Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 9.2: Contour Diagrams Section 9.2 Contour Diagrams

Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Predicted High Temperature as a function of latitude and longitude What are the predicted high temperatures in Boise, Buffalo, Topeka, and Goshen? 71, 78, 85, 80 Where do temperatures vary most rapidly? Southern California

Elevation as a function of latitude and longitude What is the elevation at point A? 5250 feet above sea level What is the elevation at point B? 5450 feet above sea level Where might this be in the US? Montana Is it steeper near A or B? A If you were hiking along the dashed trail from the top to bottom of the map, would you be going up or down? Up most of the way

Housing Prices in Houston Where are the least expensive houses located? Around the left- bottom-right edges What do the most expensive houses cost? More than $400,000.

Earthquake Risk

Tornadoes in Texas

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Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Contours/Level Curves

Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example

Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved.

Estimate f (1, 3) and f (4, 5) f (1, 3) ≈ 73. f (4, 5) ≈ 56 Example

Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example: Visualizing Draw a contour plot with at least 4 distinct contours.

Example: Steepness

Example: Interpreting

Up next… Thursday: Lab 03 Friday: 9.2 HW due, Double Quiz: Find functions from table data and functions of 2 variables, Review for Exam 1 Sunday: evening office hours?? Monday: Exam 1