Presentation Title

Slopes: A Graphical View of Differential Equations

Faculty Mentor

Tim Lucas

Start Date

18-11-2017 12:30 PM

End Date

18-11-2017 1:30 PM

Location

BSC-Ursa Minor 147

Session

Poster 2

Type of Presentation

Poster

Subject Area

physical_mathematical_sciences

Abstract

Slopes is a mobile application that allows students to immerse themselves in the world of differential equations. Designed with accessibility and intuitive interactions at it’s core, the app’s five activities provide a platform for exploring the plots of solutions to several types of differential equations and systems. In the Slopefields and Phase Planes activities users can add solutions by simply tapping on an initial point in the vector field. Waves animates the solution of a mass-spring system. Systems plots the solutions to a system of up to nine equations. Methods constructs numerical approximations using Euler and Runge-Kutta methods. Unlike other mathematics software that produces static plots using obscure commands and syntax, the Slopes interface allows users to easily enter equations and produce dynamic plots that can be manipulated with gestures. Slopes was designed following the MVC paradigm. Users interact with the controller,the equations and parameters, to update the model, the numerical solver, in order to produce the view, the vector fields and solution graphs. Our most recent contributions to the project include an improved user interface and a release for iPhone with the same functionality as the original iPad version.

Summary of research results to be presented

Developed at Pepperdine University, Slopes is the finished product of the collaborative efforts of faculty and students in mathematics, physics, computer science, and graphic design. Building the application required us to have a deep understanding of differential equations and numerical approximations, along with a solid grasp of iOS programming and design.

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Nov 18th, 12:30 PM Nov 18th, 1:30 PM

Slopes: A Graphical View of Differential Equations

BSC-Ursa Minor 147

Slopes is a mobile application that allows students to immerse themselves in the world of differential equations. Designed with accessibility and intuitive interactions at it’s core, the app’s five activities provide a platform for exploring the plots of solutions to several types of differential equations and systems. In the Slopefields and Phase Planes activities users can add solutions by simply tapping on an initial point in the vector field. Waves animates the solution of a mass-spring system. Systems plots the solutions to a system of up to nine equations. Methods constructs numerical approximations using Euler and Runge-Kutta methods. Unlike other mathematics software that produces static plots using obscure commands and syntax, the Slopes interface allows users to easily enter equations and produce dynamic plots that can be manipulated with gestures. Slopes was designed following the MVC paradigm. Users interact with the controller,the equations and parameters, to update the model, the numerical solver, in order to produce the view, the vector fields and solution graphs. Our most recent contributions to the project include an improved user interface and a release for iPhone with the same functionality as the original iPad version.