The *VisualDSolve* package was
written
by Dan Schwalbe and Stan Wagon in 1994 and was originally accompanied
by a printed book (by Springer-Verlag) containing documentation and
many examples of
differential equations modeling suitable for a university course. The
package provided a wide variety of tools for visualizing solutions of
ordinary differential equations, including commands to generate
isoclines, vector fields, flow fields, shaded phase-plane images, and
Poincaré sections.

We have recently updated the package and examples to be compatible with the latest version of*Mathematica*, using the new features such as dynamic
demonstrations, parallel computation, and more. The package includes improved documentation in the form of an electronic book with numerous new examples and one completely new chapter with some unusual
applications (see the Table of Contents below).

*VisualDSolve* can be purchased in the Wolfram Research bookstore.

We have recently updated the package and examples to be compatible with the latest version of

- Free sample chapters:
- Chapter 5 (SecondOrderPlot)
- Chapter 15 (The Duffing Equation)
- Installation instructions

Antonín Slavík Charles University Prague, Czech Republic slavik@karlin.mff.cuni.cz http://www.karlin.mff.cuni.cz/~slavik |
Stan Wagon Macalester College St. Paul, MN 55105 wagon@macalester.edu http://stanwagon.com |

- VisualDSolve
- Overview
- Loading the Package
- Basic Usage
- Options
- Setting and Seeing the Initial Values
- Style and Accuracy Control
- Symbolic Solutions
- Direction Fields
- Isoclines
- Inflection Curves
- Controlling the Numerical Method
- Using the Output
- A Comprehensive VisualDSolve Demonstration

- Auxiliary Functions
- Overview
- FreehandAttempt
- PhaseLine
- ResidualPlot
- GetPts
- ToSystem
- ColorParametricPlot
- FlowParametricPlot
- ShowTable

- SystemSolutionPlot
- Overview
- Basic Usage
- Stylish Plots
- Using the Output

- PhasePlot
- Overview
- Basic Usage
- Controlling the Style of the Orbits
- Direction Fields, Flow Fields, and Streamlines
- FlowParametricPlot
- Controlling the
*t*-Domain - Varying a Parameter
- Nullcline Plots
- The Real Orbit Graph in Three Dimensions
- Systems of Three or More Equations
- Poincaré Sections
- A Phase Plane Demo

- SecondOrderPlot
- Overview
- A Single Second-Order Equation
- The Ups and Downs of a Helium Balloon
- Second-Order Systems

- Differential Equations and Mathematica
- Rules of Solving and DSolving Equations
- Changing Politics:
*x*Moves to the Right - NDSolve
- Delay Differential Equations
- Expanding Dimensional Horizons
- Boundary Value Problems

- Some Parachute Experiments
- VisualDSolve
- Modeling a Parachutist
- Parachute to the Rescue
- Infinite Jerk Strikes Again: Kills Parachutist

- Linear Systems
- A Comprehensive View of the Two-Dimensional Case
- A Physical Application: Springs
- A Four-Dimensional Example

- Logistic Models of Population Growth
- One Population
- Two Populations

- Hamiltonian Systems
- An Example
- An Ideal Pendulum
- Higher Dimensions

- A Devilish Equation
- Skepticism Rewarded
- What's Going On

- Lead Flow in the Human Body
- The Model
- Getting the Lead Out

- Making a Discus Fly
- The Model
- Drag and Lift
- Implementing the Equations
- The Best Throwing Angles

- A Double Pendulum
- The Basic Pendulum
- Shoulder to Elbow
- Linearization
- Bringing the Pendulum to Life
- Chaos, and What Happens on the Way
- Synchronized Swinging

- The Duffing Equation
- A Stable Example
- The General Duffing Equation
- Flying Duffing Circles
- Forced Attraction
- What To Do?
- Strange Attraction

- The Tetrapods of Wada
- A Damped, Forced Pendulum
- Using the Poincaré Map
- Surprising Periodicity
- The Tetrapod
- The Curve-Drawing Algorithm

- I Tossed a Book into the Air...
- Euler's Equations
- Ellipsoids and the Conservation Laws
- Spinning a Book
- Rolling the Poinsot Ellipsoid

- Miscellany
- Fly to the Moon
- The Invisible Rabbit
- Bike Tracks
- Square Wheels
- Sharks and Fish