Mathematical Modeling

Dr. Gerda de VriesUniversity of Alberta

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

• The real world refers to

• engineering

• physics

• physiology

• ecology

• wildlife management

• chemistry

• economics

• sports…

• 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.

Playing with this…

Can lead to building this…

Construction Take 5 minutes, construct the best paper

airplane you can…

Operating on a model is better because:

1. It is easier

2. It is cheaper

3. It is faster

4. It is safer

Success FRANCE

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

• 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.

Failure Colorado

There are 4 main models we will examine in grade 11.

• Exponential

• Quadratic

• Trigonometric

• Geometric / Arithmetic