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.
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.
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.
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.
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