Calculus and Engineering: Calculus and Engineering: Like Bread and ButterLike Bread and Butter

AP Calculus AP Calculus

Bell 2 rocks!!!Bell 2 rocks!!!

October 30, 2008October 30, 2008

What do Engineers Do?

Engineers use their knowledge of science, mathematics, and appropriate experience to find suitable solutions to a problem.

What types of Engineers are there?• Mechanical engineersMechanical engineers research, develop, design, manufacture, and test tools,

engines, machines, and other mechanical devices.

• Biomedical engineersBiomedical engineers develop devices and procedures that solve medical and health-related problems.

• Electrical engineersElectrical engineers design, develop, test, and supervise the production of electrical and electronic equipment.

• Nuclear engineersNuclear engineers who research and develop the processes, instruments, and systems used to derive benefits from nuclear energy and radiation.

What types of Engineers are there?• Civil EngineersCivil Engineers design, construct and manage physical facilities,

including roadways, dams, buildings and pipelines.

• EnvironmentalEnvironmental EngineersEngineers design solutions for environmental problems. They provide safe drinking water, manage wastes, maintain air quality, control water pollution, and clean sites contaminated by spills or improper disposal of hazardous wastes.

• Chemical Engineers apply of physical science and mathematics, to the process of converting raw materials or chemicals into more useful or valuable forms.

How can I become an Engineer?

• A bachelor’s degree from a four or five-year accredited college or university program (ABET)

• Completion of the Fundamentals of Engineering (FE) examination.

• Engineer-In-Training (EIT) for 4-5 years under a profession engineer. • Pass the Professional Engineering Examination.

• Passage of this exam leads to licensure as a Professional Engineer.

• Median engineering salaries range from 60,000-90,000$ (Not too bad!)

What is Calculus?

• Calculus is the study of how things change. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models.

• It provides a way for us to construct relatively simple quantitative models of change

• With this you get the ability to find the effects of changing conditions on the system being investigated.

How do Engineers Use Calculus?

• Engineers often develop mathematical models of the devices, systems, or Engineers often develop mathematical models of the devices, systems, or processes they seek to create. processes they seek to create.

• These models allow the engineer to estimate the cost of different designs These models allow the engineer to estimate the cost of different designs and to compare their probable behavior under various conditions of operation. and to compare their probable behavior under various conditions of operation.

• These models are based on the fundamentals of calculus!!!These models are based on the fundamentals of calculus!!!

• Chemical engineersChemical engineers use derivatives describe the behavior of how a use derivatives describe the behavior of how a compound degrades over time.compound degrades over time.

• Electrical engineersElectrical engineers use derivatives to calculate how magnetic and electric use derivatives to calculate how magnetic and electric field changes certain circuits.field changes certain circuits.

• Environmental engineersEnvironmental engineers use derivatives to describe how chlorine residual use derivatives to describe how chlorine residual changes over time in a distribution system.changes over time in a distribution system.

Problem in the Greater Cincinnati Area

Problems with Combined Sewer Overflows

• CSOs – storm water– untreated human waste– industrial waste– toxic materials

• Contact with discharges from CSOs can have adverse effects on human health– Hepatitis– gastric disorders– dysentery– cholera– Swimmer’s ear

Problem in the Greater Cincinnati Area

Help be part of the Solution

• It would be helpful to know rate of change rate of change in stormwater runoffin stormwater runoff within different watershedsID problematic watersheds.

• This information could also help inform environmental scientists and engineers decide where management practicesmanagement practices need to be implemented first, and if management practices are working.

Storm Water Management Model (SWMM)

Storm Water Activity

• Three different watershed scenarios (Downtown Cincinnati, Norwood, and Batavia)

• SimulateSimulate an identical rain event over three different watersheds.

• How do physical differences within each watershed affect the rate of storm water runoff within each watershed?– Generate a graph representing storm water runoff data– Create a graph representing the derivative of that function.– Compare instantaneous rates of change in runoff across three

different graphs, representing different watershed scenarios and relate these different values to watershed characteristics.

– Recommend appropriate storm water management technologies for watershed with high rates of storm water runoff

Combined Sewer Overflow Video

• http://www.youtube.com/watch?v=MJMtUa8i4Jc

Re-Cap of Yesterday

• Simulated a rain event over three different watershed scenarios.

• How do physical differences within each watershed affect the rate of storm water runoff within each watershed?

• Measured cumulative volume of storm water runoff for several minutes following a rain storm

Objectives

– Generate a graph representing storm water runoff data.

– Create a graph representing the derivative of that function.

– Compare rates of change in runoff across three different graphs, representing different watershed scenarios and relate these different values to watershed characteristics.

– Recommend appropriate storm water management technologies for watershed with highest rates of storm water runoff

Trip to Sanitation District 1

• Leave Norwood at 8:30am Thursday, November 13.

• Arrive at SD1 before 9:30am

• Tour of Storm Water Management Technologies. (9:30am-11:30am)

• Lunch

• 12:30-1:30 (Meet with Engineers and Scientist that work for SD1)

Review and Extension