Waves vs ODE

Waves is an interactive environment for exploring graphical solutions to partial differential equations. Waves currently consists of three activities that explore Fourier series as well as series solutions to the heat and wave equations. Fourier is a tool for plotting a Fourier series that best approximates a periodic function. Diffusion plots solutions to the one-dimensional heat equation in space and animates the time evolution. Waves plots solutions to the one-dimensional wave equation in space and allows. In each of these activities you can specify the appropriate boundary and/or initial conditions. The app contains built-in examples as well as the option to save your work for future analysis. You can use Waves for homework, in-class activities or a new research project.

The ODESolverIntegrator is a simple but elegant app to find the integral of ODEs. You can solve (find the integral of) nonlinear ODEs. You can reduce the higher order ODE to a set of first order ODEs. You can solve (find the integral of) linear ODEs in the form of ẋ = Ax + Bu; y = Cx + Du. This app uses Runge-Kutta 4th order algorithm to solve the ODEs. Once the ODEs are solved, a beautiful interactive graph for each ODE's is created that you can share with other or save it locally. The reduced ODE's equations are presented beautifully in the math-equation format. You can compute definite integral (single, double, tripple). It uses the midpoint method. It automatically saves your hard work locally on your device so you can come back and pick up from where you left off as your great effort will not be lost. This app also has a Study page to help you learn important integration rules like, power rule, product rule, ect. This app is perfect for students learning calculus. Sharpen you brain by using this app and learning about the calculus. This is an app for all student groups. From high school to college to university students. Be creative. Enjoy the app!