DifferentiationCalculator vs iTurbo3D

This app calculates the analytic formula of the first derivative of a given function. Derivative represents a rate of change of a function with respect to an independent variable. This app enables to differentiate a function that depends on more than one independent variable (called here a multi-parametric case) by considering these variables separatelly. To do so, one must declare a name of independent variable with respect to which a given function is differentiated. During differentiation, the rest of variables is kept constant. The derivative found on the basis of the obtained analytical formula can be compared with the derivative found numerically. The obtained results can then be depicted in plots. In order to plot a multi-parametric case, all remaining independent variables must be set by the user. To make this app more didactic, it is possible to track and practise intermediate stages of searching for the analytic derivative. All these steps can be performed by the user himself. In this way, the final formula of the derivative sought will become more understandable.

iTurbo 3D brings interactive three-dimensional turbulence simulation to iPhone. A pseudo-spectral incompressible Navier-Stokes solver evolves the velocity field while a Metal volume ray marcher displays the flow as it develops. Explore the volume using touch controls: drag to orbit, pinch to zoom, and double-tap to restore the camera. Switch between vorticity, Q-criterion, kinetic energy, and helicity, with a selection of scientific colormaps and light or dark backgrounds. Configure Taylor-Green or random turbulence, choose a 32 cubed, 64 cubed, or 128 cubed grid, set the Reynolds number, and adjust forcing. Higher grid resolutions reveal finer structures while using progressively more memory and processing power. Pause, resume, advance one step, or reset the simulation from the bottom toolbar. Live status values show the time step, iteration, simulation time, step rate, energy, and enstrophy. Expand the diagnostics to inspect energy history and the energy spectrum. Whether you are teaching fluid mechanics, studying turbulence, or simply enjoy computational physics, iTurbo 3D turns the equations of motion into something you can see and explore directly on iPhone.