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.
Sign up for future
mailings on this subject.
See other books about:
Differential Equations and Linear Algebra-Mathematics
For combined courses in Differential Equations and Linear
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 algebramotivated throughout by high-quality
applications to science and engineering.
An abundance of quality applications to science and engineeringWith
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 applicationse.g.,
the application of the eigenvalue problem to population dynamics and
an interesting application to pollution in a stream.
An easy-to-read and comprehend approachProvides
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.
- Shows students the essential interplay between the physics
Supplemental inclusion of MapleAt 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.
Additional TopicsIncludes some nonstandard topics,
usually as optional sectionse.g., Nondimensionalization (Sec.
3.5.3), and Linear and Nonlinear Equations Contrasted. (Sec. 3.6)
- Maple is easy to use and works as an effective
tool for supporting the pedagogy of the text.
FlexibilityFeatures many optional sections
and subsections that allow topics to be covered comprehensively, moderately,
ExercisesTypically 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
- 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.
CommentsOften 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.
- Supplementary information whets the student's appetite
for more and deeper mathematics.
Historical NotesUsed judiciously throughout the
text, e.g., Footnotes on Kepler and Newton. (Sec. 3.5.2)
- Gives the examples an easier-to-read structure.
- Adds an important dimension to learning mathematics.
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.