Slopes: Differential Equations for iPhone

Slopes: Differential Equations

Slopes: Differential Equations is an interactive environment designed for exploring graphical solutions to ordinary differential equations. With five activities and the ability to input your own content, Slopes offers a comprehensive platform for studying and analyzing ODEs.

The program features two main activities: "Slopefields" and "Phase Planes". Both activities allow users to plot vector fields and solutions corresponding to multiple initial conditions, providing a visual representation of the solutions to differential equations. Additionally, the "Systems" activity enables users to dynamically solve systems of up to six equations, offering a powerful tool for analyzing complex systems.

The "Oscillations" activity focuses on solving second-order constant coefficient equations and animating the corresponding spring-mass system or RLC circuit. This feature allows users to better understand the behavior of oscillatory systems and visualize their solutions.

Finally, the "Methods" activity provides numerical approximations of a single ordinary differential equation using Euler's method, as well as Second and Fourth Order Runge-Kutta methods. This functionality is particularly useful for studying the accuracy and stability of different numerical approximation techniques.

Overall, Slopes: Differential Equations is a versatile and comprehensive tool for studying and exploring ordinary differential equations. Whether you're working on homework assignments, in-class activities, or even a research project, Slopes provides a playground for ODEs and facilitates a deeper understanding of these mathematical concepts.