
Chapter 1 __ Mathematical Modeling
Chapter 2 __ Summary of Calculus
 Functions with Parameters
 The Exponential Function (by Mike Martin)
 The Sine Function (by Mike Martin)
 The Quadratic Function (by Mike Martin)
 The Cubic Function (by Mike Martin)
 The TwoProcess Sleep Model (by Mike Martin)
 BloodAlcohol Model (by Mike Martin)
 Basic Concepts of Modeling
 The Exponential Function (by Mike Martin)
 The LotkaVolterra Equations (by Mike Martin)
 Food Consumption Model (by Mike Martin)
 The Cubic Function (by Mike Martin)
 Fitting Models to Data Using Linear Least Squares
 Fitting Data to a Linear Model (by Mike Martin)
 Fitting Data to an Exponential Model (by Mike Martin)
 Fitting Data to the Logistic Function (by Mike Martin)
 Stochastic Growth Model (by Mike Martin)
 Empirical & Statistical Modeling
 Power Functions & Allometry (by Mike Martin)
 Fitting Data to a Quartic Polynomial (by Mike Martin)
 Modeling & the Akaike Information Criterion (by Mike Martin)
 Mechanistic Modeling
 Fitting Data to an Exponential Model (by Mike Martin)
 Food Consumption Model (by Mike Martin)
 The MichaelisMenten Model (by Mike Martin)
 Hill Functions (by Mike Martin)
 The MonodWymanChangeaux Equation (by Mike Martin)
 MichaelisMenten Data & Modeling (by Mike Martin)
 Modeling & the Akaike Information Criterion (by Mike Martin)
Chapter 3 __ Probability Distributions
 Continuity & Limits
 Limit of x sin(1/x) as x > 0 (by Mike Martin)
 The Limit of sin(1/x) as x > 0 (by Mike Martin)
 The Limit of a Rational Function (by Mike Martin)
 εδ Limit Visualization (by Mike Martin)
 Hysterisis & OneSided Limits  media (by Mike Martin)
 Limits & Continuity (by Mike Martin)
 The Tangent Slope and the Derivative
 Approaching Tangent Lines for Polynomials (by Mike Martin)
 Approaching Tangent Lines for the Sine Function (by Mike Martin)
 Approaching Tangent Lines for the Logistic Model (by Mike Martin)
 Limits, Continuity, & Differentiability (by Mike Martin)
 Area & the Definite Integral
 Area Under the Curve (Polynomials) Using LeftHand Endpoints (by Mike Martin)
 Area Under the Curve (Polynomials) Using Midpoints (by Mike Martin)
 Area Under the Curve (Polynomials) Using RightHand Endpoints (by Mike Martin)
 Area Under the Curve (Polynomials) Using Trapezoids (by Mike Martin)
 Area Under the Curve (Polynomials) Using Simpsons Rule (by Mike Martin)
 Area Under the Curve (Transcendental) Using LeftHand Endpoints (by Mike Martin)
 Area Under the Curve (Transcendental) Using Midpoints (by Mike Martin)
 Area Under the Curve (Transcendental) Using RightHand Endpoints (by Mike Martin)
 Area Under the Curve (Transcendental) Using Trapezoids (by Mike Martin)
 Area Under the Curve (Transcendental) Using Simpsons Rule (by Mike Martin)
 An Improper Integral Using LeftHand Endpoints (by Mike Martin)
 An Improper Integral Using Midpoints (by Mike Martin)
 An Improper Integral Using RightHand Endpoints (by Mike Martin)
 An Improper Integral Using Trapezoids (by Mike Martin)
 An Improper Integral Using Simpsons Rule (by Mike Martin)
 Properties of the Derivative & the Definite Integral
 Limits, Continuity, Differentiability, & Integrability (in development)
 Fundamental Theorem of Calculus: Accumulation (in development)
 Fundamental Theorem of Calculus: Aggregation (in development)
 Getting the Graph of a Function from the Graph of its Derivative (in development)
 Getting the Graph of a Derivative from the Graph of the Function (by Mike Martin)
 Computing Derivatives
 Constant Functions (by Mike Martin)
 Linear Functions (by Mike Martin)
 Quadratic Functions (by Mike Martin)
 Cubic Functions (by Mike Martin)
 Polynomial Functions (Degree ≤ 6) (by Mike Martin)
 Rational Functions (Degree ≤ 4/Degree ≤ 4) (by Mike Martin)
 Sine (by Mike Martin)
 Arcsine (by Mike Martin)
 Cosine (by Mike Martin)
 Arccosine (by Mike Martin)
 Tangent (by Mike Martin)
 Arctangent (by Mike Martin)
 Extended Arctangent Function (by Mike Martin)
 Cotangent (by Mike Martin)
 Secant (by Mike Martin)
 Cosecant (by Mike Martin)
 Exponential Sine Function (by Mike Martin)
 Extended Exponential Sine Function (by Mike Martin)
 Exponential Cosine Function (by Mike Martin)
 Extended Exponential Cosine Function (by Mike Martin)
 Hyperbolic Sine (by Mike Martin)
 Hyperbolic Cosine (by Mike Martin)
 Hyperbolic Tangent (by Mike Martin)
 Limit of sin(x) / x as x > 0 (by Mike Martin)
 Limit of (1cos(x)) / x as x > 0 (by Mike Martin)
 Derivatives Drillmaster: Basic (by Steve Wilson)
 Derivatives Drillmaster: Basic Plus (by Steve Wilson)
 Derivatives Drillmaster: Algebraic (by Steve Wilson)
 Derivatives Drillmaster: Exp/Log (by Steve Wilson)
 Derivatives Drillmaster: Intermediate (by Steve Wilson)
 Derivatives Drillmaster: Trig (by Steve Wilson)
 Derivatives Drillmaster: Advanced (by Steve Wilson)
 Derivatives Drillmaster: Comprehensive (by Steve Wilson)
 Partial Derivatives & Visualization (by Mike Martin)
 Computing Definite Integrals
 Finding Integrals (external link)
 Numerical Errors (in revision)
 Estimating Numerical Bounds on Error  Polynomials (by Mike Martin)
 Estimating Numerical Bounds on Error  Exp^(x^2) (by Mike Martin)
 Estimating Numerical Bounds on Error  Sin(x^2) (by Mike Martin)
 Estimating Steps Given Numerical Error  Polynomials (by Mike Martin)
 Estimating Steps Given Numerical Error  Exp^(x^2) (by Mike Martin)
 Estimating Steps Given Numerical Error  Sin(x^2) (by Mike Martin)
 Applications of the Derivative
 Approaching Tangent Lines for Polynomials (by Mike Martin)
 Approaching Tangent Lines for the Sine Function (by Mike Martin)
 Approaching Tangent Lines for the Logistic Model (by Mike Martin)
 Absolute Extrema for a Quartic on a Closed Interval (by Mike Martin)
 Quadratic Cost Function (by Mike Martin)
 Profit with Quadratic Costs (by Mike Martin)
 Optimizing a Gene Pool's Composition (by Mike Martin)
 The Rate of Change for a Chemical Reaction  A Quadratic Function (by Mike Martin)
 The Rate of Change for the Logistic Model  A Quadratic Function (by Mike Martin)
 The Rate of Change for the Voltage Along a Neuron's Axon  A Cubic Function (by Mike Martin)
 Applications of the Definite Integral
 Accumulation: An Offspring Model (by Mike Martin)
 Aggregation: Thin Rod with Varying Density (by Mike Martin)
 Calculating Volume with Multiple Integration (by Mike Martin)
 The Average Value of a Polynomial on a Closed Interval (by Mike Martin)
Chapter 4 __ Working with Probability
 Characterizing Data
 Basic Visualizations & Statistical Measures for a Data Set (by Mike Martin)
 Concepts of Probability
 Random Experiments  Simulating the Roll of a Dice (by Mike Martin)
 Random Experiments  Simulating the Sum of Two Dice (by Mike Martin)
 Discrete Probability Distributions
 Referents for the 64 DNA Codons (by Mike Martin)
 Discrete Distributions in Biology
 The Binomial Distribution (by Mike Martin)
 The Geometric Distribution (by Mike Martin)
 The Poisson Distribution (by Mike Martin)
 The Negative Binomial Distribution (by Mike Martin)
 The Hypergeometric Distribution (by Mike Martin)
 Continuous Probability Distributions
 Continuous Distributions in Biology
 The Uniform Distribution (by Mike Martin)
 The Exponential Distribution (by Mike Martin)
 The Normal Distribution (by Mike Martin)
 The Lognormal Distribution (by Mike Martin)
 Confidence Intervals for the Normal Distribution (by Mike Martin)
 Confidence Intervals for the LogNormal Distribution (by Mike Martin)
Chapter 5 __ OneVariable Dynamics
 Probability Distributions of Samples
 Random Experiments  Simulating the Roll of a Dice (by Mike Martin)
 Random Experiments  Simulating the Sum of Two Dice (by Mike Martin)
 Stochastic Growth Model (by Mike Martin)
 Simulating a Random Walk (by Mike Martin)
 Inferences About Populations
 Estimating Parameters for Distributions
 Estimating Population Size by Mark & Recapture (in development)
 Conditional Probability
 Conditional Probability Applied to Diagnostic Tests
Chapter 6 __ Discrete Dynamical Systems
 Discrete Population Models
 Fibonacci & Related Sequences (by Steve Wilson)
 Discrete Exponential Model (by Mike Martin)
 Discrete Logistic Population Model (by Mike Martin)
 Discrete Logistic Population Model with Carrying Capacity (by Mike Martin)
 Discrete Logistic Population Model with Harvesting (by Mike Martin)
 Discrete Ricker Population Model (by Mike Martin)
 Discrete Periodic Hematopoiesis Model (by Mike Martin)
 BevertonHolt Model (by Mike Martin)
 Stochastic Growth Model (by Mike Martin)
 Derivatives & Rates of Change for Exponential Functions (by Mike Martin)
 Continuous Population Models
 The Exponential Function (by Mike Martin)
 The Logistic Model (by Mike Martin)
 The Logistic Rate of Change (by Mike Martin)
 Food Consumption Model (by Mike Martin)
 Renewable Resource Model I (by Mike Martin)
 Renewable Resource Model II (by Mike Martin)
 Renewable Resource Model III (by Mike Martin)
 Renewable Resource Model IIIA (by Mike Martin)
 Renewable Resource Model IV (by Mike Martin)
 Graphical Analysis
 Discrete Exponential Model (by Mike Martin)
 Discrete Logistic Population Model (by Mike Martin)
 Discrete Logistic Population Model with Carrying Capacity (by Mike Martin)
 Discrete Logistic Population Model with Harvesting (by Mike Martin)
 Discrete Ricker Population Model (by Mike Martin)
 Discrete Periodic Hematopoiesis Model (by Mike Martin)
 Iterating the Sine Function (by Mike Martin)
 Iterating the Cosine Function (by Mike Martin)
 Iterating a Cubic Bistable Equation (by Mike Martin)
 The Rate of Change for a Chemical Reaction  A Quadratic Function (by Mike Martin)
 The Rate of Change for the Logistic Model  A Quadratic Function (by Mike Martin)
 The Rate of Change for the Voltage Along a Neuron's Axon  A Cubic Function (by Mike Martin)
 Linearized Stability Analysis
 BevertonHolt Model (by Mike Martin)
 Discrete Logistic Population Model (by Mike Martin)
 Discrete Logistic Population Model with Carrying Capacity (by Mike Martin)
 Discrete Logistic Population Model with Harvesting (by Mike Martin)
Chapter 7 __ Continuous Dynamical Systems
 Discrete Models & Matrices
 Linear, FirstOrder System of Two Difference Equations (by Mike Martin)
 Linear, FirstOrder System of Three Difference Equations (by Mike Martin)
 LPA (LarvaPupaAdult) Model (by Mike Martin)
 AgeStructuredModels  Leslie Matrices (by Mike Martin)
 Extended AgeStructuredModels  A 12x12 Leslie Matrix (by Mike Martin)
 Leslie Matrix Model with Density Dependence (by Mike Martin)
 Leslie Matrix Model with DensityDependent Recruitment I (LMMDDR) (in development)
 Leslie Matrix Model with DensityDependent Recruitment II (LMMDDR) (in development)
 A Linear Algebra Primer
 Working with a TwoDimensional Basis (by Mike Martin)
 Projecting a Vector onto Another Vector (by Mike Martin)
 Longterm Behavior of Linear Models
 The Eigenproblem  2 x 2 (by Mike Martin)
 The Eigenproblem  3 x 3 (by Mike Martin)
 Linear, FirstOrder System of Two Difference Equations (by Mike Martin)
 Linear, FirstOrder System of Three Difference Equations (by Mike Martin)
 LPA (LarvaPupaAdult) Model (by Mike Martin)
 AgeStructuredModels  Leslie Matrices (by Mike Martin)
 Extended AgeStructuredModels  A 12x12 Leslie Matrix (by Mike Martin)
 Leslie Matrix Model with Density Dependence (by Mike Martin)
 Leslie Matrix Model with DensityDependent Recruitment I (LMMDDR) (in development)
 Leslie Matrix Model with DensityDependent Recruitment II (LMMDDR) (in development)
 Markov Chains
 Virus Mutation Model (by Mike Martin)
 Molecular Diffusion Model (by Mike Martin)
 Stochastic Simulation of the Molecular Diffusion Model (by Mike Martin)
 Simulating a Random Walk (by Mike Martin)
 CantorJukes: A Model for DNA Change (by Mike Martin)
 Pharmacokinetics
 ThreeCompartment Model for Lead in the Body (by Mike Martin)
 TwoCompartment Model for Lead in the Body (by Mike Martin)
 A TwoCompartment, OneDrug Pharmacokinetics Model with Linear Forcing (by Mike Martin)
 A TwoCompartment, OneDrug Pharmacokinetics Model with Decaying Exponential Forcing (by Mike Martin)
 A TwoCompartment, TwoDrug Pharmacokinetics Model with Linear Forcing (by Mike Martin)
 A TwoCompartment, TwoDrug Pharmacokinetics Model with Decaying Exponential Forcing (by Mike Martin)
 Continuous Antiangiogenic Therapy for Cancer (by Mike Martin)
 Discrete Antiangiogenic Therapy for Cancer (by Mike Martin)
 BangBang Optimal Control for a Cancer Therapy Model (by Mike Martin)
 Enzyme Kinetics
 Enzyme Kinetics & Product Formation  MichaelisMenten Reactions (by Mike Martin)
 MichaelisMenten Reactions  NonDimensionalized (by Mike Martin)
 BriggsHaldane Approximation Yields MichaelisMenten Velocity Equation (by Mike Martin)
 Transformations of MichaelisMenten Data (by Mike Martin)
 Phase Plane Analysis
 Phase Plane & Time Plots for a Linear 2D System (by Mike Martin)
 Enzyme Kinetics & Product Formation  MichaelisMenten Reactions (by Mike Martin)
 FitzhughNagumo System of Equations (by Mike Martin)
 MorrisLecar System of Equations (by Mike Martin)
 Stability in Linear Systems
 Phase Plane & Time Plots for a Linear 2D System (by Mike Martin)
 Stability in Nonlinear Systems
 Phase Plane & Time Plots for a Linear 2D System (by Mike Martin)
 Phase Plane & Time Plots for an "Almost Linear" 2D System (by Mike Martin)
 Nonlinear Systems I: The van der Pol Oscillator (by Mike Martin)
 Nonlinear Systems II: The Lorenz Equations (by Mike Martin)
 Nonlinear Systems III: A Mitotic Oscillator (by Mike Martin)
 Primary HIV Infection
 HIV Model (by Mike Martin)
 NonDimensionalized HIV Model (by Mike Martin)
 Reduced TwoVariable HIV Model (by Mike Martin)
please see a separate list that is organized by bioscience & medicine content or another, more general, webMathematica index of all JCCC pages.
Mike Martin
& 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 conference in
New Orleans in October of 2004. 
This page is maintained by Mike Martin.
Last updated: 15 December 2011