The Connected Curriculum Project

Each section has a guide. We suggest that you print out the guides (your instructor may have printed them for you) and that you work through each section with its guide by your side. Each guide gives a brief overview of the section and lists the homework that you should send to your instructor by email.

List of "Chapters" -- Click on each chapter for a list of sections.

Mathematical Modeling -- An Introduction Discrete Models Continuous Models Probabilistic Models Waves and Oscillations Optimization Models

Mathematical Modeling -- Reverse Engineering Our World

• Overview -- Reverse Engineering -- This section has been replaced by the following section.
• Modeling -- An Introduction
  
• Prolog for a Winter's Day
• Simple Building Blocks -- Complex Structures
• Boyle's "Law"
• "R" BL, VRBL, and GRBL
• Dynamical Systems -- Continuous and Discrete Models
• Optimization Models
• Probabilistic Models
• Summary
• Contents

Discrete Models

• World Population Growth -- Data Snooping
• Linear Models
• Cobweb Diagrams
• Logistic Models and Cobweb Diagrams
• More Realistic Population Models
• Two Theorems on Stability
• Age-Dependent Population Models
• A Difference Look at Newton's Falling Apple
• Summary
• Contents

Continuous Models

• One Variable Models -- Equilibrium Points and Stability
• Two Species Sharing a Habitat
• Two Species Sharing a Habitat, II
• Springs and Masses -- Predators and Prey
• A Neat Problem
• Newton's Model of Cooling Revisited
• Heat Flow, I
• Heat Flow, II
• Summary
• Contents

Probabilistic Models

• Simulation
• Current Events -- The Home Run Race Between Mark McGwire and Sammy Sosa
• Markov Chains
• Diffusion
• Evaporative Cooling
• Combining Random Elements and Deterministic Elements
• Summary
• Contents

Waves and Oscillations

• Introduction and Some Machinery
• Springs and Masses
• Interference

Optimization Models

• Fermat's Principle -- "Smart" Photons
• Reflections in a Flat Mirror
• Reflections in a Curved Mirror
• The Mirage
• Refraction