Math 53 Widgets

Welcome! On this webpage you can find interactive widgets that go with each chapter of the Math 53 textbook. Have fun playing around with them!

Link to the widgets

Part I. Explicit and qualitative methods.

Chapter 1: Visualizing the Chen attractor.
- Manipulating one Chen attractor trajectory.
- Sensitivity to the starting point.
Chapter 2: Visualizing a certain first-order autonomous ODE.
- Visualizing $Y’ = AY + B$.
Chapter 3: Visualizing the dynamic perspectives of first-order ODE's.
- Visualizing the logistic model.
- Playing with slope fields beyond the logistic case.
Chapter 4: Visualizing the stability of stationary points via phase line and slope fields.
- Example 1.
- Example 2.
Chapter 5: Visualizing second-order linear ODE’s and complex numbers.
Chapter 6: Visualizing second-order linear ODE’s, continued.
- Second-order linear ODE’s with constant coefficients, continued.
Chapter 7: Visualizing matrix exponentials.
- Matrix exponentials.
Chapter 8: Visualizing phase portraits and eigenvalues.

Part II. General higher-order and non-linear equations.

Part III. Numerical and series methods.

Part IV. Partial differential equations and Fourier series.

Part V. Fourier transforms.

Useful resources

WolframAlpha—a powerful computational search engine.
MIT Mathlets—a variety of dynamic Javascript "Mathlets" for use in learning about differential equations as well as other mathematical subjects.