors

Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.

David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He was the author of research papers in number theory and topology and was the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

David T. Calvis is Professor of Mathematics at Baldwin Wallace University near Cleveland, Ohio.  He completed a Ph.D. in complex analysis from the University of Michigan in 1988 under the direction of Fred Gehring.  While at Michigan he also received a Master's degree in Computer, Information, and Control Engineering.  Having initially served at Hillsdale College in Michigan, he has been at Baldwin Wallace since 1990, most recently assisting with the creation of an Applied Mathematics program there.  He has received a number of teaching awards, including BWU's Strosacker Award for Excellence in Teaching and Student Senate Teaching Award.  He is the author of a number of materials dealing with the use of computer algebra systems in mathematics instruction, and has extensive classroom experience teaching differential equations and related topics.

Need help? Get in touch

MyLab

Customize your course to teach your way. MyLab® is a flexible platform merging world-class content with dynamic study tools. It takes a personalized approach designed to ignite each student's unique potential. And, with the freedom it affords to adapt your pedagogy, you can reinforce select concepts and guide students to real results.

Pearson+

All in one place. Pearson+ offers instant access to eTextbooks, videos and study tools in one intuitive interface. Students choose how they learn best with enhanced search, audio and flashcards. The Pearson+ app lets them read where life takes them, no wi-fi needed. Students can access Pearson+ through a subscription or their MyLab or Mastering course.

Video
Play
Privacy and cookies
By watching, you agree Pearson can share your viewership data for marketing and analytics for one year, revocable by deleting your cookies.

Empower your students, in class and beyond

Meet students where they are with MyLab®, and capture their attention in every lecture, activity, and assignment using immersive content, customized tools, and interactive learning experiences in your discipline.