Dynamic Web Tools Using WebMathematica

Mike Martin and Steve Wilson received the 2004 International Conference on Technology in Collegiate Mathematics Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics for their development of a subset of these tools. The award was presented at the ICTCM conference in New Orleans in October of 2004.

Unfortunately, funding for the webMathematica license was lost in 2017, so these pages are no longer available.

Arithmetic

• Basic Addition Facts - S. Wilson
• Basic Subtraction Facts - S. Wilson
• Basic Multiplication Facts - S. Wilson
• Basic Addition Facts - S. Wilson

Business Math

• Comparing Compounding Frequencies - S. Wilson

Recreational Mathematics

• Integermania Exquisiteness Calculator - S. Wilson

Algebra

• Exploring Combinations of Functions - S. Wilson
• Roots (a synthetic division program) - N. Carpenter & S. Wilson
• The Linear Function and Its Inverse - M. Martin
• Visualizing Transformations for a Quadratic Function - M. Martin
• Visualizing Transformations for a Cubic Function I - M. Martin
• Visualizing Transformations for a Cubic Function II - M. Martin
• Visualizing Transformations for the Square Root Function - M. Martin
• A Simple Rational Function and Its Inverse - M. Martin
• The Exponential and Logarithmic Functions and Their Inverse Relationship - M. Martin
• Log-Log Plots of Two Exponential Functions and Their Allometric Relationships - M. Martin
• A Power Function, Its Graph in Regular and Log-Log Coordinates, and Allometry - M. Martin
• The Bisection Method for a Polynomial Function - M. Martin
• A Quadratic Cost Function - M. Martin
• Profit with Quadratic Costs - M. Martin
• The Rate of a Simple Chemical Reaction - M. Martin
• A Blood-Alcohol Model - M. Martin
• An Explicit SI Epidemic Model - M. Martin
• Optimal Gene Pool Composition - M. Martin
• Dosing of Children's Motrin: An Example of Function Composition - M. Martin
• Logistic Function - M. Martin
• Stochastic Growth Model - M. Martin

Trigonometry

• Standard Position Trig Ratios Drillmaster - S. Wilson
• Right Triangle Trig Ratios Drillmaster - S. Wilson
• Special Angle Sine and Cosine Values Drillmaster - S. Wilson
• Special Angle Trig Values Drillmaster - S. Wilson
• Converting Degrees to Radians Drillmaster - S. Wilson
• Converting Radians to Degrees Drillmaster - S. Wilson
• Sine Graph Characteristics Drillmaster - S. Wilson
• Trig Values and the Unit Circle - S. Wilson
• The Sine and Inverse Sine Functions - M. Martin
• The Cosine and Inverse Cosine Functions - M. Martin
• The Tangent and Inverse Tangent Functions - M. Martin
• The Cotangent and Inverse Cotangent Functions - M. Martin
• The Secant and Inverse Secant Functions - M. Martin
• The Cosecant and Inverse Cosecant Functions - M. Martin
• The Bisection Method for a More General Equation - M. Martin
• Female Body Temperature: Daily and Menstrual Rhythms - M. Martin

Euclidean and Analytic Geometry

• A Construction of π and the Area and Circumference of a Circle - M. Martin
• Rose Analyzer - S. Wilson
• Limacon Analyzer - S. Wilson
• Lissajous Curve Analyzer - S. Wilson
• Quartic Plane Curves - S. Wilson
• Visualizing Conic Sections - M. Martin
• Coordinate Systems - S. Wilson

Basic Sequences and Series

• Simple Recursive Sequences - S. Wilson
• Logistic Sequence - D. Cousino
• The Discrete Exponential Model - M. Martin
• Fibonacci and Related Sequences - S. Wilson
• Fibonacci Numbers and the Definition of ϕ, the Golden Ratio - M. Martin
• Iterating a Cubic Bistable Equation - M. Martin
• Iterating the Sine Function - M. Martin
• Iterating the Cosine Function - M. Martin
• Sequence Iteration - M. Martin
• Exploring Fourier Series - S. Wilson

Applications of Sequences to Population Dynamics

• A Model of Selection - M. Martin
• The Discrete Exponential Model: Visuals and Cobwebbing - M. Martin
• The Canonical Logistic Population Model - M. Martin
• The Discrete Logistic Population Model with Carrying Capacity - M. Martin
• The Discrete Logistic Population Model with Harvesting - M. Martin
• The Canonical Ricker Population Model - M. Martin
• The Ricker Population Model with Carrying Capacity - M. Martin
• Discrete Population Growth with Stochastic Effects - M. Martin
• The Beverton-Holt Model - M. Martin
• The Leslie-Gower Model - M. Martin
• The Reduced Neubert-Kot Model - M. Martin
• The Neubert-Kot Model - M. Martin
• The Nicholson-Bailey Model - M. Martin
• A Modified Nicholson-Bailey Model with Density Dependence I - M. Martin
• A Modified Nicholson-Bailey Model with Density Dependence II - M. Martin
• A Modified Nicholson-Bailey Model with Density Dependence III - M. Martin
• LPA Model - M. Martin
• Population Genetics Model - M. Martin
• Population Genetics Model Extended - M. Martin
• Virus Mutation Model - M. Martin
• Exploring the US Census Data - M. Martin

Applications of Sequences to Medicine

• Chalones and Mitosis - M. Martin
• Discrete Model for Simple Heart Dynamics - M. Martin & F. Adler
• Discrete Model for Periodic Hematopoiesis - M. Martin
• Chemical Concentration Model in a Breathing Lung - M. Martin
• Simulating the Two-Process Sleep Model - M. Martin & D. Terman
• Semi-Logarithmic Plots of Exponential Functions - M. Martin
• Monod-Wyman-Changeux Equation - M. Martin
• Simulating a Molecular Diffusion Model - M. Martin
• Molecular Diffusion Model - M. Martin
• An Epidemic Model (SIR) I - M. Martin
• A Discrete Epidemic Model (SIR) I (without vaccinations) - M. Martin
• A Discrete Epidemic Model (SIR) II (with vaccinations) - M. Martin
• Host-Parasitoid-Hyperparasitoid Model - M. Martin

Linear Algebra

• The Projection of a Vector onto Another Vector - M. Martin
• Two-Dimensional Bases - M. Martin
• 2D Matrix Transformations - S. Wilson
• 3D Matrix Transformations - S. Wilson
• 2D Homogeneous Transformations - S. Wilson
• 3D Homogeneous Transformations - S. Wilson
• Eigenvalues and Eigenvectors for a 2x2 Matrix - M. Martin
• Eigenvalues and Eigenvectors for a 3x3 Matrix - M. Martin
• Cantor-Jukes: A Model for DNA Change - M. Martin
• Age-Structured Models: The Leslie Matrix - M. Martin
• An Extended Age-Structured Model: The 12x12 Leslie Matrix - M. Martin
• Age-Structured Models with Density Dependence: The Leslie Matrix - M. Martin
• Leslie Matrix Model with Density-Dependent Recruitment (LMMDDR) - M. Martin
• Leslie Matrix Model with Density-Dependent Recruitment I (LMMDDR) - M. Martin
• Leslie Matrix Model with Density-Dependent Recruitment II (LMMDDR) - M. Martin
• A System of Two Linear Difference Equations - M. Martin
• A System of Three Linear Difference Equations - M. Martin

Graph Theory

• Voronoi Plotter: Input Points - M. Martin & J. Jungck
• Voronoi Plotter: Random Points - M. Martin & J. Jungck
• Quadratic Image Transformations - M. Martin & J. Jungck
• 1D Newton Fractal Basin Boundaries - M. Martin

Social Choice

• Voting and Power Indices - S. Wilson
• Apportionment Methods - S. Wilson

Probability and Statistics

• Visualizing Data and Some Basic Statistical Measures - M. Martin
• Simulating the Roll of a Die - M. Martin
• Simulating the Roll of Two Dice and Summing the Result - M. Martin
• Simulating Random Walks - M. Martin
• The Binomial Distribution - M. Martin
• The Geometric Distribution - M. Martin
• The Negative Binomial Distribution - M. Martin
• The Hypergeometric Distribution - M. Martin
• The Poisson Distribution - M. Martin
• The Uniform Distribution - M. Martin
• The Exponential Distribution - M. Martin
• The Normal Distribution - M. Martin
• Confidence Intervals for the Normal Distribution - M. Martin
• Comparing the z and t Distributions - S. Wilson
• The Lognormal Distribution - M. Martin
• Confidence Intervals for the Lognormal Distribution - M. Martin
• Modeling and the Akaike Information Criterion - M. Martin
• Fitting Data to the Linear Model (Linear Regression) - M. Martin
• Fitting Data to a Quartic Polynomial - M. Martin
• Fitting Data to the Exponential Model - M. Martin
• Fitting Data to the Logistic Function - M. Martin
• Fitting the Logistic Function to Gause's Data - M. Martin
• Estimating Population Size for the Mark and Recapture Method - M. Martin

Differential Calculus Drillmasters

• Delta-Epsilon Proofs Drillmaster
• Derivatives Drillmaster (Basic) - S. Wilson
• Derivatives Drillmaster (Basic Plus) - S. Wilson
• Derivatives Drillmaster (Algebraic) - S. Wilson
• Derivatives Drillmaster (Exp/Log) - S. Wilson
• Derivatives Drillmaster (Intermediate) - S. Wilson
• Derivatives Drillmaster (Trig) - S. Wilson
• Derivatives Drillmaster (Advanced) - S. Wilson
• Derivatives Drillmaster (Comprehensive) - S. Wilson

Limits

• Input and Output Tolerances for a Linear Function - M. Martin
• The Limit of 1/x as x goes to ±∞ - M. Martin
• The Limit of 1/x as x goes to 0 - M. Martin
• The Limit of 1/x² as x goes to ±∞ - M. Martin
• The Limit of 1/x² as x goes to 0 - M. Martin
• The Limit of (3n²-5)/(1+5n-2n²) as n goes to ∞ - M. Martin
• The Limit of ((-1)ⁿ (n+100))/(5n+3) as n goes to ∞ - M. Martin
• The Limit of a Rational Function - M. Martin
• The Limit of x/(x²+1)^0.5 as x goes to ±∞ - M. Martin
• The Limit of sin(n)/n as n goes to ∞ - M. Martin
• The Limit of sin(x)/x as x goes to 0 - M. Martin
• The Limit of (1-cos(x))/x as x goes to 0 - M. Martin
• The Limit of sin(1/x) as x goes to 0 - M. Martin
• The Limit of x*sin(1/x) as x goes to 0 - M. Martin
• The Squeeze Theorem Applied for a Sequence - M. Martin
• The Definition of e - M. Martin

Functions and their Derivatives

• The Constant Function - M. Martin
• The Linear Function - M. Martin
• The Quadratic Function - M. Martin
• The Cubic Function - M. Martin
• The Polynomial Function of Degree Six or Less - M. Martin
• The Polynomial Function of Degree Four or Less: Tangent Lines - M. Martin
• A Rational Function with Numerator and Denominator Degrees of Four or Less - M. Martin
• The Hill Function - M. Martin
• The Exponential Function - M. Martin
• The Extended Exponential Function - M. Martin
• The Basic Exponential Function - M. Martin
• The Logistic Function - M. Martin
• The Logarithmic Function - M. Martin
• The Basic Logarithmic Function (Base b) - M. Martin
• The Sine Function - M. Martin
• The Extended Sine Function - M. Martin
• The Cosine Function - M. Martin
• The Extended Cosine Function - M. Martin
• The Tangent Function - M. Martin
• The Extended Tangent Function - M. Martin
• The Cotangent Function - M. Martin
• The Secant Function - M. Martin
• The Cosecant Function - M. Martin
• The Inverse Sine Function - M. Martin
• The Inverse Cosine Function - M. Martin
• The Inverse Tangent Function - M. Martin
• The Extended Inverse Tangent Function - M. Martin
• The Product of an Exponential and a Sinusoid (Sine) - M. Martin
• The Extended Product of an Exponential and a Sinusoid (Sine) - M. Martin
• The Product of an Exponential and a Sinusoid (Cosine) - M. Martin
• The Extended Product of an Exponential and a Sinusoid (Cosine) - M. Martin
• The Hyperbolic Sine Function - M. Martin
• The Hyperbolic Cosine Function - M. Martin
• The Hyperbolic Tangent Function - M. Martin
• The Extended Hyperbolic Tangent Function - M. Martin
• The Error Function - M. Martin
• The Extended Error Function - M. Martin

Applications of Derivatives

• The Secant and Tangent Line Problem: Visuals and Data (Polynomials) - M. Martin
• The Secant and Tangent Line Problem: Visuals and Data (Logistic) - M. Martin
• The Secant and Tangent Line Problem: Visuals and Data (Sine) - M. Martin
• Visualizing Limits, Continuity, and Differentiability - M. Martin
• The Extrema for a Polynomial on [a,b] - M. Martin
• The Mean Value Theorem for a Cubic Polynomial - M. Martin
• Getting the Graph of a Derivative from the Graph of a Function - M. Martin
• Getting the Graph of a Function from the Graph of Its Derivative - M. Martin
• Discrete Change: Examining Differences - M. Martin
• Discrete Change: Examining Forward Differences - M. Martin
• Visualizing Partial Derivatives - M. Martin

Numerical Integration

• Approximating the Definite Integral of a Polynomial Using Left-Hand Endpoints - M. Martin
• Approximating the Definite Integral of a Polynomial Using Right-Hand Endpoints - M. Martin
• Approximating the Definite Integral of a Polynomial Using Midpoints - M. Martin
• Approximating the Definite Integral of a Polynomial Using Trapezoids - M. Martin
• Approximating the Definite Integral of a Polynomial Using Simpson's Rule - M. Martin
• Approximating the Definite Integral Using Left-Hand Endpoints - M. Martin
• Approximating the Definite Integral Using Right-Hand Endpoints - M. Martin
• Approximating the Definite Integral Using Midpoints - M. Martin
• Approximating the Definite Integral Using Trapezoids - M. Martin
• Approximating the Definite Integral Using Simpson's Rule - M. Martin
• Approximating the Definite Integral of a Function Using Left-Hand Endpoints - M. Martin
• Approximating the Definite Integral of a Function Using Right-Hand Endpoints - M. Martin
• Approximating the Definite Integral of a Function Using Midpoints - M. Martin
• Approximating the Definite Integral of a Function Using Trapezoids - M. Martin
• Approximating the Definite Integral of a Function Using Simpson's Rule - M. Martin
• Numerical Integration Errors - D. Cousino
• Numerical Integration Error Bounds - M. Martin
• Numerical Integration Error Bounds: Exp(-x²) - M. Martin
• Numerical Integration Error Bounds: Sin(x²) - M. Martin
• Numerical Integration: Estimating Steps for a Given Error - M. Martin
• Estimating Integration Steps for a Given Error: Exp(-x²) - M. Martin
• Estimating Integration Steps for a Given Error: Sin(x²) - M. Martin

Applications of Integration

• The Distance Problem - M. Martin
• The Average Value of a Polynomial on [a,b] - M. Martin
• Accumulation: An Offspring Model - M. Martin
• Aggregation: Calculating the Mass of a Thin Rod - M. Martin
• Calculating Volume with Multiple Integration - M. Martin

First and Second Order Differential Equations

• Slope Fields - S. Wilson
• Newton's Method - D. Cousino
• The General First Order Linear Difference Equation - M. Martin
• Exploring Differential Equations and Exponentials - M. Martin
• Logistic Differential Equation - D. Cousino
• Numerical Solutions to a Second Order ODE - D. Cousino
• Simple Negative Feedback - M. Martin
• An Euler Pathology - M. Martin
• Constant Coefficient Linear Homogeneous ODEs and IVPs - M. Martin
• Constant Coefficient Linear Homogeneous 2nd Order ODEs: System Response - M. Martin
• Constant Coefficient Linear Homogeneous 2nd Order ODEs: Transient and Steady State Response - M. Martin
• Undamped Forced Oscillations: Beats - M. Martin
• Undamped Forced Oscillations: Resonance - M. Martin
• Damped Forced Oscillations: Practical Resonance - M. Martin
• Phase Plane and Time Plots for 2D Linear ODEs - M. Martin
• Phase Plane and Time Plots for 2D Almost Linear ODEs - M. Martin
• Phase Plane and Time Plots for the Van der Pol Oscillator - M. Martin
• Fourier Spectrum from a Van der Pol Oscillator - M. Martin
• Time Plots and Phase Plane Plots for the Lotka-Volterra System of ODEs - M. Martin
• Fourier Spectrum from a 2nd Order Linear Constant Coefficient ODE with Sinusoidal Forcing - M. Martin
• Sinusoids, Noise, and their Fourier Spectrum - M. Martin
• The Lorenz Equations - M. Martin

Applications of Differential Equations to Population Dynamics

• The Logistic Function for Population Modeling - M. Martin
• The Logistic Rate of Change - M. Martin
• A Population Model with Delay - M. Martin
• Visualizing a Continuous Competing Species Model - M. Martin
• Visualizing a Continuous Model of Mutualism - M. Martin
• Visualizing a Continuous Model of Predator and Prey Interactions (Lotka-Volterra) - M. Martin
• Predator-Prey Interactions (Lotka-Volterra) with Delay - M. Martin
• Ocean Plankton Populations as Excitable Media - M. Martin
• Metapopulations and Patch Simulations: Levins Model - M. Martin
• Metapopulations and Patch Simulations: KVML Model - M. Martin
• A Renewable Resource Model I - M. Martin
• A Renewable Resource Model II - M. Martin
• A Renewable Resource Model III - M. Martin
• A Renewable Resource Model IIIa - M. Martin
• A Renewable Resource Model IV - M. Martin

Applications of Differential Equations to Medicine

• Fitzhugh-Nagumo System of Differential Equations - M. Martin
• The Rate of Change for Neuron Voltage in the Axon - M. Martin
• The Hodgkin-Huxley Model for Signal Propagation - M. Martin
• Morris-Lecar System of Differential Equations - M. Martin
• A Two-Compartment One-Drug Model with Linear Forcing - M. Martin
• A Two-Compartment One-Drug Model with Decaying Exponential Forcing - M. Martin
• A Two-Compartment Two-Drug Model with Linear Forcing - M. Martin
• A Two-Compartment Two-Drug Model with Decaying Exponential Forcing - M. Martin
• Periodic Dosing with Exponential Decay - M. Martin
• Periodic Dosing with Exponential Decay and Elevated Initial Dosing - M. Martin
• Periodic Dosing with Exponential Decay and Tapers - M. Martin
• Discrete Antiangiogenic Therapy for Cancer - M. Martin
• Continuous Antiangiogenic Therapy for Cancer - M. Martin
• Bang-Bang Optimal Control for a Cancer Therapy Model - M. Martin
• Comparing Models of Growth - M. Martin & H. Byrne
• The von Bertalanffy Model for Growth - M. Martin
• Bolie's Model for Glucose-Insulin Dynamics - M. Martin
• The Two-Pool Model for Ca²⁺ Dynamics in the Cell - M. Martin
• Epidemiology: An SI Model - M. Martin
• Epidemiology: An SIS Model - M. Martin
• Epidemiology: An SIR Model - M. Martin
• Epidemiology: An SIRS Model - M. Martin
• Epidemiology: An SIRS Model with Births/Deaths - M. Martin
• A Basic Chemostat - M. Martin
• A Basic Chemostat: Non-Dimensional Form - M. Martin
• A Basic Chemostat with Competing Bacteria Populations: Non-Dimensional Form - M. Martin
• A Basic Chemostat with Predator-Prey Bacteria Populations: Non-Dimensional Form - M. Martin
• A Delay-Differential Equation Model for Cheyne-Stokes Respiration - M. Martin, M. Mackey, & L. Glass
• Glycolytic Oscillations: The Higgins-Selkov Model - M. Martin
• Primary HIV Infection - M. Martin
• Primary HIV Infection in Non-Dimensional Form - M. Martin
• Reduced Primary HIV Infection in Non-Dimensional Form - M. Martin
• A Two-Compartment Model for Lead in the Body - M. Martin
• A Three-Compartment Model for Lead in the Body - M. Martin
• Michaelis-Menten Reactions - M. Martin
• Michaelis-Menten Reactions: Non-Dimensional Form - M. Martin
• The Michaelis-Menten Equation - M. Martin
• The Lineweaver-Burk Transformation for Michaelis-Menten Data - M. Martin
• Nutrient Uptake with Michaelis-Menten Dynamics - M. Martin
• A Model for a Mitotic Oscillator - M. Martin
• Tracking PSA Levels in Prostate Cancer - M. Martin
• Food Consumption Model - M. Martin

Complex Analysis

• Square Roots and Complex Numbers - S. Wilson
• The Complex Polynomial Function (Standard Form) - S. Wilson
• The Complex Polynomial Function (Factored Form) - S. Wilson
• The Complex Exponential Function - S. Wilson
• The Complex Logarithmic Function - S. Wilson
• The Complex Sine Function - S. Wilson
• The Complex Arcsine Function - S. Wilson
• The Complex Function - S. Wilson

Classroom Productivity

• What Do I Need on the Final? - S. Wilson
• Grades and the Final Exam - M. Martin