Differential Equations & Boundary Value Problems Computing &

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course while maintaining the solid foundation of algebraic techniques that are still essential to science and engineering students. It reflects the new excitement in differential equations as the availability of technical computing environments like Maple, Mathematica, and MATLAB reshape the role and applications of the discipline. New technology has motivated a shift in emphasis from traditional, manual methods to both qualitative and computer-based methods that render accessible a wider range of realistic applications. With this in mind, the text augments core skills with conceptual perspectives that students will need for the effective use of differential equations in their subsequent work and study. Features and Benefits Coverage of seldom-used topics trimmed - There is more streamlined coverage of certain traditional, manual topics like exact equations and variation of parameters. Elementary introduction to period-doubling in biological and mechanical systems, the pitchfork diagram, and the Lorenz strange attractor (all illustrated with vivid computer graphics). Increased emphasis on and flexible treatment of linear systems of differential equations. Section 5.5 now includes a more extensive treatment of matrix exponentials. A new section (5.6) on nonhomogeneous linear systems was added to this edition Reflects current trends in science and engineering education and practice. NEW - About half of the over 300 computer-generated graphics are new Brings symbolic solutions of differential equations to life. This text is unique in its blend of traditional algebraic material with the modern geometric approach. Coverage begins and ends with discussions and examples of the mathematical modeling of real-world phenomena. Includes about 45 Computing Projects following key sections throughout the text. Provided are parallel subsections entitled Using Maple, Using Mathematica, and Using MATLAB that detail the applicable methods and techniques of each system. This manual is free when wrapped with text. Project notebooks and worksheets can be downloaded from the supporting web site . Approximately 2000 problems. Answers to most odd-numbered problems can be found in the answer section at the back of the book. Supported by a fully dedicated DE web site. A superb direction field and phase portrait plotter is provided. Written as Java applets, all you need is a computer with a browser - no other software. This work focuses on the mathematical modelling of real-world phenomena. It contains 2000 graded problems and computer projects that illustrate the use of computer algebra systems, like Maple, Mathematica and MATLAB.