The Connected Curriculum Project

Contents

• Virtual Reality -- Mathematical Reality
• Two and Three Dimensional Geometry
• Traveling in Space
• Multiple Integration -- Volume and Probability
• Push, Pull and Twist -- Div and Curl
• Matrices and Markov Chains
• Determinants, Bases, and Volume in n-Dimensions
• The Eye of the Beholder -- Eigenvalues and Eigenvectors
• Newton's Model of Cooling -- Separable and First Order Linear DEs
• Two -- Second Order DEs and Systems of Two First Order DEs
• Outside Forces -- Undetermined Coefficients and the Laplace Transform
• Real and Complex Eigenvalues
• Partial Differential Equations

Virtual Reality -- Mathematical Reality

• Flatland -- Life on a TV Screen
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Vector Spaces, I -- Life in Two and Three Dimensions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Vectors Spaces, II -- Two, Three, ... , N, ... Infinity
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• From Three Dimensions to Two and Back
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Looking at a 3D World with 2D Eyes
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Looking for Periodicity -- The Fourier Transform
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Analyzing a Periodic Function
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Transformations from One Vector Space to Another
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Two and Three Dimensional Geometry

• Area and Torque in Two Dimensions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Area, Volume, and Torque in Three Dimensions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Using Geometry
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Lighting and Three Dimensional Graphics
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Surfaces
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Smooth Surfaces and Partial Derivatives
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• The Gradient and the Directional Derivative
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Optics and Optimization (in Calculus in a Real and Complex World)
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Traveling in Space

• Moving Around in Space
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Arclength, Tangents, Normals, and Curvature
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Line Integrals
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Mountain Hiking
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Work and Energy
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Multiple Integration: Volume and Probability

• Volume
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Cylindrical Coordinates
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Spherical Coordinates
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Probability and Integration, I
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Probability and Integration, II
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Mean and Variance
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Why the Normal Function?
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Push, Pull, and Twist

• Prologue -- Reflections in a Traffic Jam
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Divergence in Two and Three Dimensions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• From Points to Regions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Crossing the Border
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Twisting and Spinning
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Matrices and Markov Chains

• Prolog -- A Game of Roulette

• Matrices
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Markov Chains
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Gaussian Elimination
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Variations on a Theme
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Limits of Markov Chains
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Determinants and Bases

• Fields
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Determinants, Linear Maps, Area, and Volume
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Determinants and Linear Maps in Higher Dimensions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Bases and Dimension
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• A Key Theorem
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Some Key Examples
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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The Eye of the Beholder

• Prologue -- Population Models
  

• Age Dependent Population Models
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Some Two-Species Interactions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Eigenvalues and Eigenvectors
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Different Points-of-View
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Newton's Model of Cooling -- Separable and First Order Linear DEs

• Netwon's Model of Cooling
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Visualizing Differential Equations
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Numerical Solution of Differential Equations
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Separation of Variables
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• First Order Linear Differential Equations
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Putting it All Together
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Two -- Second Order DEs and Systems of Two First Order DEs

• Spring-and-Mass Systems
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Systems of two Differential Equations
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Two Species Sharing a Habitat
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Populations and Springs, I
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Populations and Springs, II
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Outside Forces -- Undetermined Coefficients and the Laplace Transform

• Is There a Spring in Your Radio?
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Simple Driving Forces and Undetermined Coefficients
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Higher Order Linear DEs
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• A Menagerie of Functions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• The Laplace Transform
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Real and Complex Eigenvalues

• Linear Systems of DEs with Constant Coefficients
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Complex Vector-Valued Functions
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Real and Complex Eigenvalues
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Steepest Descent and Critical Points
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• Symmetric Matrices and Critical Points
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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Partial Differential Equations

• The Heat Equation -- Introduction
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

• The Heat Equation -- Building a Model
  [TI-92] [Maple] [Mathematica 2] [Mathematica 3] [MathCad]

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