Visualdsolve: Visualizing Differential Equations with Mathematica(r)

ISBN-13: 9781461274735 / Angielski / Miękka / 2011 / 271 str.

Dan Schwalbe; Stan Wagon

Opis

This title presents new ideas on the visualization of differential equations with user-configurable tools. The authors use the widely-used computer algebra system, Mathematica, to provide an integrated environment for programming, visualizing graphics, and running commentary for learning and working with differential equations.

Spis treści

Contents: Seeing and Controlling the Initial Values.- Style and Accuracy Control.- Labeling Plots.- Exact Solutions.- Direction Fields.- Isoclines.- Inflection Curves.- Controlling the Numerical Method.- Checking Solutions.- Normal Form.- System Solution Plots.- Phase Plots, Controlling the Style of the Orbits.- Fields of Fish.- Controlling to t-domain.- Varying a Parameter.- Nullcline Plots.- The Real Orbit Graph in 3-Dimensions, Systems of Three of More Equations.- Poincare Sections.- A Single Second-Order Equations.- Second-Order Systems.- Troubleshooting.