This innovative text offers a modern presentation of differential
equations with an emphasis on the use of software for the numerical
implementation of relevant algorithms. Just enough linear algebra
is covered early2 chapters of materialso that systems of
differential equations are emphasized throughout. Modeling ODES is
also stressed throughout.
presents an integrated treatment of numerical methods for
both matrix algebra and differential equations, while introducing
numerical methods for differential equations initially at a basic
level and again at a more advanced, more accurate level later on.
introduces linear algebra early and uses it often throughout
the text to build student proficiency and familiarity with the subject.
Avoids excessive proofs and derivations, providing proofs only when
they aid in understanding the material or are absolutely essential.
incorporates insightful coverage of software to better prepare
students for more advanced courses, though treating it not as the
primary focus of the book, but rather as a useful adjunct.
offers a wealth of superb problem sets ranging from simple
manipulations to more complex applications of concepts. Provides answers
for most problems presented in the text.
contains numerous practical examples, proven by class-testing
to prepare students to complete problems in the text and to apply
these concepts to their other courses.
1. Matrix Algebra.
2. Ordinary Differential Equations.
3. Linear Spaces and Linear Transformations.
4. Linear Differential Equations.
5. Laplace Transforms.
6. Systems of Linear ODE's.
7. Nonlinear ODE's.
8. Series Solutions of ODE's.
9. Special Functions.
Table of Laplace Transforms.