Introduction to Differential Equations and Dynamical Systems - Hardcover

Williamson, Richard E.

Hardcover

ISBN 10: 0072325739 ISBN 13: 9780072325737

Publisher: McGraw-Hill Inc.,US, 2000

Synopsis

This text is intended for use in a course in differential equations for student of pure and applied mathematics, the physical sciences, and engineering. The text is designed to be extremely flexible and includes both theory and applications. The text has been written and designed so that the applications can be covered or omitted without a loss of continuity of core topics. The odd-numbered chapters of the book cover the core theory of differential equations with basic applications, while the even-numbered chapters include extended applications from engineering and the physical sciences. In addition, the text includes optional coverage of dynamical systems. Where appropriate, the author has integrated technology into the text, primarily in the exercise sets. Chapters 2, 4, and 6 also include Computing Supplement Sections that are devoted to using numerical methods to solve differential equations.

About this title

From the Publisher

1. INTEGRATION OF NUMERICAL METHODS The power of computers and calculators have enabled mathematicians and scientists to approach the solving of differential equations with numerical methods, as opposed to the traditional analytical techniques. Using these numerical methods, students can study and think concretely about concepts that were once considered too abstract as material for an introductory course. Rather than focusing only one section on numerical methods, this text integrates the use of numerical methods at appropriate sections throughout the text.

2. COMPUTER USAGE The sections on numerical methods also contain some sample computer code to implement what the numerical methods may look like. Students are encouraged to utilize commercial software such as Mathematica or MAPLE, or programmable calculators to work these examples. Individual exercises that are best solved using technology are specially noted. In addition, students can download author-written software for numerical methods from the World Wide Web.

3. APPLICATIONS This text includes a variety of applications of differential equations to engineering and the physical sciences. Students can choose to study these applications in greater detail through the use of computers or calculators.

4. THOROUGH TOPIC COVERAGE Because of its emphasis on both traditional coverage and the study of dynamical systems and numerical methods, this text contains sections on several topics that are not found in most books at this level. Some of these topics include the shooting methods for boundary-value problems, vector treatment of planetary motion for many bodies, and PoincarT time-sections.
Flexible approach. Instructors have the opportunity to incorporate modern applications, topics, and methods within a traditional framework. This text contains sections of several topics that are not found in most books at this level, including the shooting methods for boundary-value problems, vector treatment of planetary motion for many bodies, and Poincare time-sections.
Integration of computer and numerical methods. Computer software such as MAPLE, DERIVE, and Mathematica, as well as programmable calculators, help students to study and think concretely about concepts that were once considered too abstract to be covered in an introductory course. Icons identify problems that are best solved with the help of a computer or calculator.
A variety of differential equations. Applicable to both engineering and the physical sciences, differential equations allow you to tailor assignments according to the needs of your students.

Edition details

• Publisher: McGraw-Hill Inc.,US
• Publication date: 2000
• ISBN 10: 0072325739
• ISBN 13: 9780072325737
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 704