
Chapter 1 _ Preliminaries: Functions & Models
 Functions & Models
 Definition of a Function
 The Logistic Function for Population Modeling (by Mike Martin)
 Fitting Data to the Logistic Function (by Mike Martin)
 Stochastic Growth Model (by Mike Martin)
 The MichaelisMenten Equation (by Mike Martin)
 The Length of an Organism & Ludwig von Bertalanffy's Model (by Mike Martin)
 Population Genetics Model (by Mike Martin)
 Uniform Drug Dosing with Exponential Decay (by Mike Martin)
 Fitting the Logistic Function to Gause's Data (by Mike Martin)
 Characteristics of Functions
 Hill Functions (by Mike Martin) Exposition/Project
 The Process of Mathematical Modeling
 Optimal Control Problem for Treatment of Cancer (by Mike Martin) Exposition/Project
 The TwoProcess Sleep Model (by Mike Martin) Exposition/Project
 Algebraic Functions, Transformations of Functions, & Combinations of Functions
 Power Functions
 Power Functions & Allometry (by Mike Martin)
 Algebraic Combinations of Functions
 Combinations of Functions (by Steve Wilson)
 Polynomial Functions
 The Linear Function (by Mike Martin)
 Voronoi Diagram with Points Entered  Lines & Perpendicular Bisectors (by Mike Martin with John Jungck)
 Voronoi Diagram with Random Points  Lines & Perpendicular Bisectors (by Mike Martin with John Jungck)
 Fitting Data to a Linear Function (by Mike Martin)
 The Quadratic Function (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)
 Quadratic Cost Function (by Mike Martin)
 Profit with Quadratic Costs (by Mike Martin)
 The Cubic Function (by Mike Martin)
 The Rate of Change for the Voltage Along a Neuron's Axon  A Cubic Function (by Mike Martin)
 The Polynomial Function of Degree Six or Less (by Mike Martin)
 Rational Functions
 The MichaelisMenten Equation (by Mike Martin)
 Hill Functions (by Mike Martin)
 Graphs of Rational Functions (by Mike Martin)
 Transformations of Functions
 Visualizing Transformations for a Quadratic Function (by Mike Martin)
 Visualizing Transformations for the SquareRoot Function (in development)
 Visualizing Transformations for a Cubic Function I (by Mike Martin)
 Visualizing Transformations for a Cubic Function II (by Mike Martin)
 Composition of Functions
 Dosage of Children's Motrin via Weight & Age (by Mike Martin)
 Algebraic Functions
 Antiangiogenic Models for Cancer (by Mike Martin) Exposition/Project
 Exponential Functions
 Exponential Functions
 The Basic Exponential Function (by Mike Martin)
 The Number e
 The Definition of e (by Mike Martin)
 The Exponential Function (by Mike Martin)
 Hyperbolic Sine (by Mike Martin)
 Hyperbolic Cosine (by Mike Martin)
 Hyperbolic Tangent (by Mike Martin)
 SemiLog Plots of Exponential Functions (by Mike Martin)
 Models for Growth & Decay
 Stochastic Growth Model (by Mike Martin)
 Pharmacology: Uniform Dosing with Exponential Decay (by Mike Martin)
 Heart Dynamics: AV Nodal Response (by Mike Martin)
 LogLog Plots of Exponential Functions & Allometric Relationships (by Mike Martin)
 Fitting Data to the Exponential Model (by Mike Martin)
 Trigonometric Functions
 Periodic Functions
 The TwoProcess Sleep Model (by Mike Martin)
 Angles
 Converting Radians to Degrees Drillmaster (by Steve Wilson)
 Converting Degrees to Radians Drillmaster (by Steve Wilson)
 Trigonometric Functions
 Trig Functions & the Unit Circle (by Steve Wilson)
 Right Triangle Trig Ratios Drillmaster (by Steve Wilson)
 Special Angle Trig Values Drillmaster (by Steve Wilson)
 Standard Position Trig Ratios Drillmaster (by Steve Wilson)
 Graphs of the Trigonometric Functions
 Sine (by Mike Martin)
 Cosine (by Mike Martin)
 Tangent (by Mike Martin)
 Cotangent (by Mike Martin)
 Secant (by Mike Martin)
 Cosecant (by Mike Martin)
 Sine Graph Characteristics Drillmaster (by Steve Wilson)
 Damped Sine (by Mike Martin)
 Damped Cosine (by Mike Martin)
 Undamped Sinusoidal Forcing  Beats (by Mike Martin)
 Undamped Sinusoidal Forcing  Resonance (by Mike Martin)
 Female Body Temperature  Daily & Menstrual Cycles (by Mike Martin)
 Inverse Functions, Logarithmic Functions, Nonlinear Scales
 Inverse Functions
 The Linear Function & Its Inverse (by Mike Martin)
 A Rational Function & Its Inverse (by Mike Martin)
 Logarithmic Functions
 Exponential & Logarithmic Functions & Their Inverse Relationship (by Mike Martin)
 Nonlinear Scales
 SemiLog Plots of Exponential Functions (by Mike Martin)
 LogLog Plots of Exponential Functions & Allometric Relationships (by Mike Martin)
 LogLog Plot of a Power Function (by Mike Martin)
 Parametric Curves
 Parametric Equations & Parametric Curves
 Rose Analyzer (by Steve Wilson)
 Limacon Analyzer (by Steve Wilson)
 Lissajous Analyzer (by Steve Wilson)
 Models with Parametric Equations
 Continuous PredatorPrey Model (by Mike Martin)
 A Simple, Explicit SI Epidemic Model (by Mike Martin)
 Introduction to Probability
 Probability Theory & Terminology
 Stochastic Growth Model (by Mike Martin)
 Simulating a Random Walk (by Mike Martin)
 Random Experiments  Simulating the Roll of a Dice (by Mike Martin)
 Random Experiments  Simulating the Sum of Two Dice (by Mike Martin)
 Conditional Probability
 Molecular Diffusion Model (by Mike Martin)
 Measures of Central Tendency & Spread: Your First Statistics
 Basic Visualizations & Statistical Measures for a Data Set (by Mike Martin)
Chapter 2 _ Difference Equations, Sequences, & Limits
 Sequences & Their Limits
 Sequences
 The Definition of e (by Mike Martin)
 The Discrete Exponential (by Mike Martin)
 Fitting Data to an Exponential Model (by Mike Martin)
 Recursively Defined Sequences & Difference Equations
 The Discrete Exponential & Geometric Sequences (by Mike Martin)
 The Discrete Exponential  Visuals & Cobwebbing (by Mike Martin)
 Fitting Data to an Exponential Model (by Mike Martin)
 Simple Recursive Sequences: Arithmetic, Geometric, & Logistic (by Steve Wilson)
 Visuals & Data for 1stOrder Linear Difference Equations (by Mike Martin)
 The BevertonHolt Model (by Mike Martin)
 Limits of Sequences
 The Definition of e (by Mike Martin)
 Limit of a Sequence that Does Exist (by Mike Martin)
 Limit of a Sequence that Doesn't Exist (by Mike Martin)
 Fibonacci Numbers & the Golden Ratio (by Mike Martin) & Data/Motivation (media, link)
 Limit Laws & the Formal Definition of a Limit
 Limit Laws
 Squeeze Theorem for a Sequence (by Mike Martin)
 Limits of Recursively Defined Sequences
 The BevertonHolt Model (by Mike Martin)
 The Formal Definition of a Limit of a Sequence
 Limit Definition of e (by Mike Martin)
 Limit of a Sequence that Does Exist (by Mike Martin)
 Limit of a Sequence that Doesn't Exist (by Mike Martin)
 Geometric Series: The Sum of a Geometric Sequence
 Simple Recursive Sequences & Series: Arithmetic, Geometric, & Logistic (by Steve Wilson)
 Drug Dosage
 Periodic Dosing with Exponential Decay (by Mike Martin)
 Periodic Dosing with Exponential Decay & Elevated First Dosage (by Mike Martin)
 Periodic Dosing with Exponential Decay & Tapering (by Mike Martin)
 Discrete Change: Forward Differences
 The First Forward Difference: Increasing & Decreasing Behavior
 Discrete Change: Examining Forward Differences (by Mike Martin)
 The Second Forward Difference: Bending
 Discrete Change: Examining Forward Differences (by Mike Martin)
 Discrete Change: Examining Differences (by Mike Martin)
 Biological Examples of Discrete Dynamical Systems
 Simple Model for Gas Exchange in the Lung
 Simple Gas Exchange in the Lung (by Mike Martin)
 Population Genetics
 A Basic Model of Selection (by Mike Martin)
 A Basic Population Genetics Model (by Mike Martin)
 An Extended Population Genetics Model (by Mike Martin)
 Introduction to Markov Processes
 Virus Mutation Model (by Mike Martin)
 Molecular Diffusion Model (by Mike Martin)
 Stochastic Simulation of the Molecular Diffusion Model (by Mike Martin)
 Stochastic Growth Model (by Mike Martin)
 Simulating a Random Walk (by Mike Martin)
 Difference Equations: Density Dependent Population Models
 The BevertonHolt Model
 The BevertonHolt Model (by Mike Martin)
 The Discrete Logistic Equation
 The Discrete Exponential  Visuals & Cobwebbing (by Mike Martin)
 Discrete Logistic Population Model with Carrying Capacity (by Mike Martin)
 Canonical Discrete Logistic Population Model (by Mike Martin)
 Canonical Discrete Logistic Population Model with Harvesting (by Mike Martin)
 The Ricker Model
 Ricker Population Model with Carrying Capacity (by Mike Martin)
 Ricker Population Model (by Mike Martin)
 Canonical Ricker Population Model with Harvesting (by Mike Martin)
 Cycles & Feigenbaum Bifurcation Diagrams
 Discrete Logistic Population Model with Carrying Capacity (by Mike Martin)
 Canonical Discrete Logistic Population Model (by Mike Martin)
 Canonical Discrete Logistic Population Model with Harvesting (by Mike Martin)
 Discrete Ricker Population Model with Carrying Capacity (by Mike Martin)
 Canonical Ricker Population Model (by Mike Martin)
 Canonical Ricker Population Model with Harvesting (by Mike Martin)
Chapter 3 _ Limits & Continuity of Functions of a Real Variable
 Limits: Numerical and Geometric Intuition
 Motivation: The Derivative
 Approaching Tangent Lines for Polynomials (by Mike Martin)
 Approaching Tangent Lines for the Sine Function (by Mike Martin)
 Fitting the Logistic Model to Gause's Data (by Mike Martin)
 Approaching Tangent Lines for the Logistic Model (by Mike Martin)
 Periodic Dosing with Exponential Decay (by Mike Martin)
 Periodic Dosing with Exponential Decay & Elevated First Dosage (by Mike Martin)
 Periodic Dosing with Exponential Decay & Tapering (by Mike Martin)
 Derivatives & Rates of Change for Exponential Functions (by Mike Martin)
 Intuitive Approach to 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)
 Limit of sin(x) / x as x > 0 (by Mike Martin)
 Limit of (1cos(x)) / x as x > 0 (by Mike Martin)
 OneSided Limits
 Hysterisis & OneSided Limits  media (by Mike Martin)
 Limits: Rules for Computing Limits
 Limit Laws
 The Squeeze Theorem
 Limit of x sin(1/x) as x > 0 (by Mike Martin)
 Limits Involving Infinity
 Infinite Limits
 Limit of 1/x as x > 0 (by Mike Martin)
 Limit of 1/x^2 as x > 0 (by Mike Martin)
 Limits at Infinity
 Limit of 1/x as x > ±Infinity (by Mike Martin)
 Limit of 1/x^2 as x > ±Infinity (by Mike Martin)
 Limit of a Function as x > ±Infinity (by Mike Martin)
 The Formal Definition of a Limit
 Finite Limits
 εδ Limit Visualization (by Mike Martin)
 Limit of x sin(1/x) as x > 0 (by Mike Martin)
 The Limit of sin(1/x) as x > 0 (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)
 Limits Involving Infinity
 Limit of 1/x as x > 0 (by Mike Martin)
 Limit of 1/x^2 as x > 0 (by Mike Martin)
 Limit of 1/x as x > ±Infinity (by Mike Martin)
 Limit of 1/x^2 as x > ±Infinity (by Mike Martin)
 Limit of a Function as x > ±Infinity (by Mike Martin)
 Continuity
 Definition of Continuity
 Properties of Continuous Functions
 Limits, Continuity, & Differentiability (by Mike Martin)
 Continuous Functions, Limits, and Sequences
 The Intermediate Value Theorem
 The Bisection Method
Chapter 4 _ The Derivative
 Introduction to the Derivative: Geometric & Numerical Intuition
 The Definition of the Derivative
 Interpretation: From Difference Equations to Differential Equations
 Techniques of Differentiation I: Powers, Polynomials, Sums, & Differences
 Techniques of Differentiation II: Products & Quotients
 Techniques of Differentiation III: The Chain Rule
 Trigonometric Derivatives
 Derivatives of Exponential Functions
 Implicit Differentiation
 Derivatives of Inverses
 Higher Order Derivatives
 Slopes of Parametric Curves
Chapter 5 _ Applications of the Derivative
 The Mean Value Theorem
 xxx
 The MeanValue Theorem for a Cubic Polynomial (by Mike Martin)
 Derivatives & the Geometry of Curves
 Optimization
 Models Using Differential Equations
 Equilibria & Stability of Difference Equations; Cobwebbing
 Linear Approximations, Differentials, & Relative Error
 Taylor Polynomial Approximations
 L'Hopital's Rule
 Related Rates
 Antiderivatives
Chapter 6 _ The Definite Integral
 Riemann Sums
 The Definite Integral
 The First Fundamental Theorem of Calculus
 Interpretation of the Definite Integral: Total Change
 Numerical Integration
 The Average Value of a Function
Chapter 7 _ Integration Techniques
 Substitution
 Using Integration Tables & Computer Algebra Systems
 Integration by Parts
 Partial Fractions
 Additional Techniques
 Improper Integrals
Chapter 8 _ Applications of the Definite Integral
 Volumes by Slicing
 Arc Length
 Probability & Integration
Chapter 9 _ Ordinary Differential Equations
 Differential Equations
 Differential Equations: Definitions
 Equilibria of Differential Equations
 The Phase Portrait & Phase Line Analysis
 Examples of Mathematical Models with Differential Equations
 Simple Population Models
 Other Models
 Slope Fields & Euler's Method
 Slope Fields
 Euler's Method
 Elementary Solution Techniques for Ordinary Differential Equations
 Separable Differential Equations
 Examples of Solutions to Separable Differential Equations
 Solutions to FirstOrder Linear Differential Equations (Optional)
 Equilibria & Stability of Ordinary Differential Equations
 The Stability Criterion: Analysis & Eigenvalues
 Bifurcations
 A Glimpse at Systems of Autonomous Differential Equations
 The LotkaVolterra PredatorPrey Model
 The KermackMcKendrick SIR Model
Chapter 10 _ Matrix Models & Techniques
 Vectors in nDimensional Space
 Representations of Lines & Planes
 Systems of Linear Equations
 Matrix Algebra
 Linear Transformations: Eigenvalues & Eigenvectors
 Iteration of Linear Transformations & Matrix Exponentials
 Structured Population Models
 Markov Chains
Chapter 11 _ Differential Calculus of Functions of Several Variables
 Functions of Several Variables
 Limits & Continuity of Functions of Several Variables
 Differentiability: Partial Derivatives & the Jacobian
 Tangent Spaces & Linearization
 The Chain Rule
 Implicit Differentiation
 Directional Derivatives & the Gradients
 Optimization
 Diffusion
Chapter 12 _ Systems of Equations: Difference & Differential Equations
 Linear Systems of Differential Equations
 The Direction Field & Phase Plane
 Elementary Solution Techniques
 Equilibria & Stability of Linear Systems of Differential Equations
 Equilibria, Bifurcations, & Singular Perturbation Theory
 Examples of Linear Systems of Differential Equations
 General Linear Compartment Model
 Simple Drug Absorption Model
 A Nonautonomous Drug Absorption Model
Chapter 13 _ Nonlinear Systems of Difference Equations & Systems of Differential Equations
 Systems of Nonlinear Difference Equations: Equilibria & Stability
 Examples of Nonlinear Difference Equations
 Nonlinear Autonomous Systems of Differential Equations: Equilibria & Stability
 Examples of Autonomous Systems of Differential Equations
Chapter 14 _ Probability: Applications & Constructive Modeling
 Probability
 Definitions
 Counting
 The Multiplication Principle
 Permutations
 Combinations
 Equally Likely Outcomes
 Hypergeometric & the CaptureRecapture Problem
 Conditional Probability
 Definitions
 The Law of Total Probability
 Bayes Theorem
 Discrete Random Variables
 Definitions & the Probability Mass Function
 Bernoulli Trials
 The Binomial Distribution
 The Geometric Distribution
 The Poisson Process & Distribution
 The Poisson Approximation to the Binomial Distribution
 Continuous Random Variables
 Definitions & the Probability Density Function
 The Exponential Distribution
 The Gamma Distribution
 The χ^{2} Distribution
 The Normal Distribution
 Functions of Random Variables
 Limit Theorems
 The Law of Large Numbers
 The Central Limit Theorem
 Convergence in Probability & Distribution
 Using the Normal Approximation of Discrete Random Variables
 JukesCantor & Kimura Models
Chapter 15 _ Statistical Inference: Applications & Models
 Describing Data
 Graphical Displays of Data
 Measures of Central Tendencies
 Measures of Spread
 Estimating Means & Proportions via Intervals
 Confidence Intervals for Means
 Confidence Intervals for Proportions
 Hypothesis Testing
 Hypothesis Testing Paradigm
 Hypothesis Testing for Means
 Hypothesis Testing for Proportions
 Goodness of Fit Tests ( χ^{2} )
 Statistical Modeling
 Linear Regression
 Logarithmic Regression & DoseResponse Curves
 Other Models Including and Introduction to Nonlinear Models
 Maximum Likelihood Estimation
 Model Comparison
 Introduction to Stochastic Modeling
 Markov Chains
 Diffusion
 An Epidemiological Model
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