SageMath Widgets for Undergraduate Courses

Jeff Denny and Yuanting Lu

Department of Mathematics, Mercer University

Widgets for Calculus

• First Semester
• Quick plot  
• Plot and shade 
• Plotting implicit functions
• Squeeze Theorem 
• Linear approximation 
• Fundamental Theorem of Calculus Part I 
• Parametric plots 
• Polar plots
• Bezier curves  
• Second Semester  
• Approximate integrals
• Approximate integration (Riemann Sum on R Shiny) 
• Volume by revolution (Slices)
• Volume by revolution (Shells) 
• Simpson's method 
• Exploring arc length 
• Exploring sequences and series      
• Taylor series  
• Multivariable Calculus 
• Sage Graphic Notebook
• Surfaces and Contour Plots 
• Limits and Continuity 
• Directional Derivatives and Tangent Plane 
• Double Integral on Rectangular Region (Volume) 
• Double Integral on Rectangular Region (Mass)
• Surface Area 
• A Despicable Project 

Widgets for Differential Equations 

• Euler's method example 
• Practice matching ODE systems with their phase planes
• Plot the phase plane given a matrix for the system 
• Create a 2 x 2 ODE system given the eigenvalues and eigenvectors 
• Plot the phase plane, nullclines, and equilibrium solutions for any system. 

• Hammer lab 

• SIR model lab directions
• SIR model lab 

Widgets for Discrete Mathematics

• Clock for modular arithmetic

Widgets for Statistics

• Confidence Intervals for means
• Confidence Intervals for proportions

Other Fun Widgets

• Sudoku solver by Tyler Allee and Kirsten Brown