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
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.