Waves vs Drawing with Math

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.

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.