Linear Algebra and Differential Equations Using MATLAB / Edition 1

Hardcover (Print)
Buy Used
Buy Used from
(Save 34%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $1.99
Usually ships in 1-2 business days
(Save 99%)
Other sellers (Hardcover)
  • All (13) from $1.99   
  • New (5) from $205.70   
  • Used (8) from $1.99   


These world-renowned authors integrate linear algebra and ordinary differential equations in this unique book, interweaving instructions on how to use MATLAB with examples and theory. They use computers in two ways: in linear algebra, computers reduce the drudgery of calculations to help students focus on concepts and methods; in differential equations, computers display phase portraits graphically for students to focus on the qualitative information embodied in solutions, rather than just to learn to develop formulas for solutions.

Read More Show Less

Editorial Reviews

From the Publisher
"The topic areas of linear algebra and differential equations lend themselves naturally to be developed in tandem, and I do not know of a text that does a better job of integrating the two areas so that each reinforce the understanding of the other."

"[This text] provides a very interesting way of blending linear algebra and sophomore level differential equations course with the programming system MATLAB. . . . It . . . has the potential to be adopted by many institutions who are leaning towards the use of technology in the classroom. For one, I would use the book fore our linear algebra and differential equations course. . . ."

"The text is unique in offering a true amalgam of linear algebra, differential equations, and MATLAB. There is a definite need for such a text. The integration of the three 'legs' is well done and the ideas are introduced at a good pace."

Provides an integrated approach to linear algebra and ordinary differential equations based on computers. Includes instructions on how to use MATLAB, theories and examples, and preloaded matrices and differential equations with notes. Topics covered include: solving linear equations; matrices and linearity; solving ordinary differential equations; vector spaces; qualitative theory of planar odes; orthogonality; bifurcation theory; matrix normal forms; higher dimensional systems; and numerical solutions of odes. Also included are MATLAB commands and answers to selected problems. Annotation c. by Book News, Inc., Portland, Or.
Read More Show Less

Product Details

  • ISBN-13: 9780534354251
  • Publisher: Cengage Learning
  • Publication date: 1/18/1999
  • Series: Mathematics Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 720
  • Product dimensions: 7.40 (w) x 9.30 (h) x 1.20 (d)

Meet the Author

Professor of Mathematics at University of Houston, Ph.D. in Mathematics from Massachusetts Institute of Technology

Professor of Mathematics at University of Paderborn, Germany

Read More Show Less

Table of Contents

1. PRELIMINARIES Vectors and Matrices / MATLAB / Special Kinds of Matrices / The Geometry of Vector Operations 2. SOLVING LINEAR EQUATIONS Systems of Linear Equations and Matrices / The Geometry of Low-Dimensional Solutions / Gaussian Elimination / Reduction to Echelon Form / Linear Equations with Special Coefficients / Uniqueness of Reduced Echelon Form 3. MATRICES AND LINEARITY Matrix Multiplication of Vectors / Matrix Mappings / Linearity / The Principle of Superposition / Composite and Multiplication of Matrices / Properties of Matrix Multiplication / Solving Linear Systems and Inverses / Determinants of 2 x 2 Matrices 4. SOLVING ORDINARY DIFFERENTIAL EQUATIONS A Single Differential Equation / Graphing Solutions to Differential Equations / Phase Space Pictures and Equilibria / Separation of Variables / Uncoupled Linear Systems of Two Equations / Coupled Linear Systems / The Initial Value Problem and Eigenvectors / Eigenvalues of 2 x 2 Matrices / Initial Value Problems Revisited / Markov Chains 5. VECTOR SPACES Vector Spaces and Subspaces / Construction of Subspaces / Spanning Sets and MATLAB / Linear Dependence and Linear Independence / Dimension and Bases / The Proof of the Main Theorem 6. CLOSED FORM SOLUTIONS FOR PLANAR ODES The Initial Value Problem / Closed Form Solutions by the Direct Method / Solutions Using Matrix Exponentials / Linear Normal Form Planar Systems / Similar Matrices / Formulas for Matrix Exponentials / Second Order Equations 7. QUALITATIVE THEORY OF PLANAR ODES Sinks, Saddles, and Sources / Phase Portraits of Sinks / Phase Portraits of Nonhyperbolic Systems 8. DETERMINANTS AND EIGENVALUES Determinants / Eigenvalues / Appendix: Existence of Determinants 9. LINEAR MAPS AND CHANGES OF COORDINATES Linear Mappings and Bases / Row Rank Equals Column Rank / Vectors and Matrices in Coordinates / Matrices of Linear Maps on a Vector Space 10. ORTHOGONALITY Orthonormal Bases / Least Squares Approximations / Least Squares Fitting of Data / Symmetric Matrices / Orthogonal Matrices of QR Decompositions 11. AUTONOMOUS PLANAR NONLINEAR SYSTEMS Introduction / Equilibria and Linearization / Periodic Solutions / Stylized Phase Portraits 12. BIFURCATION THEORY Two Species Population Models / Examples of Bifurcations / The Continuous Flow Stirred Tank Reactor / The Remaining Global Bifurcations / Saddle-Node Bifurcations Revisited / Hopf Bifurcations Revisited 13. MATRIX NORMAL FORMS Real Diagonalizable Matrices / Simple Complex Eigenvalues / Multiplicity and Generalized Eigenvectors / The Jordan Normal Form Theorem / Appendix: Markov Matrix Theory / Appendix: Proof of Jordan Normal Form 14. HIGHER DIMENSIONAL SYSTEMS Linear Systems in Jordan Normal Form / Qualitative Theory Near Equilibria / MATLAB ODE45 in One Dimension / Higher Dimensional Systems Using ODE45 / Quasiperiodic Motions and Tori / Chaos and the Lorenz Equation 15. LINEAR DIFFERENTIAL EQUATIONS Solving Systems in Original Coordinates / Higher Order Equations / Linear Differential Operators / Undetermined Coefficients / Periodic Forcing and Resonance 16. LAPLACE TRANSFORMS The Method of Laplace Transforms / Laplace Transforms and Their Computation / Partial Fractions / Discontinuous Forcing / RLC Circuits 17. ADDITIONAL TECHNIQUES FOR SOLVING ODES Nonconstant Coefficient Linear Equations / Variation of Parameters for Systems / The Wronskian / Higher Order Equations / Simplification by Substitution / Exact Differential Equations / Hamiltonian Systems 18. NUMERICAL SOLUTIONS OF ODES A Description of Numerical Methods / Error Bounds for Euler's Method / Local and Global Error Bounds / APPENDIX: VARIABLE STEP METHODS / MATLAB COMMANDS / ANSWERS TO SELECTED ODD-NUMBERED PROBLEMS / INDEX

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)