1. Mathematics and Engineering

2.  Engineering uses many fields of mathematics Calculus Geometry and Trigonometry Optimization Algebra Logic  Mathematics are used to determine The materials needed How much time and how many people are required How strong, fast, big, heavy, reliable, long-lasting, expensive the solution will be

3. Ex.1: Calculus and Bridges Durability  A quarter-mile bridge rests on four concrete pillars  In the morning rush, the bridge is a traffic bottleneck  (cars are stuck on the bridge)  Every car weighs two metric tons and is about 15 feet long  How much vehicle weight does each pillar need to support? Assume equal distribution of weight among pillars

4. Ex.2: Building a Tunnel  Requirements We need to build a tunnel that will fit two traffic lanes. The tunnel will have the shape of a semi cylinder (for durability) Each lane is 12 feet wide, and the tunnel must fit trucks of up to 4 meters The length of the tunnel is 2 miles The average density of the soil is 1.6Mg/m 3 The tunnel boring machine can progress at a pace of 2m/hour  Design questions What should the diameter of the tunnel be? How long will it take to dig the tunnel? How much soil has to be dug and removed (in weight)?

5. Ex.3 Building an aqueduct  We have a source of fresh water (reservoir) Cold Springs  We have two cities: Sun City, with a demand of 1 m 3 /s Sun Valley, with a demand of 2 m 3 /s  We need to install water pipes from Cold Springs that will supply Sun City and Sun Valley  The cost of pipelines is Cost (1 m 3 /s) = $10,000 / mile Cost (2 m 3 /s) = $20,000 / mile Cost (3 m 3 /s) = $30,000 / mile  Problem: Find the cheapest pipeline network Sun City Sun Valley Cold Springs 60 miles 1 m 3 /s2 m 3 /s