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
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.