[Book Cover]

Linear Algebra and Differential Equations, 1/e

Michael D. Greenberg, University of Delaware

Coming March, 2000 by Prentice Hall Engineering/Science/Mathematics

Copyright 2000, 610 pp.
Cloth
ISBN 0-13-011118-X


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    Differential Equations and Linear Algebra-Mathematics


Summary

For combined courses in Differential Equations and Linear Algebra. Written by a mathematician and engineer who brings diverse perspectives to the text, this volume offers an extremely easy-to-read and comprehensive exploration of both ordinary differential equations and linear algebra—motivated throughout by high-quality applications to science and engineering.

Features


An abundance of quality applications to science and engineering—With a formal background in engineering and science, the author makes applications a focal point of the text, whereas other texts on mathematics for E&S students often only give lip service to the applications—e.g., the application of the eigenvalue problem to population dynamics and an interesting application to pollution in a stream.

  • Shows students the essential interplay between the physics and mathematics.
An easy-to-read and comprehend approach—Provides a solid engineering basis for the modeling of mechanical systems, uses the simple problem of the free fall of a body to explore the idea of the uniqueness of solutions to ODEs, uses the diving board example to illustrate the significance of linearity, provides an analogy between undoing a tangle of string and solution of coupled equations by Gauss elimination, has an unusual and clear approach to the method of undetermined coefficients, and a clear discussion of the connection between beats and resonance.
Supplemental inclusion of Maple—At the end of most sections. Goes through the use of Maple for the material in the section. There are also Maple exercises in the exercise sets.
  • Maple is easy to use and works as an effective tool for supporting the pedagogy of the text.
Additional Topics—Includes some nonstandard topics, usually as optional sections—e.g., Nondimensionalization (Sec. 3.5.3), and Linear and Nonlinear Equations Contrasted. (Sec. 3.6)
Flexibility—Features many optional sections and subsections that allow topics to be covered comprehensively, moderately, or minimally.
  • Gives instructors the flexibility to pick and choose topics without penalty and to be able to find a convenient one-semester course within the text.
Exercises—Typically begin with numerous drill type problems, but additional exercises ask students to fill in steps in the text or lead students into supplementary territory and physical applications.
  • Supplementary information whets the student's appetite for more and deeper mathematics.
Comments—Often follow examples. May involve going back to look at a fine point in the analysis, making a meta-level comment about the example, and so on.
  • Gives the examples an easier-to-read structure.
Historical Notes—Used judiciously throughout the text, e.g., Footnotes on Kepler and Newton. (Sec. 3.5.2)
  • Adds an important dimension to learning mathematics.


Table of Contents
    Preface
    1. Introduction to Differential Equations.
    2. Linear First-Order Equations.
    3. General First-Order Equations.
    4. Vectors and n-Space.
    5. Matrices and Linear Algebraic Equations.
    6. Linear Differential Equations of Second Order and Higher.
    7. Applications of Linear Constant-Coefficient Equations.
    8. Series Solution.
    9. The Eigenvalue Problem.
    10. Systems of Linear Differential Equations.
    11. Nonlinear Equations and the Phase Plane.
    12. Numerical Solution.
    13. Laplace Transform.


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