Differential Equations and Boundary Value Problems with Computing and Modelling - Computing and Modeling  (English, Hardcover, Edwards C. H.)

Reflecting the shift in emphasis from traditional methods to new computer-based methods, this text — in classic Edwards and Penney style — focuses on the mathematical modeling of real-world phenomena as the goal and constant motivation for the study of differential equations. It offers a fresh computational flavor in figures, examples, problems, and projects throughout, and features a broad range of real-world applications. The book also covers topics not found in other similar texts.

Salient Features

• a back–to–basics course is stressed. The computer permits the cutting of highly specialized ODEs to focus in greater depth, from a mathematical perspective, on the core ideas.
• offers an unusually early introduction to mathematical modeling, stability and qualitative properties of differential equations and to numerical methods.
• A qualitative approach is stressed throughout by emphasizing dynamical systems and phase portraits.
• provides an unusually flexible treatment of linear systems:
• Ch. 4 offers an early, intuitive introduction to first-order systems, models, and numerical computer methods. Includes numerical algorithms presented in parallel fashion for systems ranging from the TI-85 graphics calculator to MATLAB.
• Ch. 5 begins with a self-contained treatment of the necessary linear algebra, and then presents the eigenvalue approach to linear systems. Includes an large number of applications (ranging from railway cars to earthquakes) of all the various cases of the eigenvalue method.
• presents a broad discussion of nonlinear systems and phenomena — ranging from phase plane analysis to ecological and mechanical systems to an innovative concluding section on chaos and bifurcation in dynamical systems.
• presents an elementary introduction to such contemporary topics such as period-doubling in biological and mechanical systems, the pitchfork diagram, and the Lorenz strange attractor — all illustrated with vivid computer graphics.
• offers a unique treatment of higher dimensional phenomena (Ch. 10).
• shows how the ready availability of computational aids can clarify traditional manual topics (i.e. undetermined coefficients and Laplace transforms).
• brings numeric and symbolic solutions of differential equations to life — features 180 computer-generated graphics that vividly illustrate slope fields, solution curves, and phase plane portraits.
• contains approximately 2,000 carefully graded problems — ranging from routine computational exercises to conceptual and applied problems.
• contains three dozen Computer Projects that illustrate the use of computer algebra systems (e.g., Maple, Mathematica, and MATLAB) — to actively engage students in the application of new technology.