Mathematical Modeling

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Mathematical Modeling

• Dr. Gerda de Vries
• University of Alberta

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• The use of mathematics to
• describe real-world phenomena
• investigate important questions about the
  observed world
• explain real-world phenomena
• test ideas
• - make predictions about the real world

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• The real world refers to
• engineering
• physics
• physiology
• ecology
• wildlife management
• chemistry
• economics
• sports

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• Instead of undertaking experiments in the real
  world, a modeller undertakes experiments on
  mathematical representations of the real world.
• There is no best model, only better models.

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• Playing with this

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• Can lead to building this

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• Construction
• Take 5 minutes, construct the best paper airplane
  you can

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• Operating on a model is better because
• 1. It is easier
• 2. It is cheaper
• 3. It is faster
• 4. It is safer

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Success

• FRANCE

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• Problems with traffic on the route from Paris
  to Spain along the stretch passing through the
  Tarn valley near the town of Millau, during the
  summer when the roads became jammed with holiday
  traffic, required construction of a bridge to
  span the valley

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• The bridge's construction cost up to
  394 million,2 with a toll plaza 6 km (3.7 mi)
  north of the viaduct costing an additional 20
  million. The builders, Eiffage, financed the
  construction in return for a concession to
  collect the tolls for 75 years, until 2080.19
  However, if the concession yields high revenues,
  the French government can assume control of the
  bridge as early as 2044.
• The project required about 127,000 cubic metres
  (166,000 cu yd) of concrete, 19,000 tonnes
  (21,000 short tons) of steel for the reinforced
  concrete and 5,000 tonnes (5,500 short tons) of
  pre-stressed steel for the cables and shrouds.
  The builder claims that the lifetime of the
  bridge will be at least 120 years.

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Failure

• Colorado

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There are 4 main models we will examine in grade
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• Exponential
• Quadratic
• Trigonometric
• Geometric / Arithmetic