ELEMENTARY DIFFERENTIAL EQUATIONS, 6/E
ELEMENTARY DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS, 6/E
WILLIAM E. BOYCE, Rensselaer Polytechnic Institute
RICHARD C. DIPRIMA (deceased), Rensselaer Polytechnic Institute
Elementary: ISBN: 0-471-08953-2, 576 Pages, Cloth, 1997
Boundary: ISBN: 0-471-08955-9, 704 Pages, Cloth, 1997
This revision of Boyce & DiPrima's market leading texts maintains the flexible chapter construction, clear exposition, and outstanding problem material the books are known for, while reforming both versions with a more visual approach and increased emphasis on computer integration. The revision seeks to enhance the strengths of the preceding editions, by maximizing the advantages offered by new technologies.
The all new art program features an increase in the number of text figures and graphs required in the problems. In addition, many of the problems from previous editions have been modified to ask for a graph of the solution. There are also many new problems that assume technology. With the revision of the numerical methods chapter, Boyce and DiPrima now present the most current and comprehensive treatment of this topic found in any elementary DE text.
This revision, like its predecessors, is written from the viewpoint of the applied mathematician, focusing on both the theoretical and practical aspects of DE's. It combines a sound exposition of the theory with considerable attention to applying that theory in engineering and the sciences. The flexible organization that has made this text so popular in the past, remains, as does the tremendous variety, range and number of problems.
The book is intended for an ordinary differential equations course usually taught at the sophomore/junior level in math departments and occasionally in engineering departments. Prerequisites include calculus.
- The best selling text on the market noted for its sound accurate treatment of differential equations.
- Diverse problem sets in terms of number, range, and variety, provide great flexibility in homework assignments.
- Sound and accurate exposition of theory with attention to methods of solution, analysis, and approximation, prove useful in many applications.
- Self-contained chapters provide tremendous flexibility in organization. After the required introductory chapters, professors can customize the selection, order and depth of chapters to be covered. Most applications are covered in separate sections so they can be included or omitted as preferred.
- Problems on properties of solutions emphasize the importance of understanding the qualitative behavior of solutions.
- Use of technology (emphasizing geometrical interpretation of solutions), illustrations (including computer-generated graphs), and problem sets help students develop an intuitive understanding of the material.
- Historical footnotes show students how the discipline has developed over a period of time and identify some outstanding individual contributions.
- Solutions to most problems at the end of the book allow students to check their work while studying.
Changes in the new edition:
- A more visual approach including an all new art program with more figures and more graphing in the problems.
- Nearly 300 New Problems, many of which assume the use of technology (no specific platform or package is required). Many others have been modified by asking for a graph of the solution.
- Many new problems and examples that call for conclusions to be drawn about the solution, maximize the benefits of technology.
- Problems that explore the effect of changing parameter values, or ask for the long time behavior of a solution, emphasize that finding a solution is not an end in itself.
- A major update of the Numerical Methods chapter (Ch. 8), including an introduction to backward differential formulas and more discussion of other multistep methods, as well as an improved treatment of error analysis and stability, makes this the most comprehensive treatment found in any elementary DE text.
- A number of new examples, figures, and more than 40 new problems added to chapter 10, show how computers can enable students to make sense of complicated expressions obtained as solutions of boundary value problems of partial differential equations.
- An introductory module of the new ODE Architect CD-ROM accompanies each instructor's copy of the text. The CD allows students to examine properties of linear and non-linear systems, explore and construct realistic math models, and apply intuitive understanding of the behavior of solutions of ODE's to hypothetical and practical situations. Instructors will be invited to serve as class testers of the software in the Spring of 1997.
- ODE Architect
ODE Architect has been developed with NSF sponsorship by CODEE (Consortium for ODE Experiements) John Wiley & Sons and IntelliPro, Inc. to uniquely combine rich multimedia applications with powerful yet easy-to-use custom mathematical tools. The software is intended to provide a highly interactive environment for students to examine the properties of linear and nonlinear systems, explore and construct realistic mathematical models, and apply understanding of the behavior of solutions of ODE's to new real-world and hypothetical situations. It will combine mathematical simulation, graphic animation, hyper- media, and state-of-the-art numerical solvers to offer a complete multimedia learning environment, and a more friendly, efficient, and interesting way to study and explore ODE's. Instructors will be invited to serve as class testers of the software in the Spring of 1997. An introductory Module will accompany each Instructor's copy of the text.
- Student Solutions Manual (for both versions)
Provides worked out solutions to many of the problems in the text and helpful hints for the remainder of the problems. The problems chosen in each section represent, wherever possible, the variety of applications covered in the text, providing a complete set of examples from which to learn. Written by Charles Haines of the Rochester Institute of Technology.
- Differential Equations with Mathematica
Differential Equations with Maple
Kevin R. Coombs, Brian R. Hunt, Ronald L. Lipsman, John E. Osborn, Garrett J. Stuck, all of the University of Maryland, College Park
These supplements promote deeper student understanding of ODE's by using Maple as tools for investigation and analysis. They bring students to a level of understanding of these programs that allows them to use the systems in future math courses, engineering or science courses. These manuals cover most of the standard topics in ODE, but with an emphasis on using these computer tools to address them. They focus on specific features of the software programs that are useful for analyzing DE's. The manuals require no previous knowledge of Mathematica or Maple and explain use in Mac, Windows and the X Windows systems. They contain early coverage of numerical methods as well as an emphasis on qualitative and interpretive aspects of ODE's. The manuals' problem sets are easily applicable in group settings. Designed to accompany Boyce/ DiPrima 5E, they can be used in conjunction with any DE text.
- Differential Equations Laboratory Workbook
Robert. L. Borrelli & Courtney S. Coleman both of Harvey Mudd College
William E. Boyce, R. P. I.
This supplement to any standard DE textbook contains a collection of explorations, and modeling projects for the computer. Each computer problem set is a combination of pencil-and-paper and computer work intended to parallel what goes on in science and engineering laboratories. The computer experiements provide students with "hands-on" experience in the behavior of solutions of ODE's. No particular DE solver platform is required.
Table of Contents
** Contained in the Boundary Values version only.
- First Order Differential Equations
- Second Order Linear Equations
- Higher Order Linear Equations
- Series Solutions of Second Order Linear Equations
- The Laplace Transform
- Systems of First Order Linear Equations
- Numerical Methods
- Nonlinear Differential Equations and Stability
- **Partial Differential Equations and Fourier Series
- **Boundary Value Problems and Sturm-Liouville Theory