Differential Equations with MAPLE

This introduction to differential equations features an exciting interactive approach to the subject, integrating the basics of ODEs and the symbolic computation package MAPLE. Unique to this text is the extensive cross-referencing throughout between ODE theory and MAPLE exercises, thus providing readers with a solid introduction to MAPLE in parallel with a standard ODE course.
What this book offers:
* coverage of all essential topics, including some classical ones not generally found in differential equations courses at this level
* user-friendly presentation of rigorous mathematics balanced with excellent examples from many different fields of applications
* discussion of all standard solutions methods; numerous graphical interpretations of solutions
* a careful introduction to MAPLE fundamentals; students become familiar with MAPLE commands to simplify calculations, solve difficult problems, and experience MAPLE's power as a research tool
* an examination of topics that are important, but often inaccessible without the aid of a symbolic computation package such as MAPLE
* ample problems; those requiring MAPLE are indicated within boxes throughout each chapter, while non-MAPLE problems are presented at the end of each chapter
* "harder" Maple programming projects in Part II; MAPLE becomes a research tool and programming vehicle to solve challenging problems
* cross-platform CD-ROM with extensive Maple code; worksheets and additional related material also downloadable from Birkhauser and author's websites
* comprehensive index
Differential Equations is a key subject in pure and applied mathematics, engineering, biology, and physics. As colleges everywhere are moving to incorporate a programming package into the differential equations curricula, this book, with its distinctly applied orientation, provides a nice combination of basic ODE theory and MAPLE.

Contents

Preface

Maple use and programming

• Introduction to Maple

Differential equations

• Introduction to differentials equations
• First order equations
• Introduction to numerical methods
• Higher order differential equations
• Laplace transform methods
• Systems of equations
• Stability
• Periodic problems
• Impedances and differential equations
• Partial differential equations

Maple applications topics

• Introduction to Maple applications
• Plotting with Maple
• Maple and Laplace transforms
• Maple linear algebra applications
• Runge-Kutta designs
• Maple packages

Appendices