Presentation Title

Slopes: An Interactive App for Exploring Differential Equations

Presentation Type

Oral Presentation

Department

Computer Science

Major

Computer Science / Mathematics

Abstract

A proper study of differential equations requires that students visualize solutions and analyze plots related to the structure of the equations. Although there is mathematical software such as Maple or Mathematica that will perform these functions, these programs are expensive and students must invest a significant amount of time to learn the functions and proper syntax. I am currently designing a new app entitled ``slopes'' that will allow students to plot solutions, tactically explore slopefields and phase planes as well as construct numerical approximations of differential equations. No such app currently exists. The talk will focus on the issues involved in developing such an app and the collaborations with faculty and students in mathematics and graphic design that have enhanced the project. Key issues include implementing the Model-View-Controller paradigm, user-oriented design, touch input, lexically analyzing and parsing equations, numerical algorithms, visualization and error handling. I will demonstrate the first three activities, slopefields, phase planes, and methods. All of these activities interpret equations supplied by the user, construct numerical approximations, and dynamically update the graphs in response to user gestures.

Faculty Mentor

Dr. Timothy Lucas, Dr. Stan Warford

Funding Source or Research Program

Academic Year Undergraduate Research Initiative, Cross Disciplinary-Interdisciplinary Undergraduate Research

Presentation Session

Session B

Location

Plaza Classroom 189

Start Date

1-4-2016 5:15 PM

End Date

1-4-2016 5:30 PM

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Apr 1st, 5:15 PM Apr 1st, 5:30 PM

Slopes: An Interactive App for Exploring Differential Equations

Plaza Classroom 189

A proper study of differential equations requires that students visualize solutions and analyze plots related to the structure of the equations. Although there is mathematical software such as Maple or Mathematica that will perform these functions, these programs are expensive and students must invest a significant amount of time to learn the functions and proper syntax. I am currently designing a new app entitled ``slopes'' that will allow students to plot solutions, tactically explore slopefields and phase planes as well as construct numerical approximations of differential equations. No such app currently exists. The talk will focus on the issues involved in developing such an app and the collaborations with faculty and students in mathematics and graphic design that have enhanced the project. Key issues include implementing the Model-View-Controller paradigm, user-oriented design, touch input, lexically analyzing and parsing equations, numerical algorithms, visualization and error handling. I will demonstrate the first three activities, slopefields, phase planes, and methods. All of these activities interpret equations supplied by the user, construct numerical approximations, and dynamically update the graphs in response to user gestures.