Slopes: A Differential Equations Graphing Environment

Presentation Type

Poster

Keywords

Differential, Equations, Math, App

Department

Mathematics

Major

Computer Science / Mathematics

Abstract

We have designed a new app for iOS called "Slopes.'' It allows students of differential equations to plot solutions, tactically explore slopefields and phase planes, explore "wave" phenomena in second-order constant coefficient equations, as well as construct numerical approximations of differential equations. The poster will focus on the issues involved in developing such an app and the collaborations with faculty and students in mathematics, computer science, and graphic design that have enhanced the project. Key issues include parsing equations, performing efficient evaluations in Swift (for iOS), optimizing numerical algorithms, and porting to the iPhone Slopes consists of five activities. We have designed each activity to empower students to investigate various concepts in differential equations. "Slopefields'' and "Phase Planes'' both plot vector fields and solutions corresponding to multiple initial conditions. "Systems'' dynamically solves arbitrarily large systems of equations. "Waves'' animates the solution of an RLC or spring-mass system. "Methods'' interprets equations supplied by the user and constructs numerical approximations using Euler's method as well as Second and Fourth Order Runge-Kutta methods.

Faculty Mentor

Timothy Lucas

Funding Source or Research Program

Academic Year Undergraduate Research Initiative, Summer Undergraduate Research Program

Location

Waves Cafeteria

Start Date

24-3-2017 2:00 PM

End Date

24-3-2017 3:00 PM

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Mar 24th, 2:00 PM Mar 24th, 3:00 PM

Slopes: A Differential Equations Graphing Environment

Waves Cafeteria

We have designed a new app for iOS called "Slopes.'' It allows students of differential equations to plot solutions, tactically explore slopefields and phase planes, explore "wave" phenomena in second-order constant coefficient equations, as well as construct numerical approximations of differential equations. The poster will focus on the issues involved in developing such an app and the collaborations with faculty and students in mathematics, computer science, and graphic design that have enhanced the project. Key issues include parsing equations, performing efficient evaluations in Swift (for iOS), optimizing numerical algorithms, and porting to the iPhone Slopes consists of five activities. We have designed each activity to empower students to investigate various concepts in differential equations. "Slopefields'' and "Phase Planes'' both plot vector fields and solutions corresponding to multiple initial conditions. "Systems'' dynamically solves arbitrarily large systems of equations. "Waves'' animates the solution of an RLC or spring-mass system. "Methods'' interprets equations supplied by the user and constructs numerical approximations using Euler's method as well as Second and Fourth Order Runge-Kutta methods.