Waves vs Least Squares Curve Fit

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.

“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app. User inputs point sets and chooses function types. Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs. Point sets can be stored in a table and are available after app is closed. Currently available function types are: 2D: 1. Line. 2. Parabola. 3. Polynomial up to 8th degree. 4. Circle. 5. Conic section (Ellipse or Hyperbola). 6. Trigonometric function as C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x), where user can select n between 1 and 8 and enter any ω. 7. Exponential Function. 8. Bell Curve. 3D: 1. Plane. 2. Sphere. Also, there is an option to choose the Best Fit: the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals. In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD. Links to four other free apps by same developers are included in the app: 1. “Matrix Solver Step by Step” Linear Algebra Visual Guide. 2. “Polynomials and Linear Systems” Equation Solver. 3. “GraphMath” Graphing Calculator. 4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide. Developers hope to get feedback from users at graphmath@aol.com.